Process Control, A Perspective

Transcription

1 Process Control, A Perspective By: Robert L. Heider, PE Preface: The world is not linear or single variant. Throughout my work experience, I have been asked questions about process control problems and after explaining my experiences or proposed methods of dealing with the problem; people have asked me to capture these ideas. That is what this text attempts to accomplish. This is a perspective, based on experience. It is not a detailed analysis, but rather a practical one. Every effort has been made to acknowledge those in who I have referenced. Many process control problems occur because of the process nonlinearity or multi variability was not considered in the design of the controls. Examples of this are: A process runs well during the summer months, but poorly during the winter months. A process runs well during grade A, but poorly with grade B. These types of problems occur because the controls are nonlinear. The controls are tuned for some optimum point during one condition, but when conditions change, the newer tuning parameters are quite different. Multivariable control problems are those where the performance of one loop interacts with another. Almost all control loops in a plant are multi variant and some form of feedfoward, or decoupling, can improve the performance. The objective of this text is to outline some techniques that can be used to solve these problems. Problem identification will also be emphasized. Some simple simulations and mathematical treatments will also be presented. To begin, I would like to define some basic concepts that control engineers use or keep in the back of our minds when we begin to analyze a problem. I will describe these concepts by comparisons. The concept of macro will be compared to micro and deterministic will be compared to heuristic. 1

2 Macro vs. Micro: Macro is defined as "intended for use with large quantities or on a large scale" while micro is defined as "involving minute quantities". Control engineers are macro thinkers; all we need is the total picture. For examples, we are interested in knowing the degree of agitation for a ph control loop. We may perform some simple calculations to see if the tank is properly agitated. But we don t study agitation from a micro viewpoint that is designing the type of impeller, or the details of each particle in the tank etc. We are interested in the fact that the catalyst degrades in some manor. We can devise a control system to take this fact into account but the exact way it is destroyed is of little interest. We are accused of labeling problems as black boxes, a technique electrical engineers use. We are not trying to distance ourselves from the problem; rather just put the problem in a frame of reference we can deal with. We are more concerned with interactions of all process variables rather than exact solution of the details of one variable. Basic unit operations understand of the plant is usually sufficient. For control engineers the required process reading is your sophomore physics and chemistry. Most upper level courses just provide a lot of embellishments on those basic courses. This sounds like the book written several years ago; All You Need To Know In Life You Learned In Kindergarten. Deterministic vs. Heuristic: When describing behavior, control engineers like first principal controls or models to control first principals. This is called the deterministic method. One can calculate the behavior by known relationships or equations. However, many effects cannot be shown in first principals or the equations just don t show the real world or there are too many unknown factors in the whole system. This is when heuristic systems can be used. These include process model based control, smart sensors, neural networks etc. Control engineers are interested in these systems for running operations where operational data can be gathered and correlated. Heuristic controls or optimization techniques (design of experiments or DOE) determine where the plant can best operate without regard to why. DOE is a statistical technique where by the process variables (pressure, temperature, flow, agitator speed etc.) are adjusted over a range in a pre-determined order, the value of the controlled variable (rate, yield, quality etc.) is noted at each of these points. Using this array of data, a statistical model is derived which shows the critical variables (i.e. sometimes a controlled variable has no effect on the operation) and the best operational point determined, by using a minimum or maximum search algorithm. By using DOE, a production facility can hone in on its best operational point. Research frequently has voiced concerns about using this method because is doesn't explain why the optimum operational point it may find works and because they are not the prime mover in the process, they feel loss of control. I argue who cares? Let s get to the best point with whatever tools are at our disposal, start running there and find out why later. A good control engineer will position him or her self in such a way as to capitalize on this fact making the project a win win proposition. 2

3 Chemical Processes Frequently engineers fail to realize the power and energy associated with chemical reactions. They tend to think of simple flow, level and pressure effects when dealing with chemical (and for that matter, biological) processes. Chemical processes generate or consume energy and there are forces involved that we sometimes loose sight of. For example, consider the scrubbing of SO3 in H2SO4 solution. One would think the SO3 line s backpressure would be the head of liquid plus the headspace pressure. But the pressure calculation is more complicated than that because there is a solubility of the SO3 in the acid solution. These are powerful forces. Control engineers should pay attention when chemists describe the chemistry they need to control. I have some chapters devoted to the anatomy of a particular design or control problem. There are discussions about a real problem and how it was solved. In all these applications I have removed any process details to prevent disclosure of intellectual property. I have included a chapter on human factors in engineering. This was done because we all could sharpen our people skills. This chapter is based on actual experience and just as the title states a perspective. I would like to thank those who have encouraged me to write these thoughts. 15 May 2003 St. Louis, MO 3

4 Chapter 1 Basic Controller Tuning Comments The universe of single input single output control loops can be separated into two classifications; self-regulating and non self-regulating. Self regulating - These loops are such that if the controller is placed in manual, the process variable will go to some stable state, assuming the interacting variables are held constant. Examples of these are flow, heat exchanger temperature control, and even ph. This is how a self regulating process behaves. If while the controller is in manual and the process is stable, if the output is change, the process variable or signal will also change, but it will come to a stable point. If the output is moved again, the process variable will come to a different point. The system is stable at an infinite number of points. Non Self regulating - These loops behave such that if the controller is placed in manual, the process variable will go to some saturated state. Examples of these are gas pressure and tank level with a constant input or output. Imagine a gas volume with a fixed orifice in the outlet, to a "constant" backpressure. Assume that a control valve drops a gas pressure to this tank from a much higher pressure. If the loop is placed in manual and the valve moved to some point, the pressure, in time, will either build to a point almost equal to the supply pressure or drop to a point almost equal to the back pressure. The system is stable at only one point. Non self-regulating loops have "built in" reset action and therefore can be tuned without reset. Sometimes, depending on the controller's method of gain, you may experience some offset, but offsetting the set point or adding bias can compensate for this. One can see the differences in these loops by experiments done at home. Try the level experiment on your bathroom sink drain; higher level will occur for higher water flow rates. This is an example of a self regulating process. Try not to fall in the trap of assuming every control system for a particular type of physical or chemical process is one or the other. As you see with the sink level, an integrating process, it becomes self regulating because as the head increases, the flow increases. Deadtime - Now add dead time to the loop. Dead time can be compensated for in self-regulating loops much easier than non-self regulating loops. In general, reset will make tuning more difficult in non-self regulating loops, because you have placed two integrators in the closed loop. That double integrator with dead time is the most difficult loop to tune. Control behavior in process with 4

5 dead time is not considered in most classical control texts. Classical control texts frequently convert the control dynamics into Laplase transformed control function blocks, and then perform various algebraic manipulations on these transforms. Classical control theory is frequently taught in the electrical engineering departments, where things run quire fast and propagating delays are very short. In the process industries, such as chemical, food processing and the like, chemical unit operations are used. These vessels are frequently large and designed such that there is installed dead time involved in the unit operation itself. In addition, the configuration of these vessels and their interconnecting piping and ducts also contribute to the overall process dead time. Digital Filter - Digital filters should only be used to dampen hydraulic noise. The lowest frequency of this noise is around 1/3 of a hertz. To attenuate this type of noise, never use a digital filter greater than minutes. Large filter values will dampen the signal response and result in controlling the filter, but not the process. Controller tuning settings: (My experience) Process Controlled Gain Reset Rate repeats/min min/repeat Flow to 50 NEVER Temperature Pressure 20 none to 0.5 Level 4 to 10 none none Tuning Methods The Zeigler Nichols method is based on tuning non-self regulating processes. For loops where all logic doesn't work, remember that if you cannot establish a stable setting in manual, you probably will never be able to tune it in auto. On difficult loops, start with gain only. If you want to add reset, then begin to add reset, but drop the gain value to ½ of what you had in proportional only. Begin to add in reset, start at 0.1 repeats per minute. Add reset until you get the ¼ decay. Next add rate, but remember this is a derivative function, so go easy here. If you see the process change direction before you get to setpoint, decrease it. The only place I want high rate values is in ph; there I want to see a hot controller. You will have to drop the reset and gain values when you add rate. Controller tuning methods assume a linear process. Classical control theory seldom mentions non linear behavior or the effects of process dead time. Feedfoward When you have a signal that you know effects another loop significantly, feedfoward this signal to the other controller. Remember the objective here is to allow the signal to move the valve before the controller does. Go easy on the signal feedfoward gain. It doesn't take a lot of this action to see marked improvement, say 10%. 5

6 Non linearity Once I tried to tune a loop by the ultimate period method. It worked, but two days later, it went unstable. By the way, we increased capacity at that time. Why didn't it work? Probably because that process, as are most processes, non-linear. The output to input relationship is not the simple y = m*x + b. Even simple processes, like level control of an atmospheric tank discharging through an open pipe at the bottom, are nonlinear. In that case, the flow out of the tank is proportional to the square root of the head. In the case of a heat exchanger, the heat transfer coefficient varies to the 0.8 power of the turbulent flow rate. Linear behavior means that the controlled or process variable has a constant slope over the whole range of output changes. As an example, an x% change in the output would cause a y% change in input or process variable no matter where the output is set initially. This is also called process gain, the change in controller input divided by the change in output. This non-linearity causes the overall process gain to be variable. If the tuning constants are fixed over the entire span of control, the controller behavior will be different at different disturbances and set points. This requires the controller settings to be set for sluggish or sub optimum behavior because the controller needs to be tuned for the worst case or the highest process gain. The situation would seam hopeless explained that way. What can be done? This non-linear behavior is why equal percentage valve characteristics are used so often; they compensate for this non-linear behavior. The ultimate objective is to have a linear control system, but because the real world doesn't behave like that, the control engineer lets the control valve correct for this non-linearity. The equal percentage characteristic compensates many control loop's non-linear behavior by causing the installed or the total control loop to be linear. This nonlinear behavior is why some controllers work well at one set point or rate but not at other conditions. This problem was recognized many years ago with differential pressure flow transmitters used to measure flow rate. The instrument measured pressure drop in a linear range however the flow is proportional to the square root of the pressure drop. As a result of this problem, square root extractors were used to provide a linear range for the flow signal. Why does this non-linearity cause problems with control? The system closed loop gain changes as the load changes. The system gain is the closed loop gain, which should be less than one for a stable system. The process gain is the change in output signal with respect to change in input signal. When the process is non-linear, the small signal gain is a function of the load. So in the case of a heat exchanger, there is not much change in output temperature for change in inlet flow near the maximum flow rate as there is when the flow rate is lower. The control engineer is always faced with this problem. An easy way to avoid the problem is to reduce the controller gain to a very low value such that the loop gain will never exceed one. This is why most loops are over damped. 6

7 A very simple way to linearize a process such as those described is to apply a simple function to the output signal. For most industrial control systems, the derivative of this small signal gain has one direction. This means that a rather simple relationship can correct the problem. The load line shown in Figure 1 is the normalized installed characteristics of a shell and tube heat exchanger. 100 Nonlinear Compensation Network Compensation and Load Outputs Load> <Compensation Equation y=x/(l+(1-l)*x) L= Controller Output in pcnt Figure 1 This non-linearity is the result of the control valve flow coefficient, Cv, equal percentage characteristic, the pipe head loss and the non-linearity of the heat exchanger. Without the compensation, if the controller output were set at 50 percent, the process would be at 75 percent capacity. Shinskey has shown that a large number of non-linear processes can be linearized by the following equation: y = x /( L + (1 L) * x) Where x is the input and y is the output normalized from 0 to 1.0. L is a constant, set such that the overall system behavior is linear. In the above example L = For the example, a 40 percent output from the controller results in a 22 percent output from the compensation equation. This 22 percent output results in a 40 percent load. This equation can linearize most industrial processes. It also simulates the normal behavior of control valves; zero output with zero input, the way fail closed control valves behave when shut. 7

8 For electrical power used in some heating applications the solution is a bit different. Frequently electrical power is controlled by a time proportional output through a triac power controller. The triac acts as an electrical switch. The electronic circuits that control the triac switching implement a zero voltage turn on circuit. This is done to prevent electro magnetic interference that would be caused by rapid changes in voltage if the AC voltage is switched when the cycle is not at a zero crossing point. The disadvantage of this method is that the voltage is switched in half cycle increments. If the time proportioning period is too short, the resolution of the power to the heater is reduced. If the heater controller proportioning time is increased, the resolution improves but if it becomes too long it introduces dead time in the heating loop. As an example, if the time proportioning cycle is set for 2 seconds, the power resolution would be one part in 240. If the heater is 1200 watt, then the power would cycle plus or minus 5 watts because this is the best resolution the controller can resolve, or approximately 7 degrees C for a 10 pound mass. Improved electrical output power resolution can be obtained by using a Silicone Controlled Rectifier, SCR. This device can switch ac power over fractions of a half cycle. The power delivered to the load using this method has very non-linear characteristics. This non-linearity would cause less than optimum control if it were not linearized. The following MATLAB plot shows the nonlinear characteristics on a phased fired full wave rectified power controller that can be compensated with a third order polynomial. The equation is: output = *i *i^ *i^3 Where i is the normalized controller output. This polynomial can be programmed in most newer configurable controllers. This linearization will allow the use of responsive control settings. The SCR does generate transients during switching and can be falsely switched due to transients in the line power. By installing a varistor across the SCR terminals, the transient can be suppressed through the device. These devices are available from the SCR suppliers. 8

9 It has been my experience that the closed loop performance can be improved in many loops by linearizing either the transmitter or the final element. Back Mixing One concept that dictates control behavior is the amount of back mixing the unit operation has. Many unit operations have some type of back mixing or recycle. As an example, a rotary dryer has internal flights that will flow a portion of the solid back toward the inlet. Some dryer designs even recycle a portion of the dry solid and mix it with the inlet slurry to improve the handling characteristics. An agitated vessel has a portion of the liquid at the surface drawn down to the reactor bottom. All these effects result in adding a large time constant to the control dynamics. This time constant can be assumed as the process contents volume divided by the recycle flow rate, or V/F. In the case of a pipeline, this principal is complicated by the transportation delay. In this case, V/F term is the delay time. A pipeline does not provide any back mixing, however if the flow is turbulent, there will be mixing of the contents. If a step change in inlet temperature occurs in a flowing line, there will be a delay before the outlet temperature senses the change because of the transportation delay. A step change in temperature will not occur in the outlet either because the flow pattern is irregular in the piping system. Around bends or fittings and valves in the piping system the flow pattern will change, some of the fluid will travel faster through the fitting than the 9

10 other portion which will not cause a sharp temperature to change. Rather it will be approximate an exponential curve. Anyone who has ever drawn water for a bath or shower in a hotel will see the effect. When the water is first turned on, there will be a time when the temperature will not change. This is the dead time, when the temperature begins to increase, it takes time for it to get hot enough to use, that time is considered the time constant. When considering the dynamic behavior of a process control loop, on should consider the process in those terms, delay and time constants. References: "Is fuzzy logic appropriate for Process Control Applications?" F. Greg Shinskey, Chemical Processing, December General Electric SCR Manual; Third edition, Rectifier Components Dept. West Genesee St. Auburn, New York, Zero-Crossing Triac Drivers Simplify Circuit Design, Control Engineering, March Carlo Gavazzi Solid State Switching Controls Catalog, Buffalo Grove, IL. Schultz, M. A., Control of Nuclear Reactors and Power Plants, McGraw-Hill Book Company, New York, New York,

11 Chapter 2 Feedback Control Systems The ISA defines Control Systems as a system in which deliberate guidance or manipulation is used to achieve a prescribed value of a variable. This paper will define the process and control systems in mathematical terms that can be analyzed. The process system should be physically realizable and dynamic. In many cases it can be described in the form of differential equations. Differential equations can be defined to have order or the maximum number of derivatives in the equation. In control theory, a system or function is shown in a block form, with an input and output. Input System Output An example of this would be an RC electrical circuit. A first order differential equation has just a single derivative term. R e i I C e o The equation for this circuit is: 1 e i = RI + Idt C 1 e o = Idt C Taking the derivative of the equation above yields: de dt o RC eo = This can be transformed to Laplase notation as: (2) i (1) + e (3) e o = e i 1 τs + 1 (4) 11

12 Where tau is RC. Tau is defined as the single time constant that is in seconds for this example and the 1/(τs+1) term is in the transfer function block. S is equal to j2πf where f is the frequency of the input voltage. These are complex variable equations; therefore the output relationship varies as a function of both the magnitude and a phase shift of the input at each frequency. This particular circuit is called a low pass filter because low frequency signals are passed through while high frequencies are shunted or shorted by the capacitor. Another examples of a first order equation is the temperature change of a liquid volume with a constant inlet and outlet flow rate: dt dt o F T V o F = Ti V + (5) Where T o = Outlet temperature T i = Inlet temperature F= Rate of flow V = Volume Time constant = V/F For second order systems the equation can be shown in the following form: 2 d y dy 2 + 2ζω f ( t) 2 n + ω n = (6) dt dt Where ζ = damping factor ω n = Undamped natural angular frequency = 2πf n f n is the natural frequency. Mass Spring and Dashpot Electrical R L C Network, A Second Order System K B R L Mass V i C M 2 d x dt M + B + Kx = F 2 dt dx ω n = K M ζ = 2 B MK 2 di i d i R + + L = V 2 dt C dt ω = n 1 LC R ζ = 2 C L Examples of second order systems are show above. The transient response to these second order systems is described as either under damped where zeta is less than 1.0, critically damped where zeta = 1.0 or over damped where zeta is greater than 1.0. Under damped responses are not accepted by chemical plant operators because they view the behavior as cyclic and frequently they do not want the process variable to exceed the set point. 12

13 The second order behavior occurs because energy is transferred from one storage device to another and dissipated by a third. In the example of the R L C circuit, electrical energy is alternatively transferred between potential energy stored in the electrical field of the capacitor to potential energy in the form of a stored magnetic field in the inductor. The resistor dissipates the electrical energy to thermal energy. Under Damped ζ < 1.0, Over Damped ζ > 1.0, Critical Damped ζ = 1.0 Frequency Response In the field of servomechanisms studying the sinusoidal frequency response can be used to define the systems behavior. Each of the differential equations can be written in the block diagram form. This is called a transfer function. All the equations describing the process or system can be grouped as a transfer function. Each element of the system has its own unique equation. The output of the previous block is connected to the input of the next. The Laplase transform of each is multiplied together to form the total function. In the servo field, this function is written in a fractional form of Laplase transforms. For process transfer functions involving signal transmitters and valves, the overall process transfer function becomes: 13

14 Input Control Valve Process Transmitter Output The whole process can be written as a steady state non-frequency dependent term K and a time variant term G(s). KG( s) = K( τ z n s ( τ 1 p1 s + 1)( τ z s + 1)( τ 2 p2 s + 1) s + 1) (7) The s terms in the numerator are considered zeros while those in the denominator are called poles, the value of the fraction at various frequencies. This term is used in a system analysis technique called Root Locus. For most processes in the chemical process industry, the plant transfer function seldom has any zero terms. The magnitude of this transfer function is usually expressed in decibels and is defined as: db 20log10 output input = (8) Taking the log operator of each term in the transfer function yields: 20log KG( s) = 20*(log K + log( τ log( s n ) log( τ p1 s + 1) log( τ p2 z1 s + 1) + log( τ s + 1) ) z 2 s + 1) + (9) The phase angle is: angle KG( s)] = tan ωτ + tan ωτ + n(90 ) tan tan 1 1! 1 1 [ z1 z 2 p1 p2 ωτ ωτ (10) Transfer functions with delay require a Laplase operator in the neumerator that is: e τ s (11) Where tau is the dead time. The magnitude of pure dead time is 1.0 or 0.0 db. However the output is phase shifted relative to the input in degrees by: Φ = 57.3ωτ (12) 14

15 With the process described in a block diagram form, it is now possible to control the behavior by adjusting the input signal to force the output to a desired state. A feedback controller does this. The controller adds its own compensator transfer function block and summer junction where the desired output value or set point, is compared to actual value. The controller is added to the system and is shown in dotted lines as: Controller Set Point + Σ - Compensator Control Valve Process Transmitter Output A single input single output (SISO) feedback control system. This is the closed loop block diagram. The feedback signal is the line from the output to the summing junction. In control system terminology, this is H(s). Most process controllers in the chemical process industries, H(s) does not have any dynamic elements; it is just 1.0, or unity feed back. The controller, valve process and transmitter function blocks are multiplied together in the total fraction that is KG(s). This KG(s) and H(s) together are called the open loop transfer function. When the loop is closed as shown in the figure, the loop behavior is calculated by: Output Set Point KG( s) 1+ KG( s) H ( s) = (13) If a sinusoidal input is placed at the set point input, there will be a return signal at the summing point because of the amplification of the forward and feedback loops KG(s) and H(s). The return signal is compared with the set point input. If the signal has arrived at this summing point, has a phase shift of 180 degrees and of sufficient magnitude, the input signal will be reinforced which will provide a greater output and still greater signal. This process continues and the amplitude of oscillation becomes constant. If the set point reference input is removed the system will continue to oscillate. It is not even necessary to impress a sinusoid upon an unstable system to cause it to break into oscillation. Any small amplitude disturbance may bring about an oscillation. Refer to the closed loop transform equation. The condition of instability is for the Output/Set Point to become infinite. This can occur if either KG(s) becomes infinite or I + KG(s)H(s) to be equal to zero. The first possibility is a trivial case because it means that the open loop process itself is infinite. The second condition is that the denominator equals zero or KG(s)H(s) should be equal 15

16 to - 1. When this condition occurs, the gain will be infinite and the output will be theoretically capable of sustained oscillations without any input. The purpose or function of the controller is to adjust the process to a desired set point by modifying the total KG(s) term to insure that the closed loop system will be stable. The stability of the closed loop system can be studied and compensated for with the knowledge of the open loop transfer function. This is fortunate because it is not necessary to solve the entire closed loop equation to determine stability. One method is the use of a semi log plot of the system gain and phase called a Bode plot. These are usually shown as a pair of plots; gain and phase angle potted on the y-axis and a log plot of the frequency or angular frequency, omega, 2πf, on the x-axis. The Bode plots below are for a first order lag with dead time transfer function...34s e KG( s) = 0.51s + 1 (14) The gain plot begins at 0 db, and decreases because of the lag in the denominator. The phase plot shows the increasing phase lag as the frequency increases. When the phase angle is at 180 degrees, the gain is at 10.0 db. If 10 db were multiplied to the K term, the system would be unstable because the feedback signal would be equal to or greater than the input. Bode Plot; Gain db gain omega x10 16

17 Bode Plot; Phase 0-50 degrees phase omega x10 If this transfer function were subjected to a unit step input, the output would be delayed followed by a lag as the output rose to unity. 17

18 First Order with Dead Time Step Response PID Controllers The terms used in the past paragraphs, the terms output and input are generally used by servomechanism studies. In process control, the input is usually called the set point or SP. The output of the transmitter block is called the PV. The difference between the SP and the PV is the signal error or E. The signal between the controller and the process is called the output or manipulated variable, MV. The controller function block responds to the error signal. This response is called the control mode. With microprocessor circuits the digital implementation of this mode or law is called a control algorithm. The controller had modes of operation. These are used to define operational states the controller can have. The Auto mode means that the controller s algorithm is functioning on the error between the local set point, SP and the PV. In the manual mode, the user can directly set the controller s output independent of the algorithm s calculation. Other modes such as RSP, Remote Set Point will allow the output of one controller to set the set point of another. This is called cascade control. Supervisory and DDC, Direct Digital Control, are terms used where the control 18

19 logic from a supervisory computer either sets the set point of the controller or directly operates the output. Another term in the controller lexicon is action, either direct or reverse. Direct action means that the output increases with increasing error. Reverse means the opposite. The action of a controller is selected based on the failure state of the final element, usually a control valve. This is done to insure safe operation. This implies a sign term, + or -, to the overall controller algorithm. The term, PID, stands for proportional, integral and derivative. These refer to the three fundamental control elements or algorithms of the controller. The following discussion describes the classical tuning method, Zeigler Nichols. Proportional only control is the simplest of these. In this mode, proportional refers to a single static, non-dynamic gain that is inserted after the summer. The previous section discussed the ultimate gain or that gain where the closed loop control would cycle, continuously with the same amplitude, indefinitely. With a proportional only controller, there is an offset between the PV and the SP. Many controllers have a manual bias to this offset such that the PV can be set to the set point. Operators do not like to see a controller with this offset; they believe the process is out of control because the PV is not at the SP. This is a frequent criticism of proportional only control. The higher the gain, the smaller the off set is between the PV and SP. This is because the closed loop transfer function is Kc*K*G/(1+Kc*KcG*H) with Kc being the controller gain. Proportional plus Integral controller inserts an integral term to the controller algorithm. The integral term is traditionally called reset, implying that the controller output is reset so that there is no offset between the SP and the PV. Integral only is a controller type frequently used for constraint control and other advanced control algorithms. The units of reset are either in repeats per minute or minutes where per repeat is generally understood but frequently not written. The repeats term means that the error amount is repeated T times per minute. The user should read carefully the controller s instruction manual. Frequently the time units can be in seconds or hours rather than minutes. Note that it is not possible to set the reset term to zero. The user should be conscious of this because on some controllers, the user can enter a zero in the reset term, yet the internal algorithm will truncate the zero to the smallest number to prevent an internal underflow exception in the controller s microprocessor. Yet there is a small reset term available, which is not the same as disabling the function. This small value will cause the loop to develop a long, slow cycle. The D term or derivative is called rate, because its contribution to the equation is that of inserting the derivative of the change. There are two accepted ways to take the derivative, one is with the error and the other is to take the derivative of the PV. Taking the derivative of the error will cause the rate term to change due to a set point change, which can cause a large change in the output just due to set point change. The units of this rate are usually minutes or seconds. 19

20 There are two different ways to write the control algorithm for a PID controller, the ideal and nonideal transfer function. The ideal is also called the non-interactive controller because there is no interaction between the terms. The ideal controller algorithm is where E is the error term: Output E 1 = K + + T s D TI s 1 (15) The real controller takes on the following form: Output E = K 1 ( T T 1 1 s + 1 )( T s ( γ T s s + 1 ) 1 ) (16) Notice that the static gain is inversely related to the reset time, T 1. The rate time, T 2, is shown in the numerator and the denominator where it is reduced by the value of γ that is a value less than 1.0, usually 0.1. The derivative function is reduced with this added pole term in order to prevent the rate term from causing too high a contribution. The T 1 term in the numerator can be considered as a term to cancel out the dominant process lag, which would be a pole of the same time constant. The relationship between the real and ideal controller s settings is: K T + T T I = T 1 + T 1 2 = K1 2 T1 T D T1T T 2 = (17) Define the ultimate gain as Ku and the period as Pu in minutes. The Ziegler Nichols controller tuning settings can be calculated as follows for non-interactive controllers: 1) For a proportional only controller: Gain = 0.5* Ku 2) For a proportional plus reset controller: Gain = 0.45*Ku Reset = 1.2/Pu 3) For a proportional plus reset plus rate controller: Gain = 0.6*Ku Reset = 2/Pu Rate = Pu/8 Reset units are repeats per minutes. Rate units are in minutes. I For the first order with dead time process transfer function shown as: 20

21 .34s e KG( s) = 0.51s + 1 (18) The Bode plot shows the 180 degree gain to be 10 db. The gain required for sustaining the oscillation, Ku is The period, Pu, of the oscillation is 1.1 minutes. From the above calculation, the PI settings would be: Gain = 0.45*3.16 = 1.42 Reset = 1/1.2/1.1 = A composite Bode plot of the open loop transfer function of the controller, process combined yields: (19) 0.34S 1.42e (0.917s + 1) KG( s) = * (0.51s + 1) 0.917S Open Loop Bode Plot; Gain db omega x10 gain 21

22 Open Loop Bode Plot; Phase 0-50 degrees phase omega x10 The closed loop response for this system is: The degree of stability of the open loop compensated network can be defined by two terms, phase margin and gain margin. The concept is to define the amount of additional gain or phase that if added to the network would cause instability. This defines of the margin of stability. The 22

23 gain margin is that amount of gain required to product an unstable network when the phase is at 180 degrees. For the PI controller in the above example, the gain at 180 degrees is 5.5 db at an angular frequency of 5.5 radians. Therefore the gain margin is 5.5 db. The phase margin is defined as 180 degrees minus the phase lag at unity gain or 0 db. For this case, the phase margin is or 56 degrees. For the PID controller, the tuning settings are: Gain or Kc = 1.89 Reset = 0.55 minutes Rate = minutes The Bode plot for this PID controller shows what is an electronic engineering term for a V notch filter. This filter has a low point at the ultimate period of 1.1 minutes and exhibits higher gain at frequencies above and below that point. This is the correct behavior. One would expect the gain to be the lowest at the ultimate period and higher at other frequencies to compensate for the disturbance. Note the leading or positive phase angle at the ultimate period. This leading phase compensates for the dead time or rather large negative phase angle contributed by the dead time. The real PID controller transfer function is: KG( s) = K c ( TI s + 1)( TDs + 1) T s( γt s + 1) I D 23

24 The closed loop response of the PID controller becomes: For this combined process and controller, the gain margin is 2.5 db and the phase margin is 32 degrees. A convent relationship that is valid up to 40 degrees to determine the damping factor is π ζ = (phase margin) (20) 360 For the example of 32 degrees, damping factor is Note the higher closed loop frequency with the PID controller than just the PI controller. (21) 0.34 S 1.89e (0.55S + 1)( S + 1) KG ( s) = (0.51S + 1) 0.55S (0.1* S + 1) The Bode plots for the combined open loop PID controller and process are: 24

25 Open Loop PID Bode Plot; Gain db omega x10 gain Open Loop PID Bode Plot; Phase 0-50 degrees phase omega x10 Using the Bode plot to determine the stability of a control system does have limitations. If the phase shift is 180 degrees or the gain is 1 or greater at more than one frequency, the analysis by Bode will not give a unique solution and should be avoided. This situation would imply that the process transfer function contains zero terms that are not frequently observed in the chemical and allied industries. 25

26 Note that for the PID controller, the reset time constant is approximately equal to the process lag. It is frequently said that the reset time should compensate for the dominant lag in the process and the rate term should be used to compensate for the process dead time. Time Domain There are two domains that can be used to describe these differential equations or their transforms, either in the time domain or the frequency domain. Those in the chemical or allied industries most frequently analyze systems transient behavior therefore study the process in the time domain. Those who apply servomechanisms usually study these systems in the frequency domain. A critical distinction should be made relative to the two domains and the two groups of those interested in control system dynamics. Both control systems are subjected to two types of inputs. One type is considered a set point which is a signal representing the instruction to the system, where the variable should be. The other type is an unintentional, disturbance signal that interferes with and tends to prevent the system from carrying out the instruction contained in the set point. This input is an additional input injected in the process transfer function block. Control systems are often classified as being either regulators or servos, depending on their primary function. While both classifications are normally subjected to both set point and disturbance inputs, it is most common for one input or the other to be given primary consideration. Although it is essential for regulators to follow command inputs, these commands are usually left at a constant set point for long periods of time. When a set point change is made, the transient response is often of minor importance. An exception to this statement is taken for batch processes. In that application, the start up response is important and frequently the major factor in defining the control behavior. The primary function of a regulatory system is to maintain a constant value of the controlled variable or system output even in the event of severe load inputs. A servo-system is normally subjected to a continuously varying command signal or set point and it has, as its primary function, the job of causing the output to follow the command signal. An example of this would be an airplane attitude control or the steering controls of an automobile. The servo output should be made as independent of the load as possible, but, while this may not be a minor function, it is still secondary to the set point control problem. Many of the control components such as valve positioners or transmitters, are servo-systems. The term servomechanism is usually applied to the special case of a servo-system whose output is a mechanical position or any of its derivatives. In the case of chemical and allied processing industries, these control applications frequently have large dead time or transportation delayed responses. Such is not the case in servo or guidance control systems, where the dead time is most often ignored or just a small fraction of one of the smaller time constants. 26

27 Another distinguishing difference between the processing industries and other studies of automatic control is that in processing industries most processes can be considered self regulating and have many first order time constants in series as well as a significant dead time between the time the manipulated variable is changed and any change is detected in the process variable. Consider, for example, the temperature control of a shell and tube heat exchanger. A step change in the utility flow signal will not result in an immediate change in utility flow, the control valve will have some lag or first order behavior. The change in utility flow will mix with the utility volume in the exchanger, which is another lag. The heat fill flow across the tubes will behave as a first order lag also. There is a lag with the change in heat duty of the process fluid in the exchanger that will result in a new stable temperature. Finally the thermal well and temperature element have a first order lag due to the new process temperature. There are also dead times due to utility and process transportation times. The overall step response of all these behaviors can be simulated as a first order with dead time or a second order with dead time. Dynamic properties of chemical and allied processes are usually defined in the time domain. The use of the ultimate period method or testing the process through a frequency response is not the usually accepted practice. This is because ultimate period analysis requires more time than a step or impulse methods and cycling a chemical process is generally to be avoided. Operational personal believe this is harmful to the process. Therefore a step test is generally the preferred method to determine controller dynamic behavior. Other Basic Control Methods There are several other basic control methods or algorithms. One of which is on off or bangbang control. In this type of control, the PV is compared to the set point as before. The error signal is compared to some pre set value. If it exceeds the error value the output changes state. If it drops below some point, it changes to the opposite state. This type of control is like the furnace in a home. This type of control is highly non-linear. I have found it best to simulate this type of control action when possible. The problem with using this type of control is that the system will never operate at any stable state. The output is either on of off and if the output action is not taken, the process will be driven to an extreme state. Another control method is called Time Proportioning Control. This control proportions the amount of ON time and OFF time of a discrete output over a defined cycle time. This type of output switching can be the output of a PID controller. Both the on off and time proportioning control methods are frequently used in HVAC applications and make use of an electrical integrated circuit called a triac. A triac circuit switches the ac voltage at the zero-cross over point on the sin wave. The triac circuit is optically isolated between low current dc control circuits and the ac power loads (120, 27

28 240 or 380 volt, single or 3 phase). The triac device is an inexpensive electrical interface between solid-state logic circuits, microprocessors and ac power loads. The electronic circuits that control the triac switching implement the zero voltage turn on circuit. This is done to prevent electro magnetic interference that would be caused by rapid changes in voltage if the AC voltage were switched when the cycle is not at a zero crossing point. The disadvantage of this method is that the voltage is switched in half cycle increments. If the time proportioning period is too short, the resolution of the power to the load is reduced. If the controller proportioning time is increased, the resolution improves but if it becomes too long it introduces dead time in the control loop. As an example, if the time proportioning defined cycle is set for 2 seconds, the power resolution would be one part in 240, and if the heater is 1200 watt, then the power would cycle plus or minus 5 watts because this is the best resolution the controller can resolve, or approximately 7 deg C for a 10 pound mass. The end result of this type of design is that the output precision approaches that of on off control. References Bibbero, Robert J., Microprocessors in Instruments and Control, New York: John Wiley & Sons, Liptak, Bela G., Instrument Engineers Handbook, Philadelphia, PA: Chilton Book Company, Lloyd, S. G., Anderson, G. D. Industrial Process Control 1 st edition, Fisher Controls Company, Marshalltown, IA, pp , Schultz, M. A., Control of Nuclear Reactors and Power Plants, New York: McGraw-Hill Book Company, Ziegler, J. G., Nichols, N. B., Optimum Settings for Automatic Controllers, Transaction, ASME, December

29 Chapter 3 Controller Tuning What is the best way to tune a controller? How do you do it? Manual controller-tuning methods require the user to make some test of the process in order to determine the process dynamics. There are two ways to do this: ultimate period method and reaction curve method. Both these methods require you to test the process. Sometimes this is not possible. If this is the case, start with default settings based in the controlled variable. Assuming you are able to do the test, here are a few pointers. I will describe the Zeigler Nichols (Z-N) method or ¼ decay method for tuning non-self regulating processes. This method only applies to a non-self regulating process, a fact that is mentioned in their original paper but seldom quoted. With both these methods remove all the digital filters from the system before you get started. All controller tuning methods start with the principal that the process is linear, it has the same open loop small signal gains over the whole range of operation. As I have previously described, most processes do not behave this way, which makes these methods valid over a limited range. However, the have been used in industry for many years and some assumptions have to be met to simplify the task. Ultimate Period Method In this method, the controller is placed in auto in a proportional only mode. Note that with some controllers, it may be necessary to reconfigure the controller because the reset term may not be able to be set to zero. Even with a zero setting, there may be a very small reset value in the controller. Consult the controller's operations manual. The ultimate period method requires the process to cycle, something that bothers the operators. Operators like to see smooth process operations and many get very upset with cycling the process. If the cycles build up, they might even stop your test. So be sure to communicate what you are trying to do. The objective of this test, from a control theory viewpoint, is to find the controller's gain setting where the closed loop process gain is exactly At this point, the process will cycle with a sin wave that neither increases nor decays. Don't spend all day trying to get this perfectly, in most cases the operators or production won't let you run the test long enough to get the data, besides you have better things to do with your time. Once you have a proportional only controller, begin the test by making small, say 5 percent, changes in the set point and watch the cycles. If the process won't cycle, increase the gain. I generally do this in increments of two or reductions of one half. Once you get the process to cycle, note the gain and the cycle periods. Define the ultimate gain as Ku and the period as Pu in minutes. The controller tuning settings can be calculated as follows for non-interactive controllers: 29

30 1) For a proportional only controller: % PB = 2* Ku 2) For a proportional plus reset controller: % PB = 2.2*Ku Reset = 1.2/Pu 3) For a proportional plus reset plus rate controller: % PB = 1.6*Ku Reset = 2/Pu Rate = Pu/8 Rate units are repeats per minutes. Reset units are in minutes. Proportional Band is a term used many years ago when industrial controllers were first developed. Most controllers use gain instead. Proportional Band can be converted to gain simple by: Gain = 100 / % PB So a high proportional band is equivalent to a low gain. Also be conscious of the reset setting units. Some controller brands use repeats per minute, others use minutes per repeat. The concept of repeat is the that the controller will repeat the controller error so many times per time unit, usually minute. This repeat is in the form of a ramp, that is an integral of the controller error. In addition, be aware of the time unit described. Some brands will use seconds instead of minutes. Controllers marketed to the machine tool industry frequently use seconds because their processes are much faster then the process industry applications. Reaction Curve Method This is the method used most often, because it is less upsetting to the operators. If the loop is always in manual, there is no problem, you just have to get their permission to move the output a few percent and see what happens. A common problem with this method is the hysteresis of the control valve or other final element may be so large that the output will not move at all. So get permission, and cause a step change in the output of X percent, say 5 to 10 %. The process variable, PV, will, after a time, begin to change and if it is a typical loop, you haven't blown up the reactor, flooded the column or some other catastrophic event, the process variable will approach some new value. The curve traced by the change is called the reaction curve. The reaction curve has in its information all the lumped dynamics of the loop, the valve, process sensor, transmitter and control system input dynamics. Draw a line tangent to the curve. The time between the point where this line intersects with the original process variable and the point where the test began is called the lag time, L. The slope of this tangent curve, dpv/dt, is called the reaction rate or R. The output step change is DP and is expressed in percent units. 30

31 1 First order plus deadtime response Normalized PV Time Figure 1 First Order with Dead Time Temperature Process In the above curve, assume the normalized 0 PV is 130 degf and the 1.0 PV is 140 degf for an input range of 0 to 200 degf and the response was created by a step change of 20 percent or DP = 20%. The time is in seconds. R is the slope, calculated in minutes, and is: R = %PV Change / Time = (100*( )/200)/((150-70)/60) = 3.75 Lag time is the time expressed in minutes as L = 70/60 = With this information, the controller settings can be calculated as follows: 1) For a proportional only controller: % PB = 100*R*L/DP = 100*3.75*1.166/20 = Gain is defined as 100 / % PB = ) For a proportional plus reset controller: % PB = 110*R*L/DP = 110*3.75*1.166/20 = 24 Gain = 4.17 Reset = 0.3/L = 0.3/1.166 = 0.26 repeats/minute 3) For a proportional plus reset plus rate controller: % PB = 83*R*L/DP = 83*3.75*1.166/20 = Gain = 5.5 Reset = 0.5/L = 0.5/1.166 = 0.43 repeats/minute Rate = 0.5*L = 0.5*1.166 = 0.58 minutes 31

32 General Comments on Controller Tuning by Z-N Z-N tuning method should only be used for linear non-self regulating processes. The PV response is different for set point changes than for disturbances. For set point changes the PV will respond with a damped oscillation around the set point; for disturbances the PV will respond with a damped oscillation either above or below the set point, but should not oscillate around it. This fact is important, I have observed many co workers trying to get this elusive ¼ decay response and not understanding that set point changes are different than disturbances. The decayed oscillatory response is not the same waveform as sin wave decayed under an exponential curve. See the plot below. The ultimate period method yields better results because the latter requires finding slopes and is subject to graphical error. For three mode controller tuning settings, the controller responses' damped period is very close to the ultimate period. For three mode tuning settings the damping factor, ζ, is 0.22 and the first peak occurs at 77.6 degrees not at 90. This because the decayed oscillatory response is not the same waveform as sin wave decayed under an exponential curve. The so-called ¼ decay possible with a proportional only controller is more often 1/3 for PI and PID controllers Figure 2 Response Curve for Test Controller 32

33 The above-simulated temperature controlled process shows the different responses. Between time zero and 50 minutes, the time the set point changed, the PV was responding to an initial condition state change, a disturbance. The PV oscillated about above the set point, 120. Note that the PV oscillated around the set point when it was changed to 150. Also refer to the section on simulations for another example of single input single output controller behavior. In the ultimate period method, the oscillation's period is equal to four times the system dead time plus the overall system's time constant. Modified Lambda Tuning Method A very simple way to tune a controller is to use the modified lambda tuning setting. This method is made easier because it only uses two of the modes, gain and reset, and the reset setting only requires the user to measure the total time the process variable was in transition. The method calls this T 98 or the time for the change in process variable to reach 98% of its total change. This happens to be 4 time constants since 1-exp(-4) = For all practical purposes, this can be assumed to be 100%. It is far easier to note the time when the PV is finished with the disturbance than it is to calculate slopes. This method works well for many loops and can give you a quick answer to the settings required. The controller gain is calculated by: K c Output in % 1 = * PV in % λ Where lambda is the term used to increase or decrease the speed of response. Decrease to speed up and increase to slow down the control response. The reset setting, T i in minutes per repeat, is calculated by: T T 98 D T i = = + 4 T D is the process dead time and T C is the time constant. In the above temperature control example, the D PV is (10 DegF /200 DegF)*100% or 5%. The change in output is 20% Therefore the Gain should be (20/5)*(1/4) or 1.0. The reset time is 180/4 or 45 minutes pre repeat. This controller setting is tuned not have any overshoot. This is generally accepted as by plant operators. They frequently think overshoot is the sign of a plant out of control. The following simulation shows the difference between ZN tuning and a hot lambda setting. The principal behind this method is to set the reset value equal to ¼ the total time the controller was in transition. It assumes the combination of deadtime and the time constants are just one large first order time constant and sets the reset value to compensate for that assumed lag. This is the basic concept used for dryer control systems where the rate of moisture removal is controlled. 4 T C 33

34 Figure 3 Simulated First Order with Dead Time Lambda Tuning 34

35 Figure 4 Simulated First Order with Dead Time ZN Tuning References McMillan, G. K., Process/Industrial Instruments and Controls Handbook, New York, McGraw-Hill, 1999, Section Ziegler, J. G., Nichols, N. B., Optimum Settings for Automatic Controllers, Transaction, ASME, December

36 Chapter 4 Feed Forward Impulse Feed Forward Feed forward is a control technique that improves the control response by changing the controller s output in anticipation of the load change. Most control engineers apply a simple feed forward algorithm, one without a lead lag element, when they see the need for it. In this case, a scaled percentage of the signal is added or subtracted directly on the controller output. The problem with this is that the reset term is still integrating the error and the system will be offset by some fraction of the feed forward signal. Shinskey suggests a better approach that implements the feed forward signal through function blocks that create an impulse function. The technique is called impulse feed forward. Shinskey shows the feed forward signal operating directly on the controller output. The problem with this is that if the controller is placed in manual, the feed forward signal will still be active. This gives the operator loss of control of the output. Some controllers bypass the reset function and implement the feed forward signal directly on the output. This limits the reset action and forces the output to some elevated level, which the reset action will have to overcome. An alternate way is to modify the set point. This technique is similar to the one used to implement a Smith Predictor. Figure 1 shows how to configure the feed forward controller. 36

37 Figure 1 Impulse Feed Forward Function Block Diagram The feed forward signal is sent to a lag control block. The output of this block is then subtracted from the feed forward signal itself. This resulting signal s step response will be an impulse. This impulse will have a steep change almost equal to the feed forward signal. Then it will drop to zero, the time constant will be that set with the lag block. This resulting impulse is scaled, then either added to or subtracted from the remote set point signal depending on the desired control action. This modified set point is then connected to the controller s remote set point. The resulting action is to perform the feed forward action by changing the controller s set point. At a steady state feed forward signal, the set point biased term, will be zero and the controller s set point will be that set through the register value. The following simulation shows the response with a simulated heat exchanger heater. The process flow is used as the feed forward signal. The following ACSL plots show the behavior with and without the feed forward. Note that with both methods set point change has the same response. However the feed forward control has a reduced overshoot. In this simulation, the controller gain, reset, rate, feed forward gain and lag values by using a minimization algorithm on the integral error squared value. The feed forward lag value should be greater than the reset time, about 50% longer. This gives the controller time to respond to the upset. The feed forward gain should be set based on the feed forward contribution to load 37

38 changes, if the entire load change in measured, then the gain setting an be high. There is also a scaled value based on the change in load compared to the change in value position. One objection often voiced about these techniques it the number of settings that have to be adjusted to obtain good control. I recommend that the controller be tuned for good response to set point changes, then adjust the feed forward settings for load changes. 38

39 Figure 2 Impulse Feed Forward Simulated Response 39

40 Figure 3 Impulse Feed Forward Simulated Response 40

41 Figure 4 Simulated Response without Feed Foward 41

42 Figure 5 Simulated Response without Feed Foward References: Shinskey, F.G., Process Control Systems fourth edition McGraw-Hill,

43 Chapter 5 Flow Control Flow is one of the easiest variables to control. This is a general rule and based on the premise that there is little to no dead time between the valve movement and the transmitter senses the change. Flow can be either a volume measurement such as gallons per minute of SCFH or it can be mass flow as in the case of mass meters. General Comments on Flow Meters Today, many of flow meters in use are magnetic or vortex shedding. Despite that, approximately 40% of the flow meters in the industrial marketplace are head (orifice et al) meters. From a control standpoint, the user should be concerned about the linearity of the transmitted signal. In the case of magnetic and vortex shedding, the output is linear. In the case of an orifice plate, the flow signal is proportional to the square root of the pressure drop. A good rule of thumb is to select the flow meter normal reading to be about 70% of the maximum reading. A change in flow rate a the lower end of the span will result in a small change in the differential output compared to the same change at the upper end of the range. This is because the orifice plate flow is proportional to the square root of the differential. Example: Assume an orifice plate differential flow meter is used to measure a 25 GPM water flow in a 1 inch line. With a beta of 0.7, a 10% flow change from 10 to 12.5 GPM results in a 8.9% output change while the same percentage change between 20 to 22.5 GPM creates a 17% output change. Most differential pressure instruments have a square root extraction option that will linearize this signal. Vortex meters generate a linear signal proportional to flow rate, so they do not have to be linearized. The turn down or the ability to measure low flow signals should be given careful consideration when applying these meters. The flow signal will not be responsive if control is below the minimum flow reading. Pay particular considerations to piping geometry and allow sufficient straight runs both upstream and down. Magnetic flow meters now are the logical choice for electrically conductive fluids. What the manufacture now considers conductive has become a great deal lower than they were 30 years ago. Most of the problems with the installation are due to inadequate grounding. I have observed that when the meter is used on non-conductive fluids, the meter may not be responsive when a conductive fluid begins to flow. This is probably due to saturation of the input amplifier because there is no path for the static electricity that forms on the electrodes in the non-conductive fluid. Control Valves In order to obtain linear installed characteristics from the control valve, that is the same percentage change in valve travel at a lower opening valve results in the same percentage change in flow as it does at the higher flow rates, equal percentage control valve trim should be used. The equal percentage trim compensates for the non-linearity of the change in pressure 43

44 drop through a restriction, which is the same square root factor as it is for an orifice plate. Centrifugal pump s performance curve shows a drop from a maximum head at zero flow or dead head. This drop can be simulated as a function of the square root of the flow. The equation is Q = max K * H H (1) A simple test of a typical liquid flow application shows the linear installed characteristics with equal percent trim. The pump in this example is a 1 X 1.5 inch centrifugal with an 8 3/16 impeller turning at 1750 RPM. See typical centrifugal pump curve. Typical Centrifugal Pump Curve The pipe is 600 equivalent feet of 2 inch pipe and the control valve has a maximum Cv of The maximum flow is 70 GPM. The percentage travel was calculated at the required pressure drop for the given flow. 44

45 Flow vs. Stem Travel with Equal Percent Valve Trim % Flow Valve Travel in % % Flow Figure 1 Installed Flow Characteristics General Questions, Comments I once tried to measure the flow rate across a particular piece of equipment by measuring the pressure drop. The manufacture told us the pressure drops at different flow rates. I could never get it to agree with the flow meter. Why? Process equipment such as a heat exchanger has a pressure drop which increases as the flow rate increases. If someone wants to measure this drop in order to calculate the flow rate, this can become a difficult task. If two pressure gauges are used, they will probably not agree. Therefore the same gauge should be used for both inlet and outlet pressure readings. Also give consideration to any elevation change between the two points. Can valve position be used to calculate flow, providing the pressure drop is known? Does this result in an accurate signal? By applying the universal valve sizing equations, a known valve position as well as fluid states can be used to calculate flow. This is not a very accurate way, but can give relative good comparisons between low and high ranges. These applications are usually done where the installation of a flow meter is too expensive on not practical, such as a large vent line on an existing process. Why should flow loops have low gains? Almost all flow loops have low gain settings, between 0.1 and 0.3. This is because flow transmitters sense hydraulic noise. If a high gain is used, the noise is amplified which results in more noise on the output. This is also the reason rate is not used in flow loops. Reset is usually 45

46 set to give reasonable response and have little to no overshoot. This is generally 10 to 50 repeats per minute. Hydraulic noise is common in all flow systems. In order to protect the valve from small signal jitter as well as dampen the flow signal, a digital filter should be employed. Care should be taken in setting this filter time. My experience is that most hydraulic noise can be attenuated with a filter of about 1.5 seconds. How did you arrive at this number? This number is based on a representative process, a cage mounted level displacer transmitter. While this is a level instrument, I believe that hydraulic noise is present in all flowing systems this is an example that can be calculated easily and, based on my experience is representative. The level cage displacement ratio is calculated in Laplase transforms as: 1 L = (2) 2 s 2* ζ * s ω ω For a caged level transmitter 14 inches long and 3 inches in diameter inside a 4 inch diameter cage, the frequency is 0.37 Hz. The referenced text shows a dampening factor z as 0.3. At this frequency and dampening factor, the dampening ratio is 4.4 db. A general value for a first order filter is to attenuate the signal 6 db. The filter should attenuate the signal by 6 plus 4.4 or 10.4 db. This is calculated by:.4 = 20log 1+ 1 ω j N ω F 10 (3) Where ω N is the noise frequency and ω F is the filter frequency. Solving this for the filter frequency results in a frequency of 0.11 Hz or 1.35 seconds. As a rule, Never allow the digital filter to exceed 5 seconds in a flow loop. If the filter becomes too large, the controller will only be responsive to the filter and not the process itself. When should I use a positioner on a control valve? The question should be when not to use one. Even with flow loops. The positioner can be considered the outer loop of a cascade loop and must be the fastest. The major concern about positioners is that on very fast loops, the dynamics of the positioner can be slower than the loop itself. Another concern is that they are yet another device in the field that can and will fail, 46

47 requiring maintenance. Newer smart positioners have electronics that allow the user to develop signatures of the valve performance. This is helpful for maintenance. Installation Details Why should the transmitter be installed before the control valve? I don t see the difference from a control standpoint. The location of the control valve does not matter from a control viewpoint, but in general it is better to install the transmitter in the high-pressure side of the piping system. Also because of the downstream turbulence, the meter would have to be located further down stream than it would if it is mounted upstream. This way entrained gasses are at a higher pressure and lower noise results. Most flow transmitter problems are as a result of improper installation. I have found that if the manufacture s instructions are followed, problems are minimized. If the distance between the transmitter and the valve becomes too large, dead time becomes a dominant factor in the tuning settings. Split Flow Applications One common flow control application is splitting a flow stream to two different downstream processes. In the case described here, a variable flow and pressure inlet stream is split; one flow is fixed while the other flow takes the difference. See figure 2. Three way valves are not used that often in plant designs because of the availability, particularly in alloy metals. Two valves are generally used in the piping configuration as shown. For the arrangement on the left, one valve is used to control the flow rate to the bottom stream and the second is set manually, with the HC, to keep the enough backpressure to force the flow to the bottom stream. When the wild inlet flow rate or pressure varies greatly, HC will have to be adjusted to compensate. Frequently an additional pressure control loop is used to keep the pressure at the tee constant. This adds an additional transmitter and controller that result is increased cost. Another way to avoid the problem is to configure the flow control system as shown on the right. Use the same flow control signal to actuate both valves at the same time. As the bottom valve is opened, the top valve closes. The controller s reset action will locate the correct setting to keep the bottom flow rate fixed. If it is desired to allow both valves to have the same fail direction, a signal reversal function block can be used to reverse one signal to achieve the desired control behavior. This two-valve arrangement can be used in many different equipment designs such as bypassing heat exchangers for temperature control, etc 47

48 HC FC FC Variable Flow Rate and Pressure Fixed Flow Rate Variable Flow Rate and Pressure Fixed Flow Rate Figure 2 Split Flow Control Rate Setting on Loss in Weight Feeders A common rule of thumb in flow application is to avoid using the D in a PID controller, or rate unless you absolutely have to. A loss in weight feeder is an exception. If rate setting is set to zero on a loss in weight feeder, sluggish behavior will result. The feeder control loop sets mass flow, pounds/hour. Conventional wisdom would have you set rate setting to zero for flow control. After all, pounds per hour is generally considered flow signal. However a non-zero rate setting is necessary for this loop. This is because the signal is not flow rather loss in weight. Loss in weight implies that there is a delay in the control loop. The control variable is weight change and in order for the signal to know loss in weight, it has to subtract the current weight form the previous weight. This sample interval results in sample dead time. Control loops that have dead time require some rate setting to compensate for the dead time. Once the rate was set properly, the feeder will run smoothly and be responsive to disturbances as well as set point changes. This experience shows that the control engineer needs to understand the fundamental first principals of the equipment controlled. References Lloyd, S. G., Anderson, G. D. Industrial Process Control 1 st edition, Fisher Controls Company, Marshalltown, IA, pp ,

49 Chapter 6 Level Control Self-Regulating or Non Self-Regulating In the informal control community, the level property is frequently considered the hardest to measure but the easiest to control. There are some conditions that must be satisfied to make level control easy. These are that there is very little or no dead time in the level control loop and that the level process is free from interacting effects. The level control classification can be either self or non self- regulating depend in how the inlet and outlet flow are controlled. See figure 1. A good understanding of the type of level loop will dictate which controller type and settings to use. Non Self-Regulating - If there is a constant flow either in or out of the vessel, then the level control loop is non self-regulating. There is one unique solution to the other flow rate to hold the level constant, which is the same value as the other flow. If this fact were not true, then the tank would either overflow or run dry. In this case the vessel volume integrates the change in level. In classical control theory, this level can be considered as an integrating process. In this case, proportional only control will allow the controller to reach its set point with some offset. This is because the forward controller and process transfer function is: K K c p (1) s Where K c is the controller gain and K p is the process gain and s is the Laplase operator. When this controller and process transfer function is forward transfer function in a feedback control loop, the classical control response becomes: 1 tau * s + 1 (2) Where tau is 1/(K c *K p ). This is a first order response. The time constant is inversely proportional to the controller gain. If the level is relatively free from noise, very high gains are possible. I have been told of a reflux accumulator level control loop configured as proportional only with a gain of 128. Adding reset or large filters to this type of controller will only cause the control loop to cycle. The reset action will effectively act an additional integrator element to the closed loop response and result in the complex loop cycling. Another interesting observation is that it is theoretically impossible for a true integrating process to become unstable. This assumes that there is no dead time in the process. Practical considerations, such as hydraulic noise, dictate that the controller should have a moderate gain setting, perhaps no more that 10. I recommend starting at 4. 49

50 Self-Regulating - If one of the flows is load dependant, that is, as an example, a gravity draining tank, then the outlet flow rate will be proportional to the tank level. In this case the flow rate will be proportional to the square root of the liquid height. This effect can be observed in a sink, when the tap flow increases, the level increases to a point where the output flow rate is equal to the inlet flow rate. In this type of level process, a moderate amount of reset can be used. h LC LC Non Self-regulating Level Control Loop Constant flow out Self-regulating Level Control Loop Flow = K*sqrt(h) Figure 1 Non Self-Regulating and Self-Regulating Level Controllers Proportional Only There are two excellent references that discourage the use of reset in level control loops. In both these articles, the user should consider the reason for the vessel. In many cases, the vessel is used for surge and an exact level setting is not required. Rather the tank is used to absorb disturbances or accumulate inventory, or act as a liquid reservoir for pump suction. In these cases, rapid response is required, but the level setting can be allowed to vary some from the set point. Reset causes a lag in the control response, which can be a detriment to many level control loops. For many controllers, selecting a proportional only or proportional plus derivative controller requires a different configuration or set up selection than a proportional plus integral plus derivative (rate) or PID controller. Most PID controllers will not permit the user to set the reset term to zero. Therefore when configuring a level control loop, a conscious effort should be made to evaluate the level dynamics. Adding a filter to a level signal is frequently done to reduce the measurement hydraulic noise. This filter should not be confused with the reset term provided by a controller, even though the initial step response to both functions is the same, which is a tendency to lag the output response. Further on in time after the set point change or disturbance, the integral will continue to ramp the error while the filter will just lag the response and not continue to ramp the output in either direction. A proportional only controller has a manual bias 50

51 setting. The bias setting is used for the operator to introduce a term to offset the controller s output so that the level is equal to the set point. If the level control is non self-regulating, this should not be necessary because the integral action of the tank level itself will act as the reset term. In a perfect non self-regulating system, there will be a small steady state off set, which is an inverse function of the process gain and the controller gain. With high process gains, it may not be noticeable. Recycle Flows In many processes, a series of tanks are piped together and a portion of the outlet flow is recycled to one of the tanks upstream. If reset is used on all the level controllers, the total system will be conditionally stable. Any upset in one of the wild flows will cause all the levels to oscillate with a very long period. If a series of tanks are piped together with a recycle flow, one of the tanks must have a level controller with no reset. This is necessary to break this multiple integral cycling. For many tanks, there are multiple inlet and outlet flows, complicating the self-regulating, non self-regulating distinction. As a rule, the user should use a proportional only unless dictated by other process considerations. Anatomy of a Level Control System What is the most difficult process you have ever tried to control? Despite the fact that level is generally considered an easy process to control, the most challenging process I ever had to control was a Graver water treatment system. A quick check in the Internet shows the name Graver is used by several companies. The vessel has several chambers and is quoted by one of the companies from their Internet sight as: 51 Hot Process Softener An integrated system combining a number of water treatment processes into a single unit. An integrated system consisting of water treatment processes such as chemical treatment at elevated temperatures, clarification of chemically treated water, and deaeration and storage of makeup and condensate. The Hot Process Softener, designed specifically for boiler feedwater purification, reduces hardness, alkalinity, silica, oxygen and suspended impurities to prescribed values, regardless of variations in flow or chemical composition of the incoming feedwater. I attempted to control a Graver over thirty years ago. I can only estimate some of the vessel s size, and construction. The vessel consisted of a large, perhaps 100 feet high by 50 feet in diameter conical shaped structure, see figure. The top portion consisted of an internal coned section and a standpipe that extended almost to the bottom. The water flowed down the standpipe and filled the inside portion, then overflowing across a rectangular weir. The overflow was collected in a second chamber, which was vented to the atmosphere. The outlet of this chamber was the boiler feed water line. The control system consisted of a level controller

52 controlling the level in the overflow chamber. The output of this controller became the set point of the standpipe level controller. This level controlled the water height in the weir and therefore the flow to the second chamber. The power plant s turbine exhaust steam was piped to a 36-inch manifold header that acted as a steam pad on the top of the vessel s interior chamber. The coldwater inlet was heated by condensing this steam. In order to prevent loosing the water level in the standpipe, the steam was pressure controlled. However this control valve was located several hundred feet from the vessel. The hydraulic head difference between the water levels in the two compartments, h2 minus h1, was equal to the static pressure in the top of the vessel. Control was not a problem at lower water flow rates. However when the rates became high, the large flow of cold water in caused the steam pressure to collapse that caused the water to rapidly flow up the standpipe. The pressure control valve closed attempting to increase the pad pressure. The graver volume then lowered the level across the weir that caused the chamber level controller output to increase the set point to the outer level controller. This caused increased demand for cold water, which added more water than required. When the steam pressure increased enough to push the water down the standpipe, there was too much water in the vessel. This increased the weir level, increased the chamber level and caused the chamber level controller to reduce the vessel level. This lowered the cold water inlet flow. The amount of water was not enough to condense the right amount of steam in the pad. That caused the pressure to rise and begin the cycle over again. Many control experts tried in vain to fix the problem. I simulated the problem in MATLAB to try to investigate what types of controls could help control the levels. A simulation of this process showed some interesting behaviors. One interesting observation is that the flow rate across a rectangular weir is reasonably linear. See figure two. The equation for flow across a rectangular weir is non linear. F 1.5 = 3.33*( W 0.2 * H ) * H (3) Where F is the flow rate in cubic feet per second, W is the weir width in feet and H is the weir height in feet. The simulation showed that if both level controllers were proportional only, the offset in the chamber level was too great. A PI controller was used for the chamber level and a proportional only was used for the vessel level. This would be a good choice since the offset in the vessel would not present a problem for the operators. They were most concerned with the chamber level because this held the reserve boiler feed water. Any dramatic reduction in that level would require the plant to use untreated water or cut back steam to the users. The process was simulated by assuming that the level increase in the vessel was necessary to flow water from the vessel into the chamber. 52

53 Figure 2 Rectangular Weir Flow vs. Height The other problem was that the chamber volume is much smaller than the vessel volume. In a normal cascade loop, the outer loop should be much faster than the inner loop. That is not the case here. If a proportional only controller is used for the outer loop, the vessel level control, this was not a problem. There was no dead time between the change in water flow and change in vessel volume. The pressure control loop behavior was the major disturbance. The problem was the long pipeline between the pressure controller and the vessel. This length of line created a pressure wave that caused most of the problem. As I recall, once the flow increased beyond a certain point, the pressure dropped very rapidly and the system became upset instantly. The loops would have to be placed in manual to dampen the oscillation. One suggestion was to relocate the pressure controller and vent valve to the top of the vessel. This was rejected because of the high cost. Another idea was to relocate the pressure transmitter to the to of the vessel. This was rejected because the owner was interested in maintaining the proper turbine backpressure for steady turbine operation. 53

54 Graver Water Treatment Vessel Vent feed foward signal Low Pressure Steam from Turbines PC 5 psig set point LC RSP velosity limiter Flow In several hundred feet 36" diameter Spray Nozzle (typical of several) LC Rectangular Weir Chamber Flow Out Standpipe h2 h1 Figure 3 Graver Water Treatment Vessel This control system was installed over 30 years ago. Controllers on the market today have many other functions than they did at that time. If I were solving the problem today, I would consider using feed forward control to the pressure loop. The feed forward signal would be the vessel level controller s output signal, which is the inlet water valve. As this valve is opened, the vent valve should be closed. This will force more steam to the vessel pad to compensate for the increased cold-water demand. A velocity limit control block between the controller output and the valve would also be helpful. A velocity limit function block limits the rate at which an analog input value 54

55 can change. This function has a different response than a first order filter. A first order filter may exhibit too steep a change to a step input, because the derivative of a first order response is the inverse of the filter time constant. This may be too fast for some processes. The rate of change limits can be configured for increasing and decreasing outputs. This would prevent rapid changes in water flow and allow time for the steam flow to increase. The simulation showed the effect of increasing the boiler feed water flow rate. At time equal to 150, the feed rate was increased that caused a drop in the pad pressure as shown in figure 4. Note the increased weir height after the increased boiler feed water demand. Figure 4 Graver Levels and Pad Pressure Internal levels are shown in figure 5. Note how the standpipe level increased as the pressure decreased. 55

56 Figure 5 Graver Internal Levels When simulating a liquid level control problem, it is necessary to calculate the change in flow in and out of the vessel. This change is then integrated to calculate the vessel volume. In this simulation, the water flows are simply the flow in minus the flow out. The volume in the vessel has to increase because the weir level is increased to allow more capacity. 56

57 Figure 6 Graver Flows and Volume 57

58 Figure 7 Graver Standpipe Level and Set Point Figure 7 shows the offset between the standpipe level and the set point. In this application, this off set is not critical. The use of reset in this level loop adds extra complication to an already difficult control application. Proportional only controllers can help smooth out plant disturbances. Adding reset to a level control loop should only be done after some thought is given to the overall performance under both normal and abnormal conditions. References Lloyd, S. G., Anderson, G. D., Industrial Process Control 1 st edition, Fisher Controls Company, Marshalltown, IA, Smith, Cecil L., Is Reset Action Always Necessary?, Instruments and Control Systems, p 42, Feb Shinskey, F. Greg, Averaging Level Control, Chemical Processing, p 58, September Considine, Donald M., Process Instruments and Controls Handbook, p 4-85, McGraw-Hill Book Company, New York, New York,

59 Chapter 7 Pressure Control Introduction Pressure control can be either a self-regulating or non self-regulating process. Pressure can be exerted by either liquid or gas forces. The medium phase does not dictate the control behavior rather the forces pressurizing it and how the media is manipulated dictate the behavior. The process dynamics are determined by the methods used to control the inlet or outlet flows. Pressure Regulator The most simple pressure controller is a pressure regulator. A pressure regulator, either selfcontained or pilot operated, is a proportional only controller built into its internal design. Refer to the cross section schematic shown in figure 1. In this example, the regulator is built to control the downstream pressure. At rest or on the shelf, the regulator is fully open. When piped to its service and operating, the downstream pressure P acts on the diaphragm area A to create a force F. This force will compress the regulator spring proportionally to the spring constant. The distance traveled will be x. F = K * x (1) The top set screw that presets the spring is used set the regulator downstream pressure. set screw K s A x Q P Figure 1 Pressure Reducing Regulator As the downstream pressure increases, the resulting force acting on the diaphragm compresses the spring and closes the internal valve. As the downstream flow demand increases, the valve has to open more to allow the backpressure to balance the spring force. This will require less pressure at higher flows. In regulator terminology this is called droop. Droop is the loss in 59

60 downstream pressure as the flow increases. The table below is from a Cashco Company Model 1000HP instruction manual shows the proportional action. Figure 2 Regulator Table This is a classical proportional action because the amount of off set, droop in this case, is proportional to the demand or load. Liquid Pressure Control If a centrifugal pump is used to pressurize a pipeline or a particular piece of equipment, the dynamics will behave similar to a flow loop, that is a low gain setting and a moderate reset value. The centrifugal pump curve has a flow curve that reduces the head as the flow increases. The increased flow will cause the inlet pressure to decrease, which acts to reduce the flow. This loop is considered to be self-regulating. One common application for pressure controls on centrifugal pump discharges is to use the control loop to prevent dead head condition. Deadheading a pump is not a very good idea; it can cause premature seal failures as well as may create critical process problems with certain fluids. Usually the pressure control valve is used to flow a portion of the pump discharge back to the supply vessel. When using a pressure control loop in this manor, it may be necessary to use an override control to drive the valve closed for high demand services. Gas Pressure Control Gas Pressure control is quite similar to level control in that the control behavior, either selfregulation or non self-regulating, depends on the control in or out of the vessel. If a flow controller controls either the inlet or the outlet flow rate, the process is non self-regulating. This is because the other flow has one unique flow to balance the pressure. If on the other hand, either the inlet or outlet flows set through a restriction, such as an orifice, the process is self-regulating. As an example consider a vessel that is pressurized by an inert gas such as nitrogen. The tank supply pressure is reduced by a pressure reducing regulator followed by an orifice. The tank is pressure controlled by venting the off gas to atmosphere. This is frequently done with flammable liquids to lower the flash point of the vapor space above the liquid surface, Figure 3. 60

61 PC Orifice Vent Pressure Reducing Regulator Figure 3 Self Regulating Pressure Control In this case as the pressure increases closer to the downstream regulator set pressure, the flow through the regulator will decrease. That decreasing behavior will help contribute to reducing the rate of pressure increase. The pressure in the tank can be simulated easily by integrating the number of moles in the tank by the following: ' calculate the initial mass in tank p=nrt/v P_tank = (xnew(1) / MW) * R_gas * t / vol ' calculate the change in pressure ' first we need the outlet flow dp = P_tank - p_atm If (dp > P1_orifice - p_atm) Then dp = P1_orifice - p_atm End If If (dp < 0#) Then dp = 0# End If Qout = Cg_valve(Index) * P_tank * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_valve) * (((P_tank - p_atm) / P_tank) ^ 0.5)) Q_valve = Qout Qout = Qout / minperhr n_out = Qout * spgr / 13.1 ' the flow across the orifice plate dp = P1_orifice - P_tank If (dp > P1_orifice - p_atm) Then dp = P1_orifice - p_atm End If If (dp < 0#) Then dp = 0# End If Qin = Cg_orifice * P1_orifice * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_orifice) * ((dp / P1_orifice) ^ 0.5)) Qin = Qin / minperhr n_in = Qin * spgr / 13.1 x_dot(1) = n_in - n_out 61

62 SP & PV for Press Controller PSIG Psp P Time, min Gas Flows SCFM 6 Qin Qout Time, min Figure 4 Gas Flows and Pressure for a Self Regulated Pressure Control 62

63 As the pressure is increased, the flow in and out of the tank decreases. This assumes that the tank pressure is somewhat close to the regulator set pressure. If, on the other hand, The inlet gas is flow controlled for a much higher pressure source and the gas is either used to pad the tank or react with one of its contents yielding an off gas flow rate that is directly proportional to the inlet gas flow, then the gas pressure could be assumed to be nonself regulating. FC PC Orifice Vent Gas Flow Controller Figure 5 Non-Self Regulating Pressure Control In this case, as the pressure in the tank increases, the action of the flow controller, assuming it is tuned to operate much faster than the pressure control loop, will be to maintain the same flow. In this case there is only one unique stable valve position. This dictates an integrating behavior therefore non-self regulating control. As the plots show, the inlet flow was constant. After the pressure set point change, the outlet flow is equal to the inlet flow, but the tank is at a higher pressure. The gain for the self regulating pressure control was 7.5 while the reset was at 2.5 repeats per minute. For the non self regulating pressure control the gain was 20 while the reset was at 10.0 repeats per minute. As a rule, non self regulating control loops require a higher gain setting. 63

64 SP & PV for Press Controller PSIG 45 Psp P Time, min Gas Flows SCFM 20 Qin Qout Time, min Figure 6 Gas Flows and Pressure for a Non Self Regulated Pressure Control 64

65 Even though the non self regulating behavior is seen as inlet flow limiting, for small pressure changes, both loops can exhibit integrating behavior. This is because the rate of change for an increasing exponential is greatest at the start or beginning of the change. For a short interval, both self and no self regulating loops can show similar behavior. For this case, assuming integrating behavior can lead to a higher gain setting. It should be emphasized that in this case, loop instability can occur because the resulting gain may be unstable for extreme disturbances. 65

66 Chapter 8 Temperature Control The following discussion describes the behavior of various temperature control loops. In general, a basic understanding of the physical system, in terms of size, material physical and chemical properties, is usually sufficient to make a good selection of sensor location, algorithm and final element selection, placement and size. Temperature control of non-reactive materials is generally considered to be self-regulated. A fixed valve position will result in a constant temperature for a constant load. For large insulated un-agitated tanks, the temperature sensor and the heat source should be located at the bottom of the tank. The sensor should be located below or on the same vertical plane as the heat source. The sensor should also be placed close to the heat source. The concept is to control the heat to the tank contents from the source to the probe. This hot material will rise to the surface of the tank and cold liquid will displace it. This creates a thermo-siphon. If the sensor is located too far from the source, the bulk temperature will overheat. If the tank probe is located above the heat source and the probe is in a vapor space above the liquid surface while the heat source is in contact with the liquid, the contents will overheat because little heat can be transferred to the probe. In some cases it is possible to boil or vaporize the remaining contents. Shell and tube heat exchangers very frequently used to heat or cool liquids. If the thermo-well is placed close to the exchanger outlet, the transient response approximates second order with dead time. The thermal lag through the exchanger is usually short compared to the thermo-well. As an example, consider a 157 square foot 4 pass 104 tube, 1 ¾ # 16 BWG, exchanger transferring one million BTU per hour heat. The tube side has 100 GPM water flowing through it while the shell side has 150 GPM water. The shell has an internal tube volume of 33 gallons. The jacket thermal lag can be approximated as V/F (volume / flow rate) or 0.33 minutes. The exchanger is 3 feet long and 12 ¾ diameter shell. For a shell and tube heat exchanger, the thermal lag through the tubes can be ignored because they are usually very thin. In most cases, the shell flow rate is higher than the process flow rate. The void volume in the shell is a fraction of the tube volume. Therefore the shell thermal time constant is smaller than the tube volume time constant. There are time constants associated with the thermal mass of the shell and heads, however these are usually small because the specific heats are low. The dead time can be calculated by noting the velocity through the tubes that is shown on the exchanger design sheet that is 0.65 ft per second. The tube length times the number of passes is 3 X 4 or 12 feet. The transportation or dead time would be 12 feet divided by 0.6 feet/second or 20 seconds. The thermo well time constant cannot be ignored in this case. It is usually the largest 66

67 lag in the entire control loop. A 316 stainless steel thermo-well in the pipeline exiting the exchanger would experience a lag time of about 1 minute. PID Temperature Control Response Deg F TwF Tsp Time, minutes Figure 1 Normal PID response to Set Point Change This curve shows the normal response to a PID controller set point change. In this case, the dead time was set at one minute while the thermo well time constant is also one minute. The other time constants contributed to the total overall lag of about1.5 minutes. The temperature oscillates at a period equal to 4 times the dead time plus the time constant or 5.5 minutes. If a thermo well is mounted in a pipeline, it is best to provide a pipe section of slightly larger diameter around the well. In addition, it is best to have the flow enter at 90 degrees rather than a large radius elbow. This method keeps the well in contact with the flowing process fluid. 67

68 Thermowell Concentric Reducers Thermowell Mounting Detail Figure 2 Thermowell pipe mounting The thermowell time constant can be calculated by the following formula: 1560GC = Uf P τ (1) Where τ is the time constant in minutes G is the specific gravity of the thermowell C p is the specific heat of the thermowell material BTU/lb-degF U is the heat transfer coefficient in BUT/hr-ft^2-degF f d is a dimension factor D is the outside diameter in inches D is the inside diameter in inches f d d D 2 3( D d = (2) 2 ) 68

69 Set Point Profiles What can be done to prevent overshoots during startup? I have a process that interlocks out on high temperature every time we start up. PID controllers have an effect called reset windup. During the startup, the process variable is well below the set point for so long that the reset value saturates. This causes overshoot when the process variable finally reaches the set point, it way too late to begin lowering the output signal through the reset value. Many controller companies market fuzzy logic or neural network controllers that can solve the problem. Many of these problems can be corrected with conventional controllers together with linearization and set point profiles. A way to avoid this problem is to lower the set point for the first part of the startup. This allows the controller to begin lowering the reset value at a point below the set point. Once the process variable reaches its peak and begins to drop, the set point can be increased. The objective is to program the control system to act the way an intelligent operator would. The following plot shows a reactor simulated temperature set point profile and the resulting temperature. In many cases, a ramp is not required just change the set point to the final value some point in time after the start of the process. Temperatures Deg F 190 Set Point Temp Time, min Figure 3 Set point profile minimizes temperature overshoot 69

70 Heat Transfer Coefficient The plot below shows that the heat transfer coefficient for in industrial heat transfer fluid is proportional the flow rate to the 0.8 power. In order to achieve rapid response with heat exchangers, it is highly desirable to keep the flow rate as high as possible through the exchanger. One way to obtain this is to use a tempered heat exchange loop. For a tempered loop, a pump circulates the utility fluid through the exchanger at a high rate. Adding a quantity of the utility fluid to the loop changes the temperature across the exchanger. This produces a flywheel effect and the result is very responsive control. In addition, this design will also permit good control at a reduced load. One disadvantage with this is that fouling can occur on the heat transfer surfaces. Heat Transfer Coeff. HTC HT Coeff. Btu/hr-ft^2-degF HT flow^0.8 Velosity ft/sec Figure 4 Heat transfer coefficient as a function of flow rate 70

71 TC Utility Return Utility Supply Figure 5 Tempered Loop Chemical Reactor Temperature Control All the processes discussed above could be considered as mechanical systems. Any heat generation due to a chemical reaction was not considered. For chemical reactors, the amount and direction of heat transferred by the reaction is very important in the design of the cooling system, the reactor itself as well as the control system. The following discussion is taken from Shinskey s text. Anyone involved in the design of reactors is strongly encouraged to review the reference. Chemical reactions are either endothermic or exothermic. Endothermic reactions require heat input to the reactor mass to initiate and sustain the reaction. Exothermic reactions generate heat during the reaction. The method of this heat removal and reactor design is very important for these reactions. Chemical reaction rates are calculated by a reaction rate coefficient, k. For a continuous backmixed reactor, k is equal to: Where a, E are the reaction constants, R is the gas constant and T is the absolute temperature. This equations shows that the reaction rate increases with increasing temperature. As a general rule, the reaction rate doubles for every 10 Deg C increase in temperature. 71 E RT k = aε (3)

72 For a backmixed reactor the conversion, y is calculated by the residence time and the reaction rate constant: y = 1 V 1+ k F 1 (4) Where V is the reactor volume and F is the volume flow rate. For each reactor controlled, the slope of the reaction conversion vs. temperature should be calculated. This calculation is made considering the reactor type whether plug flow or back mixed. A continuous plug flow reactor will yield higher conversions than a comparable back mixed reactor with the same volume and flow rate. The maximum slope for both will occur when kv/f = 1, where V is the reactor volume and F is the feed rate. For a backmixed reactor, the slope is: δy = δt E RT For exothermic reactors, the heat transfer coefficient and surface area, UA, and the coolant temperature can calculate the amount of heat removed: The heat evolved due to the reaction is: Q T Q 2 y (5) = UA T T ) (6) ( c = H Fx y (7) r r 0 Where H r is the heat of reaction, x 0 is the inlet concentration. These relationships, as well as the sensible heat gained or lost, can be used to calculate the rate of temperature change: H r Fx dt y UA( T Tc ) Fρ C( T T f ) = VρC dt 0 (8) Where ρ is the density. From these equations, the thermal steady state gain can be calculated as: K And the thermal time constant is: dt UA T = = (9) dtc UA + FρC H r Fx0 ( KTVρC t UA = (10) δy ) δt Note that it is physically possible of this term to be negative. If the steady state gain is negative, the reaction is steady state unstable. This should be avoided. One way to do this is to limit the reactor feed rate, F, by using an override control. This implied valve position control reduces the reactor feed if the cooling demand becomes too great. For a batch reactor it is best to control the reaction by controlling one of the reactants. This is called semi-batch. Varying the amount of coolant can control the rector temperature. A flow 72

73 controller can be used to control the flow of one of the reactants. An implied valve position controller, IVP, would override or lower the reactant flow if the cooling demand became too great. Another term for this type of control is called constraint control. Solid Thermal Time Constant Solids have a thermal time constant. When a solid object or group of solid objects are heated with hot gasses at a constant flow rate and temperature, the outlet temperature will rise to a steady state value. This time constant, τ, can be calculated by: M * C p = A k * tk τ (11) Where M is the mass, Cp is the solid specific heat, k is the thermal conductivity, A is the exposed surface area, tk is the thickness. This time constant is dominant if there is sufficient gas flow with respect to void volume. That is V/F is much less than τ. This equation will calculate the same result if a single particle is considered or if the entire mass and area is used. This is because the mass divided by the area will have the same relationship independent of the number or particles being heated. An analogy of this is to consider the thermal time constant across an insulated pipe. Neglecting the end effects, a given insulation type, thickness and diameter will have the same time constant for a foot as it will for a mile. The shape of each particle defines this equation. For very small objects, such as a powder, the time constant is quite low. This equation is valid for any heated object be it a catalyst sphere or an agricultural product. The Anatomy of a Temperature Control Project The following project will illustrate some simple concepts that can be implemented for good temperature control. This project involved the temperature control of a small vessel to study fundamental reaction chemistry. It is important to provide good, reliable and accurate temperature control to develop an understanding of the reaction kinetics involved. These reactors are agitated with 1/8" tubing cooling coil, wound in a hairpin loops. Heat is introduced by an electrical heating element on the outside of the reactor. The reactor had temperature control problems. The problems are as a result of the control scheme used. This scheme control uses a split ranged output signal where ½ of the output span is to provide electrical power to the external heater and the other ½ of the output span is signaled to control cooling water flow through an internal cooling coil by a control valve, mounted in the supply tubing to the cooling coil. This design results in cycling between heating and cooling 73

74 phases. The reason for the cycling is because the dynamic response due to the heating cycle is much slower than the cooling response. This is counterintuitive; one would think that electrical power would respond faster. In actuality, because the heater is mounted on the outside of the autoclave, the thermal time constant is larger than the thermal time constant of the cooling coil. This cycling behaves in the following manor. Assume the temperature is below the set point and the electrical power is on, while the cooling water is off. Heat is slowly transferring across the reactor jacket. Meanwhile because the control valve is piped to the water supply to the cooling coil the water in the coil is at atmospheric pressure. This water begins to degas and even boil if the reactor temperature is high enough. These gasses and vapors displace the water in the coil that reduces the heat transfer inside the coil. Because of the large thermal lag across the reactor, by the time the temperature is above the set point, the power shuts off and water begins to flow through the coil. Good heat transfer across the coil does not occur until the gasses and water vapors are swept out of the coil and a sufficient velocity of water is established. By then, the temperature undershoots causing the output signal to shut off the water flow and switch on the power, repeating the cycle. Improved temperature control of a small vessel can be accomplished by implementing an implied valve position control. This method requires the use of two PID controllers, one for the vessel temperature and one for the temperature controller's cooling water outlet. The reason this method performs better is that the temperature control response is faster with changes in the water flow rate than through changes in the power to the electrical heater. The power to the heater is controlled to provide sufficient cooling water flow through the coil to improve response. Balancing the heat and cooling loads do not cause excessive utility uses because of the size of the reactor. Other changes made were: Installed a valve positioner in the cooling water valve. This makes the valve more responsive to signal changes. The control valve was sized to keep about 7 feet per second flow in the cooler. This would be for normal flow or about 70% open. Use equal percent trim. As previously explained, the heat transfer improves with increased flow to the 0.8 power of flow rate so it would be best to keep cooling water flowing through the coil at all times. The control valve should be piped to the outlet of the reactor coil rather than the inlet. This is to keep the water in the coil at a higher pressure, which will minimize the water degassing. Degassing the water results in increased volume and poor heat transfer inside the coil. An RTD was used rather than a thermocouple for the primary controlled measurement. Many temperature element suppliers have documented references that show the RTD to be superior accuracy when compared to thermocouples. Accurate repeatable temperature measurement 74

75 and control is essential to calculate reaction kinetics. Typically, reaction rates double every 10 degrees C. Therefore accurate measurement is essential. A proportional plus reset controller was used to control the heater by the position of the cooling water valve. The set point is set for about 70 to 85% open. The output of the position controller adjusts the power to the heater. The reset value of this controller is set to compensate for the thermal mass of the heater or 1.5 repeats per minute. The time constant was calculated before start up as shown below: For the 316 stainless steel reactor wall, the constants in English units are: G=8.02 specific gravity Cp = 0.12 specific heat k=13 thermo conductivity Reactor dimensions, in feet D1= inside diameter D2= outside diameter L= Vol = pi*l*(d2^2)/4 - pi*l*(d1^2)/4 + pi*(d2^2)*(2.25/12)/4 Vol = cubic feet M = G*62.4*Vol M = pounds A= pi*d1*l A = ft^2 hw=2*k/(d2*log(d2/d1)) hw = tau_wall = 60*M*Cp/(hw*A) tau_wall = minutes The integral time constant of the power controller is set to compensate for the thermal time constant. In this case 1/ = repeats per minute. In actuality 1.5 repeats per minute were used. In addition to this calculation, a calculation was made to predict the cooling rate from the coil. 75

76 Figure 6 Reactor Temperature Control In many applications, electrical power is controlled by a time proportional output through a triac power controller. The triac acts as an electrical switch. The electronic circuits that control the triac switching implement a zero voltage turn on circuit. This is done to prevent electro magnetic interference that would be caused by rapid changes in voltage if the AC voltage were switched when the cycle is not at a zero crossing point. The disadvantage of this method is that the voltage is switched in half cycle increments. If the time proportioning period is too short, the resolution of the power to the heater is reduced. If the heater controller proportioning time is increased, the resolution improves but if it becomes too long it introduces dead time in the heating loop. If the time proportioning cycle is set for 2 seconds, the power resolution would be one part in 240, if the heater is 1200 watt, then the power would cycle plus or minus 5 watts because this is the best resolution the controller can resolve, or approximately 7 deg C for a 10 pound mass. The end result of this type of design is that the output precision approaches that of on off control. 76

77 Improved electrical output power resolution can be obtained by using a Silicone Controlled Rectifier, SCR. This device can switch ac power over fractions of a half cycle. The SCR does generate transients during switching and can be falsely switched due to transients in the line power. By installing a varistor across the SCR terminals, the transient can be suppressed through the device. These devices are available from the SCR suppliers. The power delivered to the load using this method has very non-linear characteristics. This nonlinearity would cause less than optimum control if it were not linearized. Linearization was previously discussed in this book. A simulation mass and energy balance was written in the controller itself. This was done to allow the operators to experience the different control behavior. The temperature control system started up quite well and good agreement between the heating and cooling loads was obtained. One interesting observation was that as the inlet water temperature was reduced, less electrical power was required. This is surmised to be due to the reduced heat transfer across the cooling coil due to the increased water viscosity. References Hendershot, D. C., A Checklist for Inherently Safer Chemical Reaction Process Design and Operation,. Center for Chemical Process Safety, Jacksonville, FL, October 8-11, Richmond, D. W. "Selecting Thermowells for Accuracy and Endurance." InTech, February 1980 Shinskey, F.G., Process Control Systems fourth edition McGraw-Hill,

78 Chapter 9 Control of Steam as a Heating Media Introduction Frequently the control or instrument engineer is asked to design or solve problems with steam control systems and, after checking the usual sort of items such as the regulator and control valve sizing, span and range of the transmitter, they are at a loss as to the solution of the problem. This article addresses the whole system, some of the frequently overlooked problems, and solutions. Steam, as a heating media is ubiquitous in the process industries. There are very few process plants that do not rely on steam for some sort of heating application. The applications are infinite but can be placed in a few general categories. Steam Flow Control Here steam is actually controlled by flow rate to a heat sink. Examples of these are column reboilers and strippers. Steam can be used to control a variety of process variables such as level, pressure etc. In most of these applications what is really required is the control of heat input in the process. This is indirectly steam flow control. The flow rate in many of these applications actually sets the capacity of the unit. In this type of system, the primary process variable controller's output sets the set point of the steam flow controller. Tuning of this type of control system is best done if the steam flow controller is tuned in "local" before the primary process variable controller is tuned. Either a vortex-shedding meter or an orifice plate with a differential pressure, d/p, and transmitter usually measures steam flow. For some process applications, heat flow is a better measurement than steam flow itself. This is true in the case of column re-boilers. For orifice plates, the flow signal can be modified to correct for the enthalpy based on the supply pressure. In the case of saturated steam, the correction can be calculated by: Q k * h *( a * p + b) = (1) Where h is the meter differential, p is the absolute pressure. Constants are k, a, and b. To calculate the constants for a given orifice plate size, calculate the steam flow rate over a range of pressures at the same meter differential. Multiply the steam flow rate by the enthalpy change to calculate the heat flow. Next use the EXCEL solver to calculate the constants. The following graph shows the actual heat flow compared to the calculated heat flow based on the above equation. Q is the actual heat flow, Q^ is the calculated heat flow. A similar method should be used if a vortex meter is installed and the user wants to meter heat flow. 78

79 Energy Flow Calculation 4,500,000 4,000,000 3,500,000 3,000,000 BTU/hr 2,500,000 2,000,000 Q Q' 1,500,000 1,000, , Pressure If a vortex meter is used, make sure that condensate doesn't hit the shedding element. Watch the temperature limits on the meter and electronics. Many manufactures have separate electronics located remotely form the meter. A major problem with orifice plates is preventing the condensate from freezing in the sensing lines. Traced sensing lines and commercially available insulation instrument bundles keep the d/p cell from freezing. The orifice pipe taps should be placed on the top or side to prevent plugage. Depending on the impurities in the steam and if the d/p elements require large volume displacements, condensate reservoirs should be piped directly off the pipe taps for accurate d/p measurements. Because steam is a vapor, pressure variations may cause errors in the measurement. It may be necessary to use a reducing regulator upstream of the orifice plate. Temperature Control Steam is often throttled to a heat sink to keep the process at a controlled temperature. A major problem is overshoot of the temperature due to the dead time in the heating process because of changes in load. Proper placement and selection of the temperature thermowell can reduce this. It is important to place the thermowell in an active portion of the process. Frequently the thermowell is placed in a non-flowing or cross-ambient location in the process; this insulates the thermowell from the bulk temperature. The thermowell should be immersed in the process between 5 to 12 diameters of the thermowell. It should be in a flowing stream and as close to the heat source as possible. For fluids in a pipe, it is important to measure the temperature in the 79

80 center of that pipe. Except for large diameter pipes, this is achieved by the installation of the thermowell in a pipe elbow. The immersion length of the well piped in the side of a pipe elbow can result in a cross-ambient condition if the elbow's radius is not taken in consideration. Flared or low schedule pipe can be bent at a long radius. In one application it was necessary to purchase a 12-inch thermowell to measure the temperature in the center of a 2-inch pipe. If the well is located too far from the heat source, (i.e. heat exchanger or coil) or in a stagnant portion, by the time the thermowell temperature reaches the set point temperature, the bulk temperature is considerably higher due to the temperature gradient between the source and the thermowell. One exchanger company even mounts a thermowell parallel but not touching the exchanger tubes. See Figure 1. Figure 1 Thermowell inserted in heat exchanger For tanks, the thermowell should be located in the same horizontal plane or lower than the heat source. This is very important in tanks of varying inventory. If the thermowell is located above the heat source and the level drops below the thermowell, the thermowell is then sensing the vapor temperature and over heating may result. This overheating may result in wasted steam, and possibly product degradation. Low mass and sheathed elements as well as high thermal conductivity fills and metals can be used to improve response time and thereby improve control. In most shell and tube exchanger temperature control systems, the dominant lag in the system is due to the thermowell. Care should be taken in the selection of the element, RTD or thermocouple etc. As a general rule, an 80

81 RTD is a sheath sensitive element while a thermocouple is tip sensitive. Frequently overlooked is the possible contamination or destruction of the product due to corrosion of the well in any filled system, both vapor and liquid types. The response time can be improved by placing the element directly in the process. Periodic inspections of the well or element should be taken. Commercially produced thermowells should be considered before fabricating one. These wells are available in a wide variety of materials and connections both screwed and flanged. Lagging extensions should be used when pipe insulation is required. This prevents insulation removal when the well is removed. There must be an annular gap between the ID of the well and the element that is large enough to allow for thermal expansion yet small enough for rapid temperature response. The ID of commercial wells is machined to fit most types of elements to assure proper the fit. A fabricated well's temperature response can be improved by filling that space with a liquid fill. Care should be taken in the selection of this liquid fill. The liquid will frequently boil away or decompose in the well. Process compatibility with this liquid should be considered. Frequently several uncontrolled heat sources are all piped to a vessel in addition to the controlled source of heat. This can result in complete loss of control. An example of this is a fully insulated 30,000 gallon storage tank with an internal coil which is the controlled source; 2 semi circular plate coils 1/3 the way up the tank which are trap limited and not controlled. The tank had a circulation flow of 100 GPM that went through about 50 feet of 2 inch of steam traced and insulated pipe. On startup, with the tank about 1/4 full, the temperature continued to rise above the set temperature. A manual valve was closed upstream of the steam control valve and the temperature kept rising. The plate coils were shut off and the temperature still kept rising. The product in the tank was ruined due to the high temperature. The tracing from the 50 feet of 2-inch pipe was the remaining uncontrolled source of heat. An orifice was placed in the pump discharge of the 50-foot line that corrected the problem. Regulators and Relief Valves Regulators are used to reduce the steam pressure for a variety of reasons. Reduction of pressure may be necessary to protect the steam or plate coil, which may be rated at a lower pressure than the supply. It is frequently required to reduce the skin temperature of the coil thereby preventing product decontamination. The reduction in pressure through a regulator is an adiabatic expansion and superheat will result. Reduction of this superheat should be considered if skin temperatures are important. This may be accomplished by placing a small thermostatic steam trap together with a length of uninsulated pipe on the discharge side of the regulator. If the steam supply is in the quality region, containing some condensate, a steam trap on the supply side of the regulator will be necessary. Passage of condensate through the regulator will result in reduced capacity. This trap is a must if the regulator is located lower than the main supply header. A strainer should be placed upstream of the regulator to filter pipe scale. 81

82 If a regulator is required, a relief valve on the discharge side of the regulator should be considered and should be placed upstream of the control valve, see Figure 2. If the control valve were piped upstream of the regulator, turning on the steam would result in "machine gunning" the relief valve since the regulator would be fully open. A small steam trap should be placed on the discharge side of the regulator. The trap will remove the condensate and prevent pressure buildup since some steam regulators do not shut off tightly, because they use metal to metal seating surfaces. Whenever possible, avoid the use of pilot operated regulators. The maintenance of the pilot piping is a problem with both plugage and freezing. Self-contained pressure reducing regulators are preferred; however, they usually have a lower capacity rating than a pilot operated device of the same line size. Another use for a pressure regulator is to provide a constant upstream pressure supply to the control or modulating valve. If no regulator is present and the control system is at steady state, supply pressure fluctuations will result in steam flow upsets and therefore a process upset. A regulator will quickly correct this problem, preventing the process upset. The pressure regulator is not a precise pressure control device. It has droop; the outlet pressure will decrease slightly as the flow rate increases. In many applications requiring wide flow range or the need for precise control, a pressure controller is necessary. The uses of a steam supply pressure controller as a secondary (slave) loop for a temperature control loop offers a performance advantage. For changes in heat load, the pressure loop will automatically correct for the change in condensing rate before it affects the temperature loop. Steam Supply Piping for Shell and Tube Heat Exchanger Take off on top of header STEAM MAIN Control Valve T Strainer Regulator T Vacuum Break Check Valve Cold Stream 82 Dirt Trap Trap Below Exchanger T Shell and Tube Heat Exchanger Test Valve Condensate Return Figure 2 TT Hot Stream

83 Control Valves Control valves underwent considerable change in the 1970s. This is when the cage trim design was introduced. The main advantage of the cage trim is the balanced actuator forces required and therefore a lower sized actuator can be used. The cage valve performs well in steam service. Valve manufactures offer low noise design for large pressure drop applications. On low-pressure applications, cast iron body with stainless steel trim is suitable. On higher-pressure applications, piping codes dictate certain type of bodies and may require extended bonnets. A rule of thumb is to size the valve pressure drop for 20% of the supply pressure at a maximum heat load. With steam service, use equal percentage trim characteristics for heat exchanger temperature control. This is because the change in the outlet temperature is inversely proportional to the change in process flow rate. However, the change in outlet temperature is directly proportional to the change in process inlet temperature and to a set point change for a properly sized exchanger. For flow control applications, use equal percentage trim. In all cases, the objective of trim characteristic selection is to match the process behavior, equipment-piping etc., to obtain linearly installed flow characteristics. If a larger turn down is required for proper control over the whole application, rangeability becomes a problem. In this case consider two valves with split range or implied valve position control (see Reference 2). For higher temperature service, an extended bonnet is required together with high temperature gaskets. Steam Traps The largest amount of heat transferred in steam heating is due to condensing the steam to condensate. This is also done with the highest heat transfer coefficient, or heat transferred per unit area. As a result, most heating systems are sized based on the transfer area acting as the condensing surface. Should any condensate be trapped in the equipment, less heat will be transferred. The device, which acts as the condensate passer, is called the steam trap, trapping the steam in the steam chest of the equipment while allowing the condensate to pass. Steam supplies contain entrained air and carbon dioxide, formed during the corrosion of steel that needs to be vented from the trap, a secondary objective of the steam trap. Proper steam trap design and installation is just as important in steam heating systems as other items addressed in this article. Some examples of the consequences of incorrect steam trap design and installation are: i) A batch reactor start up cycle time was increased by several percent. ii) A dryer preheater was operating with higher priced electrical power because the preferred steam source had a trap blowing steam through. iii) A gas superheater temperature control system was operating with large swings. There are three groups of steam traps: thermostatic, thermodynamic and mechanical. Some trap manufactures have literature that covers their operation in detail. The discussion here will be directed toward applications where throttling the steam supply is required for good control. 83

84 Thermostatic type traps use a temperature sensitive bellows with a plug and seating orifice, Figure 3. The principle is for hot steam to expand the bellows and close off the orifice trapping the steam upstream for condensing. The bellows is allowed to cool opening the plug, allowing the condensate to pass. The trap is good for freeze protection because it fails open during cold temperatures. Condensate flows through the trap when bellows contracts Steam is "traped" in the body when bellows expands Figure 3 Thermostatic Steam Trap The problem with using this trap for control service is the time required for the bellows to cool enough to open and allow the condensate to pass. This time results in increased process deadtime. It also makes control less responsive to increases in load because the time spent in opening the valve is used to push the condensate out the trap. Increased heat transfer is not available until this condensate is removed from the steam chest. While the controller's reset action continues to drive the valve further open, increased steam flow (and heat flow) is not fully realized until the added condensate is passed through the trap. Then the full area is available for 84

85 condensing. However, by this time the valve has opened too far and the heat delivered is too much, resulting in steam blowing through the trap. The bellows heats then closes and the cycle repeats. One manufacture cautions using this type of trap where waterlogging the steam space cannot be tolerated. Thermodynamic traps consist of a housing with an inlet and outlet port connected through a small chamber with a disk blocking the flow. When condensate enters the inlet, the disk is pushed up and the condensate is allowed to flow out. When steam begins to enter the trap, some of the condensate flashes to steam in the chamber increasing the pressure above the disk and closing it against the inlet flow. The condensate cools and the pressure is reduced above the disk and flow continues. The problem with this design is somewhat the same as the thermostatic trap. Time is required to cool the steam in the chamber. This trap requires a minimum inlet pressure and doesn't work well if the backpressure is too great. Backpressure of the condensate is another design concern for trap selection since most industrial plants using steam recover their condensate. The mechanical group consists of three types: floats, float and lever, and the inverted bucket, Figure 4. The float type contains a float and some way of linking it to a lever arm and a seating orifice. When condensate enters the chamber, the float rises opening the orifice and allowing more condensate to pass. In the inverted bucket design, the inverted bucket is connected to a lever arm, which is connected to a plug and a seating orifice. The orifice is located in the outlet of the chamber. As steam enters the chamber, the bucket becomes buoyant and closes the orifice. The advantage of this type of design is the trap's proportional action and rapid response to changes in demand on the system that is steam flow. NL designation in the figure is the neutral line, or the level line where the trap begins to open. 85

86 Condensate flows through the body, the bucket is low, permitting it to flow through the orifice. When steam enters the body, the bucket is buoyant, closing the orifice thereby trapping the steam. Figure 4 Inverted Bucket Trap Another advantage of the mechanical trap is its ability to correct for backpressure variations in the condensate return. A good analogy of a mechanical trap can be a self contained proportional only condensate level control system, such as a float valve or displacer. These devices operate very rapidly, much faster than the dynamics of the heating process. Assume the system is operating at a steady state condition, and then the condensate backpressure increases. Immediately the condensate level in the mechanical trap increases, which causes the trap to open further, keeping the same level in the trap. With a thermostatic trap, time is required for the bellows to cool and open more. This time can cause a decrease flow of steam, decreasing the process temperature. One disadvantage of the inverted bucket trap is that the condensate doesn't fully drain and may freeze. A small thermostatic trap placed in a low spot in the trap inlet piping can prevent this. The float design can trap air and carbon dioxide, however gasses can be vented with the inverted bucket design. Frequently overlooked is the need for vacuum breaking in the steam chest. Steam condensing in the chest will cause a vacuum to form if the supply is closed. This vacuum could pull condensate from the trap into the cavity. A vacuum breaker piped in the condensate line before the trap will allow air to enter the steam chest, thereby allowing the cavity to drain. When sizing the trap, consider that most of the system pressure drop occurs across the trap orifice. Make allowances for the condensate backpressure and the gasses in the steam. Vent them should the trap not have that capability. Use vacuum breakers to prevent condensate 86

87 buildup. Pipe the trap below the condensing cavity. It is recommended that the trap and the condensate piping one-foot up and down stream of the trap not be insulated. (It may be necessary to install a guard around the installation for personal protection.) An insulated trap can cause sluggish operation and make maintenance difficult. Most trap manufactures have design guides on trap installation, which should be helpful. Proper installation and maintenance of the steam trap is just as critical to the loop operation as is the control valve. Providing valves around the trap can inspect trap performance. These valves should be piped to allow visual inspection of the trap discharge. Condensate and "flash steam" would be present with a normal trap. Alternately, one could measure of the temperature of the piping one-foot upstream and downstream of the trap. High differential temperatures across the trap assure normal operation. In critical applications, using two pipe clamp adapters each with a spring loaded bayonet style temperature element can make a permanent installation. Direct Steam Injection In some applications steam is directly injected in the process, where it is necessary to add water and heat the process, thereby combining two processing steps. This is done through a sparger ring in the vessel. A problem with this design is how to prevent the process from backing into the steam supply should the steam supply be closed or shut off. As the steam cools in the piping upstream, it condenses and will draw a vacuum, which can result in filling a large part of the steam supply piping with the process material. Vacuum breakers as well as automatically actuated valves interlocked to steam supply pressure and check valves should be considered as prevented measures. Steam De-super Heater Control When high-pressure steam is reduced to a lower pressure, the reduction is adiabatic and higher temperature steam results. It is known that high temperature superheated steam is ideal for work but not for heating. It is best to use saturated steam for heat transfer because all the exposed heat transfer area is used for condensation and not to decrease the temperature to the saturation temperature. The heat transfer coefficient is a great deal higher for condensation than for de superheating. One way to reduce the superheat is to use a shell and tube heat exchanger. For small loads, this is a practical method. A very expensive exchanger is required if the load is large and the pressure high. To reduce the superheat from 650 degrees F to 500 degrees F of 100,000 pounds per hour of 600-psig steam supply would require an exchanger of approximately 2500 square feet. Adding boiler feed water, BFW, directly to the superheated steam, will reduce the steam temperature. The high temperature steam delivers heat to the water to vaporize it. The resulting 87

88 vapor mixture is mixed in the line to obtain a steam with lower superheat. The BFW is injected in the steam line through a nozzle. See figure below. BFW Flow SteamFlow Figure 5 Steam De-super heater One disadvantage with this simple system is that, despite the best efforts to remove solids from the BFW, solids and scale is deposited in the pipe due to completely flashing the BFW. This scale will cause line to plug and restrict the flow. Generally a PID controller is used to control the superheat temperature by modulating the BFW flow. The problem with temperature control is that it does not compensate for pressure variations. As the load increases, the pressure will usually decrease. If the same temperature set point is maintained on the de-super heater temperature controller, the steam will have a higher heat content. Another method for controlling superheat is to control the superheat vapor pressure. Shinskey proposed using a vapor pressure transmitter, actually a d/p cell with one side connected to a capillary system. The sensing bulb is filled with water, so the d/p cell measures the pressure difference between the steam pressure and the saturated pressure at the superheat temperature. A vapor pressure transmitter has not been available for over 30 years. Another way to accomplish this is to calculate the equivalent saturated pressure of the superheat temperature by a simple regression of the steam tables. The pressure can be calculated by a least errorsquared fit of the following equation: b = a * exp ( T + c) P (2) Where P is the pressure in psig, T is the temperature in degrees F, and a, b and c are constants. The steam line pressure is subtracted form this calculated pressure. This resulting differential pressure is the controlled variable to a PID controller. The following diagram shows the control strategy. 88

89 BFW DPC + - PT f(t) TE Super heated Steam Figure 6 De-super Heater Control Diagram The temperature sensor is usually a thermocouple or an RTD. The element should have a rapid thermal response. If the element is installed without a thermo well, make sure that the sheath is capable of withstanding the forces of the high velocity steam and occasional condensate. The element should be mounted per the de-super heater manufacture s instructions, usually 30 feet downstream of the injection point for a 12 inch pipe. The control system has very fast dynamics and should be tuned similar to a flow controller with low gain and moderate reset term. This method produces better control than temperature alone because the change in pressure actually acts as a feed forward compensator. The control is now measured by differential pressure rather than temperature alone. References: Lloyd, Sheldon G., Anderson, Gerald D., Industrial Process Control, Marshalltown, Iowa: Fisher Controls Company, 1971 McMillan, Gregory K., Tuning and Control Loop Performance, Research Triangle Park, NC: Instrument Society of America, 1994 Richmond, D. W. "Selecting Thermowells for Accuracy and Endurance", InTech, February, 1980 Chemical Engineering Deskbook Issue, October 15, 1979 Mackay, B. "Avoid Stream Trap Problems", Chemical Engineering Progress, January, 1992 Shinskey, Francis G., Energy Conservation Through Control, New York: Academic Press,

90 Chapter 10 ph Measurement and Control The most authoritative source on this subject is Greg K. McMillan. His work is an excellent guide for this subject. The following perspectives are based on this author's experience. ph electrodes - Most of their problems can be solved by following the instructions published by the manufactures. Operating the electrodes outside the velocity and temperature limits usually result in reduced life. Consider using one of the many inexpensive electrodes, usually a NPT screwed process plastic connection before relying on some other design. ph measurements in low salt concentrations are not a serious problem with coating or drift. If the solution has a high concentration of dissolved salts, it is important to condition the electrode prior to use. This conditioning involves placing the electrode in a standard sample of the solution at the operating temperature for several days. ph electrode glass is permeable and it takes time for the ions in the solution to permeate the glass. For high reliability concerns, consider using three electrodes and transmitters with a mid select algorithm. The user should provide the proper valves and drains to facilitate electrode removal while the process is running. Agitators The following equations estimate process deadtime and time constant for agitated vertical vessels. Correct agitation is very important for good ph control. Calculate Volume of Vessel, neglect bottom dish Di Tank diameter in feet h Tank height in feet V_ft3 Tank volume in cubic feet V Tank volume in gallons Agitator Da Agitator diameter in feet N Agitator speed in RPM Calculate the pumping rate in gpm Fa = 7.48*(0.4*N*(Da^3))/((Da/Di)^0.55) = Inlet Flow; Fi inlet flow in gpm Calculate the dead time in minutes td = V/(2*(Fa + Fi)) Calculate the time constant in minutes tc = (V/Fi) - td The dead time divided by the time constant should be less than 0.05 for good control. 90

91 Tank Baffles Most literature states that the vessel for ph control should be baffled. I would like to take exception to this comment in particular for slurry applications. An agitator that is off set from the center of the tank without baffles can provide good agitation. Three impellers are frequently used instead of the usual two. Because the impellers are offset, the impeller diameter is shorter than if the agitator is installed in the center of the tank. This is the reason why more impellers are needed to obtain the same degree of agitation. The agitation profile circulates the slurry the same way the baffled tank does, except the center of the vortex is not at the center of the tank. This design is quite common in the pharmaceutical industry. The reason for not using baffles is to avoid using crevices that cannot be cleaned properly and there are no surfaces for the slurry to dam up the solids. Agitator manufactures have pilot facilities as well a CFD, computational fluid dynamic, design capabilities and should provide the proper design for the application. What is critical in agitator design is to provide the correct level of agitation and establish a profile that allows for back mixing. Make sure the manufacture is fully knowledgeable about the ph control service. ph Control Valves Control valves should have linear trim. It is very important with small sized reagent control valves to mount them as close to the process as possible. A large volume between the control valve and the process act as a tank and lag the reagent delivery. With very small flows, even a closecoupled pipe nipple can contribute to this problem. Think of the internal volume in the tank compared to the reagent flow. This volume to flow ratio is the time constant of the reagent delivery system. Control valve sizing is not very accurate at very low flows therefore viscosity errors can become significant. Consider purchasing extra trim sets that can be changed out during startup. Control valve positioners are an absolute must for ph control. ph Control Basics - Rule one; know your process. This is very important in ph because of the possible non-linearity of the process. There are several companies that market special fuzzy logic and other types of controllers for these applications. Not all ph applications require this type of control. If the application requires operation on a flat portion of the titration curve, conventional PID controller should work. This is because the closed loop small signal gain is linear in that region. The controller's reset action will place the output at the correct position. Another way to improve control is to use multiple stages. Neutralization waste treatment plant frequently uses this technique. Each stage can then use a narrow span ph control. With some applications the ph measurement is simply a ratio of two reagents. Control with this system is not very complicated. ph control is considered a self-regulating process, that is if the controller were placed in manual, the ph would come to a steady value. However, if the span of the controller is small, the small signal gain will give the appearance of a non-self regulating controller. This can allow for high 91

92 gains and low reset controller settings to be used for ph. With a sufficiently large residence time, no controller rate is necessary. What should I consider if I want to use an inline ph control system? ph control is an electrolytic process, so the process kinetics are very fast, not even measurable. Because of this, an inline system becomes an attractive alternate because of reduced project and maintenance costs. If both streams have all the ions dissolved, the risk is minimal. If one of the streams contains a solid, such as lime, there is a risk that not all the solids will be reacted quickly. In that case, a tank should be used. McMillan and Shinskey both have recommendations about tank design and agitation, which should be followed. If solids are involved, a minimum of 10 minutes residence time should be used. Lab tests should be conducted to insure that all the solids are dissolved. The dynamics of an in line system are very fast, similar to a flow loop and should be tuned accordingly. There are several other concerns that should be considered when designing an in line ph control system. One is the design of the mixer itself. There are several companies that make inline mixers at a very reasonable cost. They can be consulted and can prove to be a valuable source of information for the design. Another concern is the heat removal. Acid base reactions are exothermic and heat removal may be a concern. Make sure that the resulting process temperature is not high enough to cause flashing at the system pressure. From a safety standpoint, designs need to prevent back flow of the reacted product into any of the reagent supplies. This is a major concern of inline systems. Many plants refuse to consider this type of design for that concern. There is a distinct advantage of an agitated tank because if the reagent is allowed to free fall into the tank, back flow is harder since a siphon break is inherent in the design. If the ph control system involves a solid, such as lime, it is very important to consider the degree of agitation over and above the concerns of the above equation. The type of agitation becomes critical to insure that the solid is back mixed into the liquid. If the solid tends to float at the surface of the liquid, the baffles need to be lowered to obtain a vortex action at the top of the vessel thereby pulling the solids down in the vessel. If the agitation is thought to be a concern, consider discussing the problem with an agitator manufacture or supplier. If the agitation only involves liquids and no gasses are released, computational fluid dynamic study of the vessel agitation should not be necessary. The Anatomy of a ph control Project; Example 1 The following project can show some of the potential problems encountered in ph control. Problems can occur in if the feed flow is erratic and no feed forward signal is used. This project did its homework; developed titration curves for the reagents and sized the control valves 92

93 properly. An in line mixer was used which performed well. Disposable ph electrodes were used with success. What was not evident was the pulsating nature of the flow, which was a centrate flow from a batch centrifuge. The client failed to tell the designers that production liked to run with the centrate feed tank almost empty. There was no way for the inline system to respond fast enough. McMillan's ph book shows a way to recycle the treated stream back to a storage tank. The feed stream and reagents are introduced to the pump suction and the control is after an inline mixer. The tank acts as a damper to the disturbances. The modified design and the tank became a large section of 316ss pipe, which was just a wide space in the line. McMillan shows a tank with a level control however in our case the pipe was hydrostated and operated at the system pressure. Agitation is not necessary because the in line mixer provides agitation of the feed stream and reagent. It is necessary to periodically drain out solids that form as well as purge the trapped gasses. This design is quite simple and could be used in place of some of these more complex control algorithms on the market today. A piece of pipe is easy to maintain. On this project, the team attempted to calculate the ph for the treated stream. When McMillan s ph charge balance equation could reproduce the general shape of the ph curve, but was not able to calculate the absolute reagent required. The plant reported a different amount and the lab study showed the plant was correct. The stream contained enough organic species to render most conventional ph charge balance calculations inaccurate because the water pk is shifted. Calculation of ph in organic solutions is complex and beyond the scope of this book. 93

94 ph Transmitter, Controller Reagent Treated Waste Out Inline Mixer Waste In Figure 1 PFD of ph control with a tank used to smooth process disturbances The Anatomy of a ph Control Project; Example 2 The following project involved adding two different basic reagents. The stated objective was to have the ph controlled by adding one reagent and an analyzer would measure the concentration of the second reagent. The process consisted of an un-agitated tank, a circulation pump a cooler to cool the treated stream and the down stream circulated process. The design called for the reagents to enter at the bottom of the tank through two dip pipes. The ph and second reagent would be measured downstream of a pump. The treated stream would then be circulated through another process where acid stream came in contact with the two bases and the equivalent molar amount of salts are formed. 94

95 Downstream Recycled Process First reagent location Base 2 ph % Base 2 Cooling Tower Water Exchanger ph Neutralization Tank Proposed Location Level Control Purge Base 2 Base 1 Figure 2 Two Reagent ph Control System In order to properly size reagent control valves, an approximate material balance should be calculated. In this example, the design team made use of a chemical engineering simulator. However, this simulation did not calculate ph. The ph of the circulation loop and neutralization tank was calculated by using a FORTRAN subroutine developed by Greg K. McMillan, phion3. This routine calculates the ph of any number of acids and bases with up to three dissociation constants per acid or base. A ph set point of 10 is required in the stream supplying the downstream equipment. Once the material balance was developed, the phion3 subroutine was used to calculate the amount of basic reagents required. From this calculation it was learned that the required base flows were much less than originally calculated. The titration curve also shows that there should the linearity in the range of interest does not require implementing any nonlinear compensating elements in the control algorithm. 95

96 Figure 3 Base 1 to Acid Titration Curve Armed with this new information, there are several considerations that need to be addressed with this system. First is the entry point of the two reagents. By entering an un-agitated tank, the change in ph and base 2 concentrations would result in poor control. The tank had no agitation and the dip pipes would provide large volumes which would result in long dead times. Since the objective is to control the ph of the liquid entering the down stream equipment, a delivery system was proposed to add the flows in the pump suction. This results in mixing the reagents with the liquid as well as improving the system response. Another problem is the concerns that by adding two basic streams to the same stream and control the ph by manipulating one base flow the second base flow change would act as a disturbance to the ph signal. The degree of interaction was calculated by use of the Bristol relative gain array. This calculation showed that the degree of interaction was not significant. Using the steady state material balance generated by the simulator, a PID control simulation was written in MATLAB and later converted to EXCEL using macro code for more wide spread use. It uses the same reaction chemistry as described in simulator material balance. Proportional plus reset controllers were employed to control the ph and the second basic concentration. The controllers should be tuned with low gains and high reset values, similar to flow loops. This is because the controls are inline applications. The following control simulation shows the ph behavior as well as the ph in the tank. 96

97 Figure 4 ph Control Response, Set Point at 10.0 The following sketch shows the piping necessary to deliver small flows of reagent to the system. If large volumes of reagents are in supply piping between the control valve and the process, the resulting installed dead times result in unstable control. This is because of the liquid mixing in the reagent supply piping between the valve and the process line. There can be mixing problems by introducing a small flow in the pump suction however these were not experienced on this installation. Because of the small volume lines between the control valve and the process line, tubing was used. A Plexiglas cover should be placed over the tubing portion for personal protection. Any check valves should be installed between base and the control valve. 97

98 Figure 5 Reagent Piping References: McMillan, Gregory K., ph Measurement and Control, Second Edition, Research Triangle Park, NC, ISA,

99 Chapter 11 Dryer Control Summary: Drying of bulk solids has been a difficult problem in the process industry. Attempts to measure solid moisture directly have had mixed success and are usually expensive. As a result, material is over dried at an extra cost for energy. In addition, over dried material is sold at a lower moisture than specified resulting in a loss of revenue. A need exists for a reliable inexpensive method of moisture measurement and control. Over dried product sometimes places as extra load on the dust collection system, resulting in higher maintenance costs and production down time. The dryers proposed in this study are forced air continuous adiabatic type dryers, the type used frequently by the chemical process industries. Adiabatic dryers are the type where the solids are dried by direct contact with gases, usually forced air. With these dryers, moisture is on the surface of the solid. This drying process in this study is not the process used in molecular sieve gas drying. Frequently adiabatic dryers supply air is heated by natural gas combustion. This study is for the, simulation and piloting of a proposed method of moisture control. The approach is to cross link two techniques, inferential moisture measurement and dynamic matrix control. Both these techniques are based on published material. Inferential Moisture Measurement The adiabatic drying process has two zones to describe the rate of water removal, falling rate and a constant rate. When the product becomes sufficiently dry that there are dry areas on the product surface. Further drying results in a falling rate of moisture removal. This is the zone where most industrial dryers discharge product operate. Inferential measurement of product moisture is accomplished by the measurement of temperatures of the gas entering and exiting the dryer and performing a calculation using these temperatures. This technique uses mass and energy balances of the dryer to calculate the product moisture and is valid during the falling rate zone only. The relationship between outlet moisture and the temperatures is: Xp = k*ln( (Ti - Tw) / (To - Tw) ) where Xp = Outlet Moisture Ti = Inlet Dry Bulb Temperature Tw = Wet Bulb Temperature To = Outlet Dry Bulb Temperature k = Dryer Constant. 99

100 For water and air systems, the wet bulb temperature is the same at the inlet as it is in the outlet. An interesting relationship exists for natural gas combustion; the wet bulb temperature is related by an empirical relationship that is: Tw = ( /Ti) Where the temperature is in degrees Fahrenheit. A simulation of the combustion of methane in a chemical process simulator over a wide range of inlet air ambient conditions shows this equation accurate. The validity of both equations was checked by completing a mass energy balance of both air and product as well as a regression of the wet bulb temperature against the dew point temperature of the combustion air. In other words, if the above equation showing the relationship between wet bulb and inlet temperatures is correct then there should be a strong correlation between the wet bulb temperature and dew point at a given inlet temperature. With natural gas combustion, only two measured temperatures, the inlet and the outlet, are required to implement inferential moisture control. If an indirect heat source such as electrical heater or steam coil is used then a measurement of the inlet wet bulb temperature is required. The usual method of outlet moisture control is to control the outlet temperature by adjusting the combustion gas flow valve. If a moisture analyzer is used, a moisture controller is used and the output of that controller sets an inlet temperature controller set point. Attempts by control engineers to use conventional PID (proportional integral and derivative) controls with the inferential method have resulted in poor or quasi stable control, because the technique exhibits non linear disturbances. The problem in controlling this relationship is that the dynamics of the equation result in reverse action, i.e. if the moisture set point is lowered, the instantaneous action would be to increase the inlet temperature, which causes the calculated moisture to increase before the outlet temperature is increased to such an extent as to lower the moisture to its new stable set point. This is because of the dead time and time constant between the inlet and outlet temperatures. Using conventional PID control on this relationship results in unstable control. Dynamic Matrix Control Dynamic matrix control (DMC) is a technique used to calculate the least squared error of a process variable disturbance where the disturbance is described an array of numerical coefficients. This is accomplished by matrix manipulation. This technique is excellent for non linear disturbances and a logical choice for inferential moisture control. DMC first appeared in the control literature in the early 1980's and has found some support in the process industries. An example shown in one of the DMC papers is of furnace temperature response due to soot blowing. This shows a reverse acting response similar to the inferential moisture calculation. To implement this control, data is taken on the response values due to a step input disturbance. This data is normalized and described in sample intervals over the entire response to a steady state point, usually 30 to 36 samples for the total response. This array of future values is used to 100

101 define a matrix of future values and used to develop a least squared error of the response, a control matrix. This matrix is used to calculate a control response required for a change in input error or the process variable minus the set point. Since an array of step responses is known, an array of future responses is also known. Because the matrix contains the known response pattern, the control system can correct for the reverse control response inherent with inferential moisture measurement. Once the response matrix is found, the actual control equation is rather simple since it only uses the first row of the matrix, an array. The calculation of the matrix can be done off-line, even in an Excel spread sheet. One important technique in implementing DMC is to update all future values of the projection of future values based on the error from the previous iteration. This has the effect of error correction. To simulate feed forward compensation, changes in dryer wet feed rate and air flow will change the outlet moisture. If these variables can be measured, it is possible to adjust the inlet temperature to compensate for the changes. This technique is called "feed forward". In either case of the air or the feed can be changed and the change in outlet temperature can be noted during the change. This array is then used to determine future changes in the outlet moisture and calculate the changes in inlet temperature to compensate for the disturbances. The following summarizes how the DMC is calculated. Shown here is as a listing of the data from a test used to calculate the DMC program. In the step test, the temperature was lowered. The response is the moisture decrease followed by an increase to the final value. The delta column is the normalized step response of the outlet moisture. This is also the array of forward model coefficients used to predict the future values of product moisture based on changes in inlet temperature. This array of normalized values is placed in the first of a 10 column matrix. Other columns are shifted as shown; this matrix is called Abar. 101

102 Abar = Note the inverse response. The control matrix, Cbar is calculated as: Cbar = (( Abar' * Abar ) + const * I )^-1 ) * Abar' where I = 10 by 10 identity matrix Abar' = Abar transposed The change in the output is reduced by constant is used for tuning called move suppression. This constant has the effect of limiting the output otherwise the program will attempt to make the 102

103 required change in one sample iteration, resulting in wild control. Cutler gives no mathematical derivation for this; perhaps it is to increase the eigenvalues of the inter matrix to increase stability. This is due to the non linearity of the inferential moisture calculation. Only the first row of this matrix is used as the control matrix. The control program is summarized as follows: Initialize steps Measure the process variable, PV. Set the future values of Ybar equal to PV. Repeating Code Measure the process variable, PV. Correct the previous values for modeling error by adding PV Ybar(1) to all elements in the Ybar array. Shift all projections Ybar(1) = Ybar(2), Ybar(2) = Ybar(3) Ybar(36) = 2*Ybar(35) Ybar(28). Calculate the output change Delu. Delu = Σ Cbar(I) * (Ybar(I) - SP) for I = 1 to 36. Reduce the output move by the gain term Delu = Delu * gain. Calculate the future values of Ybar. Ybar(I) = Ybar(I) * Delu for I = 1 to 36. A good way to obtain operator acceptance of the system is to display the future values of the outlet moisture. This plot is an example of 36 time periods in the future of the estimated outlet moisture. X axis, Future Time; Yaxis, Predicted Moisture Dryer Control Algorithm Improvements Dynamic Matrix Control (DMC), falls into a general classification of control called model based control. A lot of current attention has been given to these control algorithms. A joint alliance 103

104 dedicated to this study has been formed by Universities of Texas and Wisconsin. One paper from a recent conference given by this alliance addressed work done by Richalet where control of nonlinear systems was implemented by adjusting the sample time to linearize the response. Using that thought, one way to remove the inverse response of the inferential moisture response calculation would be to delay the inlet temperature before the calculation is made. If a moisture analyzer was installed on the outlet of a dryer operating at steady state and a step change was made to the inlet temperature, the moisture signal would remain constant for a time, ( the system dead time due to transportation delays ), followed by a lag, eventually approaching a new steady state value. If the inlet temperature signal was transformed through a dead time and time constant control function blocks in the control algorithm, then applied to the inferential calculation, the resultant response would be closer to the actual moisture. This is because the present time observation of outlet temperature is the result of a past inlet temperature. This approach for the control similar to that proposed by Shinskey except he did not use a deadtime operation on the inlet temperature. A corollary to this approach is to lengthen the sample time sufficiently long enough to ignore the inverse response. This results in a long sample deadtime. However, control is possible in this manor using a PID controller. This was simulated and the results proved erratic. Signal Characterization: After some experimentation, the best transient response occurs if the deadtime applied to the inlet temperature is slightly longer than the system delay and if the lag time is shorter than the outlet temperature lag. The intent is to allow the initial movement of inferential calculation not to exhibit the inverse response. Since the calculation is related to the inverse outlet temperature, an increase in outlet temperature infers a decrease in moisture and visa versa. Since it is desirable to replicate this behavior in the modified calculation, the first observed temperature change should be the outlet. In like manor, to avoid undershoots or overshoots, the last observed temperature change should also be the outlet. It is reasonable to expect the inlet temperature to have a faster response than the outlet. The thermal element is in direct contact with the inlet air, after the heat source, with a high velocity. A ceramic filled 304 stainless steel tubing thermocouple element should only have a few seconds time constant. An ISA article by Richmond estimates the lag time of a thermowell. The outlet temperature would show a longer time constant due to the back mixing occurring in the dryer. By adjusting the dead time and time constant of the inlet temperature term in the control algorithm coupled with an outlet temperature response of a deadtime, and second order under damped response results in the calculated inferential moisture. There are a number of control algorithms that can be used to control this response. Gallier Otto Model Predictive Control Algorithm 104

105 Second order systems with deadtime can be controller by an algorithm which was originally proposed for direct digital control (DDC), a control technique used extensively before distributed control came into use. This model predictive control algorithm was published by Gallier - Otto in The algorithm calculates the output based on past values of error and output values. Specifically: M i = b 0 (e i + b 1 e i-1 + b 2 e i-2 + a 1 m i-1 + a 2 m i-2 ) Where M is the output at time i e is the error at time i e i-1 is the error at time i-1 e i-2 is the error at time i-2 m i-1 is the output at time i-1 m i-2 is the output at time i-2 b 0, b 1, b 2, a 1, a 2 are constants Gallier - Otto's algorithm is derived from state space variables. They assume, through the use of eigenvalues that the response to a step input to be second order plus deadtime and calculated the time constants on that basis. There are several errors in the original published article. Bibbero later corrected these errors, however it is necessary to study both articles because Bibbero omitted the b 0 term in his discussion. Bibbero shows that the constants are calculated from the two time constants τ 1 and τ 2 and the control sample time T for each iteration. From Bibbero the constants are calculated as follows: First find α and β as intermediate terms α = e - T/ τ1 and β = e - T/τ2 Assume the steady state gain of the system is K, then: a 1 = K(1 + (α τ 1 - β τ 2 )/( τ 2 - τ 1 )) a 2 = K(αβ + (β τ 1 - α τ 2 )/( τ 2 - τ 1 )) b 1 = - ( α + β ) b 2 = αβ b 0 = 1/( a 1 + a 2 ) Note: this term is not in shown in the Bibbero text but is shown in the Gallier - Otto paper. In the field of industrial process control, the process response is not referred as a first order time constant, but rather to a reaction rate found from the unit step response curve. Most literature on controller tuning refers to developing step response time, tangent to the response curve, not locating two time constants. In order to find these times, Gallier - Otto refer to a paper on least square optimization to obtain the two time constants. Gallier - Otto reported that with a true second order process with deadtime, the error would be zero at the end of two sample periods plus the deadtime. This results in violent behavior of the 105

106 controller output, not very practical for plant use. A filter should be used in the output to avoid cycling. One of the important benefits of this control is its insensitivity to process deadtime. Note that the control equation does not use process deadtime in the equation; but sample time is used by the algorithm. This has obvious benefits and improves the robustness of the controller. Practical Considerations Representative temperature measurements can be a problem with dryers. The inlet temperature should only measure the air temperature and not receive any radiated heat from a flame. The thermowells should be placed in the dryer at positions that will not build up with either wet or dry product. Frequently it is necessary to locate these wells away from the solids. The additional installed deadtime should not be a problem because of the high air velocities usually present in adiabatic dryers. References Bibbero, Robert J., Microprocessors in Instruments and Control, New York: John Wiley & Sons, Cook, DuMont, Process Drying Practice, New-York: McGraw-Hill, Cutler, C. R., Ramaker, B. L. "Dynamic Matrix Control - A Computer Algorithm", AICh_E 86 th National Meeting, April, 1979., "Dynamic Matrix Control - A Computer Algorithm", JACC Proceedings, Paper WP5-B San Francisco, CA, Cutler, C. R., "Dynamic Matrix Control for Unbalanced Systems", ISA National Meeting, Gallier, P.W. and Otto, R. E., " A Self -Tuning Method for Direct Digital Control." 22ed Annual ISA Conference and Exhibit, September 11-14, 1967, Chicago, Il, Preprint Number 10-4-ACOS-67. Liptak, Bela G., Instrument Engineers Handbook, Philadelphia, PA: Chilton Book Company, McCabe, Warren L., Unit Operations of Chemical Engineering, New York: McGraw-Hill, Qin, S. Joe and Badgwell, Thomas A., "An Overview of Industrial Model Predictive Control Technology." Chemical Process Control V, Tahoe City, CA, January 7-12, 1996 ( also Texas- Wisconsin Modeling and Control Consortium, February 22-23, 1996 ) Richalet, J. et al, "Model Predictive Heuristic Control: Applications to Industrial Processes." Automatica, Vol 14, pp. 411 to 428. Richmond, D. W. "Selceting Thermowells for Accuracy and Endurance." InTech, February, 1980 Shinskey, Francis G., Energy Conservation Through Control, New York: Academic Press, Williams-Gardner, A., Industrial Drying: Cleveland, Ohio: Chemical Rubber Co. 106

107 Chapter 12 Non-Adiabatic Dryer Control When a dryer does not use heated air or other gasses to provide the energy required the drying process is considered a non-adiabatic. The objective of this control scheme is to control the product moisture exiting the dryer. In this scheme, steam is condensed in a shell portion of vessel. An application for this type of dryer is drying paper passed over a jacketed mandrel. The steam condenses in the vessel that allows the product to give up moisture linearly through the length of the steam-jacketed section. Frequently moisture analyzers are difficult to install on these applications. As with other dryers found in the process industries there is a need for some improved product control. An inferential calculation of the exit product moisture can be made based on the dryer s steam and temperature measurements. This calculation is explained as follows. A fundamental basis for this calculation is that the heat transfer coefficient, U, is a function of the average moisture of the product in contact with the surface. Assume the product s solid specific heat value is constant while that for water is 1.0. This resulting mixture heat transfer should be proportional to the weight percentages of each in the product. * UA = K ( w w ) / 2 (1) f f + Where U is the heat transfer coefficient, A is the jacket area, w f is the inlet feed moisture and w* is the moisture percentages exiting the dryer and K f is a constant. This equation is rearranged to solve for feed moisture. w f 2UA K * = (2) f w Neglecting sensible heat and the dryer mechanical heat added, the heat balance equations for the condensing steam and evaporated water are written as: * Q = FH ( w w ) = F ( H H ) (3) v f s s o Where Q is the heat flow, F is the dryer mass flow, H v is the enthalpy of the water evaporated, F s is the steam flow rate, H s and H o are the enthalpy of the steam and condensate. 107

108 The amount of steam superheat is assumed to be low and ignored in these calculations. The heat transferred through the jacket is also a function of the heat transfer coefficient and the area written as: Q = UA T T ) = F ( H H ) (4) ( s p s s o Where T s is the steam condensing temperature and T p is the product temperature. The product is assumed to be drying in the constant rate zone so the product temperature should be the same across the dryer through this heated section and equal to the wet bulb temperature. If a d/p cell measures the steam flow rate, the steam flow the equation for steam flow becomes: F K h = s s (5) Where K s is the orifice meter factor and h the differential pressure. Arranging equation 4 as a function of UA and substitute F s term with equation 5 results in: UA = K h H H ) /( T T ) (6) s ( s o s p Arranging equation 3 as a function of the moisture differences becomes: w f * w = ( F ( H H )) /( FH ) (7) s s o V Substitute w f in equation 7 for the right side of equation 2 and UA for the right hand side of equation 6 then arrange to solve for w*, the exit moisture: w * = K s h( H s H o ) K f 1 ( T T s p 1 ) 2FH v (8) The combined terms h H H ) K is the steam heat entering the jacket, which can be s ( s o calculated by the orifice plate differential, combined with the steam supply pressure, P, in the form: Q K s h( ap + b) = (9) 108

109 Where a and b are constants. For the non-adiabatic control system, refer to the figure below. A PID controller cascading to the dryer jacket pressure controller controls the calculated moisture. This pressure controller may have to be a self-contained regulator with a pneumatic set point, as a Cashco Model 1000HP differential pressure-reducing regulator because the small jacket volume may make control by a normal PID controller sluggish. The value for T s can be regressed through the jacket pressure signal. Product temperature should be constant through the length of the jacketed section. The dryer inlet mass flow, F, can be reasonably measured and controlled by using a loss in weight feeder. The evaporated water enthalpy, H v, is calculated based on the product temperature. The steam flow signal must be lagged before the calculation can be made to insure the control system stability. The lag time should be slightly longer the thermal lag time across the jacket. The steam trap size and placement is very critical in this design. A bucket trap and vacuum break should be used for this application. The condensate should not be permitted to back up and flood the steam jacket cavity. The advantage of this control strategy is that no moisture analyzer is required. One possible disadvantage is that the assumed heat transfer relationship may not be valid because the dryer s wall heat transfer does not behave as proposed. The referenced examples for this control technique are a fibrous material and soaps. 109

110 Wet Product Feed WC Loss in Weight Feeder Vacuum Break Water Vapor Out to moisture calculation Non-Adiabatic Dryer Motor Jacket T Bucket Steam Trap Steam Supply FT PT PC RSP w* ctrl Dry Product Out PT PV f(x) Lag f Inferential Mositure Calculation Figure1 Non-Adiabatic Dryer Inferential Moisture Control References: Shinskey, Francis G., Energy Conservation Through Control, New York, New York: Academic Press,

111 Chapter 13 Multivariable Control A control problem arises when manipulating one output causes changes in two or more process variables. This is called a multivariable control problem. There are several references in the control literature that describes the problem and how to correct it. Lloyd and Shinskey are excellent sources. I will not detail these sources here, but will summarize them. Identification Recognizing a multivariable control problem is the first step. Multivariable loops are not intuitively obvious. A classical method of identification is the Bristol relative gain array. This shows the degree of interaction and input output paring. The objective is to pair the variables such that the resulting matrix will not create a negative array and result in the best controller to valve operation. Both previously mentioned references detail this identification method. Classical Decoupling Both these references describe a decoupling network as transfer function blocks connected in a forward and cross coupling manor, see Figure 2. An interesting observation by Lloyd is that static transfer function blocks are usually sufficient. Should one implement this method, one is confronted with a problem. How can one properly put such a system in manual and assure bumpless auto to manual transfers? Inverted Decoupling A technique described by Wade shows an improved method by using the feed forward portion of a conventional PID controller to act as the summation element. The output of the each controller is connected directly to a final element. The advantage of this technique is that it allows manual operation of either controller and is better understood by the operators. Example The dilution of 20% NaOH and water to 15% NaOH is a multivariable control problem, see Figure 1. The total flow controller's output is connected to the 20% NaOH control valve while the composition controller's output is connected to the water valve. As the flow of water is increased, the composition of the diluted caustic is decreased and as the flow of the 20% NaOH is increased so is the diluted caustic concentration. This calculation demonstrates how to decouple this interaction. The concentration is calculated as: X1 = mass flow rate of water to reactor X2 = mass flow rate of concentrated (20%) NaOH to reactor h = normalized concentration of "20%" NaOH in Molar fraction ( 0.2 for 20% ) 111

112 The composition controller's process variable, A, is the NaOH concentration in percent of the mixed flow. NaOH Concentration of Aqueous Mix : A = [ ( h * X2 )/( X1 + X2 ) ] * 100% The total flow is the sum of the 20% NaOH and the water mass flows, shown as Q or Q = X1 + X2. Multivariable Control Problem Two Component Mixer Flow and Composition Control Water X1 X2 20% NaOH Mixer FC 1 AC 1 FT AT Q A Mixed Stream Figure 1 The system block diagram of figure 1 is shown in figure 2 illustrates the signal flow through a two input two output multivariable process. Controller inputs or process variables as shown as A and Q. Terms X1 and X2 are the controller outputs. Blocks G1 through G4 represent first order principal process transfer function blocks, while the decoupling network are the D1 through D4 transfer blocks. Blocks G3 and G4 represent the interactions between the two control loops. 112

113 Multivariable Decoupled Process Figure 2 Decoupling can be accomplished by neglecting any dynamic terms and assuming only steady state interaction. In this case the process transfer blocks G1 through G4 can be assumed as steady state gains K1 through K4. Calculation of these can be made assuming a coupled process (ignore the decoupling for this part of the analysis). Stream Meter Calibration Setting X1 (Water) 0 to 500 lbs./hr 250 lbs./hr X2 (20% NaOH) 0 to 1200 lbs./hr 750 lbs./hr This mixed stream results in a total flow of 1000 lbs./hr flow and a composition of 15% NaOH. Notice that the decoupling network is implemented on the controller outputs. Assume that a 1% change in controller output represents an output change of: deltaflowx1 = 5 deltaflowx2 = 12 The percentage change and steady state process values for this analysis are: deltapcnt = -1 X1ss = 250 X2ss = 750 Full scale readings of the controllers are: Qmax = 2000 Amax = 20 Relative Gain Matrix The Bristol relative gain array is calculated to show the degree of interaction. A property of this array is that the sum of each row and column equals 1.0. An interesting property of this matrix is 113

114 that it is not necessary to scale the values, just as long as the inout and output units remain the same for all element calculations. Determine the change in composition while changing just the X1 value: K1 = (pcnt scale change in composition)/( change in X1 valve) A1 = (0.2 * X2ss/(X1ss + X2ss))*100 X1 = X1ss - deltaflowx1 X2 = X2ss A2 = (X2 * 0.2/(X1 + X2))*100 da = ((A2 - A1)/Amax)*100 K1 = da/(deltapcnt) K1 = Next determine the change in composition with change in X2 value: K4 = (pcnt change in composition)/( change in X2 valve) X1 = X1ss X2 = X2ss - deltaflowx2 A2 = (X2 * 0.2/(X1 + X2))*100 da = ((A2 - A1)/Amax)*100 K4 = da/(deltapcnt) K4 = Determine the change in composition while changing X1 value while keeping the total flow constant: k1 = (pcnt scale change in composition)/( change in X1 valve) with the total Q constant A1 = ( 0.2 * X2ss/(X1ss + X2ss))*100 X1 = X1ss - deltaflowx1 X2 = X2ss + deltaflowx1 A2 = (X2 * 0.2/(X1 + X2))*100 da = ((A2 - A1)/Amax)*100 k1 = da/(deltapcnt) Calculate the relative gain interaction: I11 = K1/k1 l11 = l12 = 1 - l11 l12 = Calculating the other row: 114

115 k4 = (pcnt scale change in composition)/( change in X2 valve) with the total Q constant. A1 = (0.2 * X2ss/(X1ss + X2ss))*100 X1 = X1ss + deltaflowx2 X2 = X2ss - deltaflowx2 A2 = (X2 * 0.2/(X1 + X2))*100 da = ((A2 - A1)/Amax)*100 k4 = da/(deltapcnt) k4 = l21 = K4/k4 l22 = 1 - l21 The total relative gain matrix: l = l11 l12 l21 l22 l = The lack of symmetry in the matrix is due to the non-linearity of the equation. Pairing of manipulated variables shows the use of X1 for the water flow valve and X2 for the 20% NaOH flow valve give the best pairing. Relative gains are within the range to consider decoupling: no term 0.8 < l < 1.2 While some of the terms are close to 0.8 in this example, lowering the composition controller's set point will result in decreased stability without the decoupling Classical Decoupling Other steady state gains are calculated as: K2 = (pcnt change in flow )/(change in X2 valve) K2 = (( - deltaflowx2)*100.0/qmax)/(deltapcnt) K2 = K3 = (pcnt change in flow )/(change in X1 valve) K3 = (( - deltaflowx1)*100.0/qmax)/(deltapcnt) K3 = Calculate the decoupling network that allows a change in composition controller output to only effect the composition (not the flow ) and a change in flow controller output to only effect the flow (not the composition ). Using matrix notation; let the steady state gain matrix be K: K = K1 K4 115

116 K3 K2 K = Calculate the decoupling matrix by inverting the steady state gain matrix: D = inv(k) D = Decoupling results when there is no interaction between the interactive variables. interact = D * K interact = This is the identity matrix. The zero terms imply no interaction. Inverted Decoupling The improved method proposed by Wade uses the feed forward portion of a conventional PID controller to act as the summation element. The outputs of the each controller are connected directly to the respective final element. The advantage of this method is that the operators more easily understand it. In manual each controller operates only one valve. With any multivariable control system, care should be taken when placing one of the controllers in manual. The other control loops may experience erratic operation. Following this method, first assign the transfer function blocks D1 and D2 to 1.0 and then calculating new off diagonal elements, which will be the controller's feed forward gains. Designate the new decoupling network as H; H1 = 1.0 H2 = 1.0 H4 = K4/K1 H4 = H3 = K3/K2 H3 = Note that the sign of the new terms in the network should be the same as the original network to obtain the same action, therefore the sign of H4 should be reversed in our case as well as H1. 116

117 H1 = - H1 H4 = - H4 The new network in matrix designation is: H = H1 H4 H3 H2 H = In this case the order of the matrix multiplication becomes reversed. Test the decoupling of this network by: interact = K*H interact = Note the decoupling because of the off diagonal zero terms, but the loss of the identify matrix. This decoupling method may permit the use of controller gains greater than 1.0. This fact was proven by simulation. Non Matrix Method Matrices are hard to work with. Are there any other techniques to decouple interactive loops? Dumbie presented a method, which does not use matrices. This technique uses a feed forward block in the output signal to the final controller's setpoint. The example shown in Figure 3, is a temperature controller of a tempered water system with a cold and hot streams mixed. Total flow and temperature of the combined streams are the interactive controls. Two equations and two unknowns are written as: Fw = Fc + Fh mass balance and F * T + F * T = F * T energy balance c c h h w w These two equations are combined and solved for the hot flow: F h = F T T T T w* w c The combined temperature in this equation is the output of the h c temperature controller T w '. This system is similar to Wade s method because feedfoward control is implemented in both. This system is actually half coupling because the other flow is not compensated. The technique which implements a controller with a process model is called Model Predictive Control. 117

118 Multivariable Control Problem Hot Water Mixer Flow and Temperature Control Fh ctrl Set Point Fw( Tw' - Tc) (Th - Tc) Hot Water; Th degr Tw' Fh Fh Fc Cold Water; Tc degr Tw ctrl Fw ctrl FW Mixed Stream; Fw Figure 3 Care should be taken in implementing this system. One should make sure that the engineering units are correctly scaled when implementing the controls. Division by zero can also be of a concern if the system is run from a cold start, with both temperatures at the same temperature. The following plots from an ACSL simulation show that the concept does provide decoupling. The analysis and implementation is a great deal easier, but does not provide full decoupling. This design is better than that proposed by Lloyd because manual control is possible and bumpless transfer can be achieved by output tracking techniques. Care should be taken with output pairing so that the controller is controlling the output with the maximum sensitivity. 118

119 Mixer Temp Control DegF, lb./min FW TW_F Time, min Steam Water Mixer Flows lbs./min FC FH*10 FW Time, min 119

120 Decoupling by Tuning Can tuning be used to decouple interactive loops? Just tuning the PID control constants can, in some circumstances, decouple interactive control loops. Consider a very simple process, two spray towers, Figure 4, supplied by a common sump and sump pump. For specifics, each tower requires 100 GPM of water supply. The pump is a 3X1-½ 3500 rpm centrifugal with a 5 5/8 inch impeller. The head follows the normal square root characteristics falling from 135 feet at dead head to 105 feet at 200 GPM. The towers are elevated 40 feet from the pump suction. For piping and flow meter pressure drop, assume 2 schedule 40 carbon steel pipe, 100 equivalent feet are required. The 2 control valve has a maximum flow coefficient, Cv, of 56. The spray nozzle has a 10-psid drop at 100 GPM. From the Crane manual, assuming turbulent flow, the K factor for the nozzle is 31.6 and the pipe is When this type of process was started with both controllers tuned to normal flow controller settings, low gain and high reset, the system cycled indefinitely. As the flow to one tower reduced, that controller would open its valve further, increasing its flow. The pump would develop less head which lowers the second flow also, causing its controller to open its valve further and the cycle would continue. An easy way to stop the cycling is to tune one of the controllers more sensitive than the other. This way the faster controller can keep up with the changes introduced by the slower controller. This simple process has been simulated and the results shown are shown. Symmetrical processes can be usually being decoupled this way. 120

121 Multivariable Control Twin Towers, Decoupling by Tuning Spray Nozzle Spray Nozzle TOWER B TOWER A FC A FC B SUMP Figure 4 121

122 Results of Tuning to Reduce Interaction 120 Tower Flows, GPM Unstable flow control; same settings for each controller. 120 Tower Flows, GPM Stable flow control; one loop tuned less sensitive than the other. 122

123 Multiple Controllers Can more than one controller be used to control the same variable? Under certain conditions, more than one controller can be used to control the same variable. An example of this is a large utility of chilled water serving several floors of a sight. It is desired to maintain the same differential pressure across each user. This is accomplished by controlling a bypass valve and controller for each floor circuit. It is important for only one controller to have reset enabled. This is the controller that will control the pressure drop to the set point for the entire system. The other controllers will serve to maintain their separate pressure differences through proportional only action. Bibbero shows an example where four controllers are used to decouple the temperature and relative humidity interaction. Two controllers are used for temperature and two for humidity. The outputs of the controllers are cross-multiplied. This actually is another way of implementing the decoupling techniques described by Lloyd in that the extra controller for each loop is actually acting as a transfer function block. Once again there should be only one reset for each controller. Neural Networks There is a lot of talk about these networks. Are the good for process control? One thing is certain these days; there will be some article in the trade journals about neural networks. It is unfortunate that early in their development, many inappropriate problems were tried and failed, which gave them a bad name. A neural network is nothing more than a non-linear regression. The regression is usually based on some hyperbolic function of the sums of the input weights. The network is just a diagram of these equations. The inputs and outputs need to be scaled so that the hyperbolic function does not saturate. Network Development First investigate a polynomial regression. Frequently this is all that is required. If that doesn t work, then try a neural network. In order for regressions to be useful, it is important that the data used to calculate the network follow the same rules that designs of experiments require, mainly that the design be balanced and orthogonal. The objective is to prevent "over training" which means the network very accurately measures the process at one point. Commercial neural network programs can work with very large data sets and what you pay for is the ability of this system to work with the large data set, i.e. filter and throw out various data points. It is better to use fewer points in a balanced design than it is to use a lot of data around one operational point. Once you know this technique, you can use any number of free or shareware neural network programs available off the Internet. Neural networks have been shown to work as smart sensors, that is find some relationship with other variables in the process that results in a relationship to some analytical value. Another use is to use a neural network as a process model for control. Ramchandran and Rhinehart show an example of this in an article in InTech, ISA's technical periodical. In this paper, a HYSYS model of a distillation column was regressed into a neural network, which was used as a model predictive 123

124 controller. PI controllers were configured such that their outputs are inputs to the network, similar to the method proposed by Dumdie as described in this article. That technique uses first principal methods, which would be complicated in a real time simulation. Neural networks can be placed as compensators with process controllers. Yes, but that is only an approximation. Why would it work with process control? Because the model is only used to provide feed forward information to a process controller. The model only has to show overall magnitude and direction. The reset value in the PI controller will place the outputs at the required point. This is why model based control doesn't require an exact model. The neural network can be described as a "shorthand notation" simulation of the process. Remember, as long as the loop gain is less than one, the loop will be stable. So if the feed forward signals are not precise, the controller will find the right point and maintain stability. An 85 percent accurate models are all that is required for process control. References: Lloyd, S. G., "Basic Concepts of Multivariable Control" Instrumentation Technology Vol. 20 No 12 p 31 (1973) Shinskey, F.G., Process Control Systems fourth edition McGraw-Hill, 1996 Wade, Harold L,. Ph.D., "Inverted Decoupling: A neglected Technique", paper ISA/96 Chicago, IL, October Also reprinted in the ISA Automatic Control Systems Division Newsletter; winter Dumdie, D. P., Nonlinear multivariable control made easy InTech May, 1998, p 48 Bibbero, R., Microprocessors in Instruments and Control, John Wiley & Sons, New York, 1977, pp. 160 to 162. Ramchandran, S; Rhinehart, R. R., "Do neural networks offer something for you?" InTech November 1995, p

125 Chapter 14 Multivariable Batch Control Multivariable control does have application in batch processing. Multi component solutions and blended products frequently exhibit interactive behavior. Small changes in one component can change the analysis of all components. If the interactions of each component on all analysis were known, the correct formulation can be made. Older processes may not have accurate instruments and may have to weigh small trim charges to correctly formulate a batch. Each of these charges can affect the analysis of the batch. A program is required to insure the correct analysis is made. The following example shows how this can be accomplished. This example solution has four components, two organic liquids, comp1 and comp2, water and salt. In this example, the liquid s solubility can be ignored. The solution is sold within a volume specification, 9.81 lb. per gallon, 38.3 percent water, with 1.5 lb. of comp1, 2.5 lb. comp2. The density of pure comp1 liquid is 9.5- lb. per gallon. Short charging all components, mixing this solution and analyzing it makes the batch. Based on the analysis, small amounts of comp1, water and salt are added to the batch to trim the analysis. Water is added to the batch to change the analysis of comp2 in the solution. The total batch volume is 9400 gallons. An interaction matrix is defined which show the effect of known small changes of each component on the resulting analysis. The relationship between the change in densities and change in mass charged is: den_matrix M. mass_matrix Where den_matrix is a 3x1 matrix, M is a 3x3 matrix and mass_matrix is a 1x3 matrix. For the first row, determine the change in comp1 concentrations for each constituent. The change in density of comp1 due to adding 100-lb. of comp1 to the batch is defined as: den vol 100 vol a11 den a11 = Change in comp1 made by water addition, adding 100-lb. water den2 vol. 1.5 vol a12 den2 1.5 a12 = Adding 100 lb. of salt produces no change in comp1 concentration because the salt is only soluble in the water. 125

126 a For the second row, determine the change in comp2 concentrations for each constituent. By adding 100-lb. of comp1 to the solution: den vol vol den4 = a21 den4 2.5 a21 = Change in comp2 made by water dilution, adding 100-lb. water to the solution: den vol vol den5 = a22 den5 2.5 a22 = Adding salt does not change comp2 concentration. a For the third row, determine the change in aqueous density for change in each component. Adding 100-lb. of comp1 produces no aqueous density change. a Add 100-lb. of water to change comp2 concentration tot_wt vol. product_density tot_wt = water_wt tot_wt. %water water_wt = vol_water water_wt 8.33 vol_water= mass_disolved_solids ( ). vol_water mass_disolved_solids = den6 vol_water mass_disolved_solid vol_water den6 = spgr1 den

127 a32 spgr a32 = Add 100-lb. of salt to batch. An experiment shows that by adding 0.33 lb. of the salt to 1 lb. of water changes the density from to delta_den water_wt delta_den = a33 delta_den Set up the interaction matrix M and invert: M a11 a21 a31 a12 a22 a32 a13 a23 a M 1 = For the example batch, a set of lab results is shown. Determine the amount of each component required making the target batch specifications. target_den_comp1 1.5 target_den_comp2 2.5 target_den_water lab_den_comp lab_den_comp lab_den_water delta_comp1 target_den_comp1 lab_den_comp1 delta_comp1= delta_comp2 target_den_comp2 lab_den_comp2 delta_comp2 = delta_den target_den_water lab_den_water delta_den = 0 Calculate the amount of each component based on the specification s errors. 127

128 M 1. delta_comp1 delta_comp2 = mass_matrix M 1. delta_comp1 delta_comp2 delta_den delta_den mass_comp1 mass_matrix= mass_comp2 mass_matrix mass_salt mass_comp1. mass_comp mass_comp2. mass_comp2 100 mass_salt mass_salt Trim amounts are: mass_comp1= mass_comp2 = mass_salt = In actual practice, each batch is not exactly 9400 gallons. There in variability in the equipment, sampling and analytical errors. So if the theoretical change were made in each batch, the analysis would continue to vary. Use an exponential weighted moving average or EWMA of the changed amount. EWMA is calculated as: delta _ mass = λ * delta _ mass + (1 λ) * delta _ mass _ old This will allow the process to approach the target set points without overshoot. Upper and lower statistical limits can be calculated for each variable. As long as the variables are operating within these limits, it is not necessary to change the trim settings. 128

129 Chapter 15 Model Based PID Control Why use a process model in the control loop? Conventional PID controllers have a closed loop period equal to 4 times the process dead time plus the time constant for self regulating, non integrating processes. For processes with a large time dead time, this means the loop takes a long time to stabilize after a set point or disturbance change. There is also a tendency for loops with dead time to overshoot the set point because the reset term will cause the output to ramp to a value too far from the required output because there is no reduction in error until the process variable begins to change. The change in error can occur only after the dead time has passed. Summary of Dead Time Compensation Algorithms There are several control algorithms in the published literatures that can correct for process dead time. These techniques can be classified as internal model control, model free adaptive control and model based PID control. Internal model control is a technique that implements an algorithm that is based on a process model. Parts of the algorithm may include parts of a PID control algorithm, but the whole control algorithm is based on an understanding of the process. There are specialized algorithms and not well understood by most process technicians or engineers. An example of this is the dynamic matrix control or DMC, where a forward projection of a process change is placed in an array and output changes are based on a least error squared value of the projected process variable. Another model-based control is the minimal prototype controller, where the controller output change is based on a projected change in process variable. This algorithm does not even use any elements from a conventional PID algorithm. Model free adaptive control is a relative new technique that uses neural networks to control the process. The output will move the process variable to the set point based on an internal mathematic network, which is not determined by the user. It needs some basic understanding of the process dynamics to begin. These assumptions do not need to be exact, but should be reasonable. The process dynamics can change and the algorithm will learn the new conditions without being told to retrain itself. As an example, assume the controlled variable is at the exit of a plugged flow reactor. The control valve is at the inlet of the reactor and only adds a small fraction of the total flow through the reactor. The dead time experienced due to a change in valve position is a function of the rate through the reactor. The model free adaptive controller will learn the change without intervention. These algorithms are proprietary, somewhat expensive, most often run in a PC platform. Therefore they require some network interface to a distributed control system, DCS or programmable logic controller, PLC. Interfacing to legacy control systems frequently is a major part of the installed cost. On the plus side, many of these companies are starting and are willing to partner with the user to gain acceptance. 129

130 Model based PID controllers have been in the industry for several years. These algorithms are called Smith Predictor or Dahlin algorithms. Frequently these algorithms are described in Laplase or Z transforms and they are difficult to implement by casual users. The technique is to provide a representation of the process model in a feedback path between the controller output and the error term. The signal from the model can be used to modify the error to cancel out the feedback measurement. Other techniques manipulate internal signals within the PID algorithm such as integral tracking. Many commercially available PID controllers do not have these features, which is a disadvantage. Practical Form of the Smith Predictor Most technical papers written on the Smith Predictor describe how a model of the process is placed in the feed back path. The user believes that an exact calculation and representation is required to implement the technique. This is not practical in an industrial plant. A better concept is to view the elements in the feedback path as compensation elements. However, the compensation elements are calculated based on the process model, so the user will need to obtain a model, but it need not be exact. The process model is divided into two sections, one that models the process first order time constants and a second that models the process dead time. The process model dead time and time constants can be obtained by applying an open loop step test, that is the changing the manipulated variable, the valve, by a known amount and noting the change in process variable. Processes with dead time and multiple time constants can be simulated as a dead time with two time constants, frequently called second order. The resulting trace can be fit by placing the data in Excel and using the solver to calculate the two time constants. The dead time can be estimated by inspection. Once the terms are calculated, the modified values can be calculated and placed in the controller s feedback path as shown below in figure 1. The value of these terms should not be set exactly equal to the process model. The controller s compensated dead time should be smaller that the process dead time and the time constants should be slightly longer than the largest time constant. A good estimate would be about 25 percent; the compensated dead time should be 25 percent shorter than the process dead time and the compensated lags 25 percent longer than the process time constants. Because the compensated values are not exactly the same values as the process, it is not necessary for these compensating constants to be precisely defined. The estimated values are usually sufficient. It is not necessary to know the exact process gain, that is the percentage change process variable per change in output. It is also not necessary to have linear behavior either because the algorithm is configured to compensate for the model error. 130

131 A conventional standard PID algorithm with a remote set point can be used if the model compensating terms can be implemented in a separating computing function block external to the controller. Smith Predictor with Compensation using Standard PID Controller RSP Input Standard PID Controller with Remote Set Point Controller Output Process ( Dead Time and Time Constants ) Process Variable, PV Set Point, SP Model Correction, MC PV W W Compensated Process ( Dead Time ) X Compensated Process ( Time Constants ) f(x) RSP = SP + MC *( W X ) Figure 1 Percent Percent The output from the time constants function is the X term and the output from the dead time function block is the W term. The actual set point for the control loop is a separate register value, the SP term. In order for the proposed system to function without an offset between set point and the algorithm output, and to correct for modeling error, a model correction term, MC is the ratio of the actual process variable to the output of the total process model, W. With this correction implemented, at steady state the output of W will be equal to X and the controller s remote set point will become the external set point. The compensative action is done in the form of modifying the remote set point to the controller, while the user need only input the desired set point in the dedicated register. As a note of caution, it is important to scale the PV, process variable, within a range that does not contain zero. This is to avoid dividing by zero by the model correction term. Many newer configurable control systems do not employ a dead time programming function. If this is the case, Smith Smith Predictor Predictor Setpoint Startup Change the user can program sever small first order filters to simulate the dead time and the compensating term was set to be 80% of the highest process gain :50 12: :04 12:57 16:19 13:12 16:33 13:26 16:48 13:40 17:02 13:55 17:16 14:09 Time Time Simulation Test A simulated control using this technique was modeled in a Honeywell UMC800 analog CTRLOUT programmable controller. The following traces show the performance during start up, set point PV change and adding a disturbance. The process function included a non-linear steady state gain R-SP SETPT W X

132 Smith Predictor Disturbance 60 Percent CTRLOUT PV R-SP SETPT W X 30 9:21 9:36 9:50 10:04 10:19 10:33 Time Note that the R-SP or remote set point value changes in a direction that lowers the controller error term. This reduction in error allows the controller to moderate the output to avoid excessive overshoot. With this technique, controller settings can become optimal. In the above simulation, the gain term was equal to 0.15, the reset was equal to 2 minutes and the rate was equal to 0.2 minutes. The disturbance test was done without implementing any feed forward. I recommend that feed forward be implemented external to predicted algorithm. It becomes difficult to suppress the compensating action based on the feed forward signal, rather it is better to move the valve some amount and not try to allow the compensating algorithm to adjust for the change. The algorithm will correct for model errors as designed. The following block diagram shows the simulation tested. The process dead time is simulated as 6 one-minute first order lags while the process time constants are simulated as 2 first orders, one at 2 minutes and the second as 3 minutes. The compensation blocks are simulated as 5 oneminute lags while the compensating algorithm was simulated as a 3 minute and a 4 minute lags. 132

133 The compensation algorithm was reduced by 80%. The process was given a non-linear behavior through the math block. 133

134 Potential Problems The main difficulty with this algorithm is that the control is good as long as the process model remains reasonable. If the process dead time and time constants change significantly, the control loop will operate with choppy behavior and not stabilize. The compensating algorithm will shift in and cause control instability. Because the algorithm compensates for the actual magnitude of the process variable, process non linearity can be compensated. However, the model cannot compensate for process changes that modify either the process dead time or time constants. Consider as an example the plug flow reactor previously mentioned. As long as the production rate remains the same, the dead time will remain the same. It the rate is increased, the dead time will be lower. This lower value may become lower than the compensated dead time. In that case, the control will become erratic and never become stable. Similar circumstances can occur with the time constants. For these cases, the non-linear adaptive controllers appear to have an advantage because the controller can change as the process conditions change. Integral Delay Another way to provide improved control to a process with dead time is to configure a delay before the integral function. In this way a change in the error value will result in an immediate change in the proportional action, however the reset or integral behavior will be delayed. The 134

135 integral delay time should be equal to the process dead time. This prevents excessive integral action. The simulation was written in ACSL. The delayed integral reset term was written as: e = Tsp - TwF ed = DELAY(e,0.0,c_td,10000) a = INTEG(ed, 20) + K*e a1 = LEDLAG(T1, Tf, a+ff, 20) a2 = LEDLAG(T2, alpha*t2, a1, 20) Pcntout1 = BOUND(5.0, 100.0, a2) The lead lag elements provide the rate term. The proportional gain is the K value. The ff term is a feed forward term that was not used in this simulation. A change in set point was used to simulate dynamic behavior. A simulation of this control behavior is shown below. The compensated or delayed response is shown as TwF comp, the solid line. The dashed line is the same process without the integral delayed, TwF. In this simulation, the dead time was set at one minute. Most commercially available controllers will not allow the user to configure the controller s internal elements. Many do not offer delay or dead time function blocks. A delay function block requires the controller manufacture to use more dynamic memory, which increases the cost. Integral Delay Temp DegF Tsp TwF comp TwF Time 135

136 References: Lloyd, S. G., Anderson, G. D. Industrial Process Control 1 st edition, Fisher Controls Company, Marshalltown, IA, pp , Gallier, P. W., Otto, R. E., Self-tuning Computer Adapts DDC Algorithms, Instrumentation Technology, 65-70, Feb Blevins, T. L., Modifying the Smith Predictor for an Application Software Package, Advances in Instrumentation, Instrument Society of America, Research Triangle Park, NC, Volume 34 Part 2, McMillan, G. K., Process/Industrial Instruments and Controls Handbook, 5 th edition, McGraw-Hill, pp , 1999 Tan, K. K., Wang, Q. G., New Approach to Analysis and Design of Smith-Predictor Controllers, AIChE Journal, June 1996, Vol. 42, No. 6, pp

137 Chapter 16 Statistical Process Control Controller in a Spreadsheet Frequently a process will require control for a variable that has a lot of noise or variability in the signal. This variability can come from a number sources, if the signal is the result of a laboratory analysis, there are sampling errors. Because of this variability, the true value of the variable at any given time is not known exactly. In these cases, it is best to control this variable through statistics. The use of a statistical process control single input, single output is described below. An EXCEL spreadsheet that performs the control will be described. The controller spreadsheet has three features. The first is the use of a cumulative sum or CUSUM to trigger control actions. The second is the use of a self-tuning filter used to filter the controlled variable. The third is the use of a proportional plus integral, PI, velocity controller. CUSUM Because of analytical and sampling errors, there is variability in the process variable or PV. This means that even with a prefect plant, there will be some variability in the analytical results for a control sample. This data's variability is assumed to have a statistical normal distribution. The reasons for the data's variability are instrument error, analyst error, which is the sample preparation, requires a lab technique that will produce different results between the analyst, and field sampling errors. Small changes in the control output only add additional noise to the process. The objective of the CUSUM is to only make process changes when the controlled variable exceed a certain threshold and not make any changes if the process is operating within the normal variability. This is based on the sample standard deviation, σ x. Calculating the standard deviation can require many past samples. A technique employed by this controller is to calculate this based on an exponentially weighted moving average or EWMA of the sample variance, the square of the sample standard deviation, or (σ x ) 2. This technique is also employed for the digital filter. Define the sample mean for a population on N samples as: x = 1 N N i= 1 X i (1) The sample standard deviation of this population is defined as: 137

138 σx = 1 N N 2 xi x 1 i= 1 ( ) (2) This equation is not practical to implement for process control because of the large number of points required calculating σ. If we define another variable, ρ, as: ρx = 1 N N xi xi i = 1 ( ) (3) This variable, ρ, is related to the sample standard deviation by: σ x = ρ2 2 (4) Since ρ is based on the limited information of two samples, an EWMA of this value is calculated. This is defined as deltaf in the program where deltaf = ρ 2 = 2σ 2. For each sampled value deltaf becomes: deltaf = 09. * deltaf *( xi xi 1) 2 (5) Deltaf, a calculated value related to the standard deviation, is used in both the digital filter and the CUSUM calculation. In order to prove this calculation, A MATLAB program that performs these calculations for 2000 random points demonstrates the accuracy of the above relationships within a couple of percent. CUSUM is the accumulative sum of the error, where the error is the difference between the process variable and the set point: cusum = cusum + ( pv pisp) (6) Control is signaled when the cusum exceeds a trigger, trigger_cs, that is related to the EWMA of the standard deviation: IF ( abs( cusum) > trigger_ cs * deltaf / 2 ) (7) THEN take control action. 138

139 The size of trigger_cs is a function of the width of control band, for a 95% confidence interval or 2 σ, the value is 2. An advantage of this technique is that changes in the process are only made it the process variable extends outside the normal variability. Digital Filter The spreadsheet controller equation uses a filtered value of the process variable. ACSL simulations show that an unfiltered variable causes poorer control. The filtered signal is an EWMA of the current variable and the past filtered signal: PV = λst * PV + ( λst)* PV f current 1 f (8) The calculation of the filter factor, λ st, is based on deltaf from the CUSUM calculation. This filter will automatically adjust the filter factor to keep the filter value within a predefined confidence interval λ st = [0. 5+ ( t_ stat * deltaf ) / ( 4* E )] (9) t_ stat =., is the t statistic for a 95% confidence interval for a sample size of 13. E , is defined as the 95% confidence half interval of the filtered value. The size of E should be based on the plants sample variability. A good estimate is based on the analytical variability: E = 2*σ analytical (10) In actual practice, this calculated filter factor is clamped between 0.05 and 1.0. This prevents saturation of the filtered variable. The advantage of this filter is that the degree of filtering is adjusted to keep the confidence interval within this band. From a control viewpoint, filtering introduces a signal lag and can be detrimental to good control. This filter will regulate itself to keep the variability within the band, only allowing the degree of filtering required for good control. This filtered signal is the input signal to the controller equation. 139

140 Self Tuned filter Variable 40 x red xf self tuned green xf1 weighted blue Samples The above plot demonstrates the response of a step input noise induced signal, x trace, a self tuning filter, xf trace, and a conventional or weighted filter, xf1 trace. A weighted filter has a constant filter factor. Velocity PI Controller The spreadsheet controller implements a simple velocity PI or proportional plus integral controller. This controller calculates the change in output based on the controller tuning settings and the magnitude of the error, which is the difference between the filtered process variable and the set point. The advantage using this control algorithm is that prior knowledge of the absolute output is not necessary. The controller does need to keep the last previous iteration values. The actual control calculation is made with the gain term acting with the change in error and the reset term acting with the error. The control equations are as follows: 140

141 Calculate the new error term: pierr1 = pvf pisp (11) Where pisp the desired set point and pvf is the filtered value of the process variable. The PI velocity control algorithm then becomes: delu = pigain *( pierr1 pierr2) + pii * pierr1 / ctrli (12) Where pierr2 is the value of the previous control calculation's error, pigain is the proportional gain, pii is the reset gain and ctrli it the controller iteration time in minutes. The reason for the division is to make the value of the integral time reasonable. References R. Bibbero, Microprocessors in Instruments and Control, John Wiley & Sons, New York, 1977, pp. 160 to 162. R. Russell Rhinehart, Songling Cao, "A Self-tuning Filter", ACOS Newsletter, Instrument Society of America, Research Triangle Park, NC, Summer 1997, pp. 3 to 8. R. Russell Rhinehart, "An on-line SPC-based trigger for control action", Proceedings SPIE - The International Society for Optical Engineering, October 20-21, 1994, Austin, TX, SPIE Vol. 2336, pp. 50 to

142 Chapter 17 Robust Statistics Hampel Filter There is a growing field of robust statistics. This field has some different ideas about what to do with outliers. As we all are told, most signals are assumed to have a normal distribution. In the real world of process industries, process variable noise may at times have spikes impressed on the signal, which becomes the outliers. This is because the instruments are sometimes measuring process conditions that are not normal. Perhaps the flow meter is measuring a gas and a slug of liquid strikes a sensing element. Or the liquid flow has some entrained gas or vapor. In these cases, the process variable response is not normal ; rather there is a spike. Most engineers would just add a filter to the signal. The problem with that is the resulting signal still has a spike, just one that is smaller than the disturbance, and worse yet, the signal takes time to recover. Exponentially weighted moving average or EWMA filters compute a filtered value based on a fraction of the current signal plus one minus the fraction times the previous filtered value. The robust filter takes a "reality check" of the point, that is, does the point lie outside the range where it is considered reasonable. A filter that can correct this problem is called a Hampel filter. This filter places the variable in a series of pervious variables, seven is a common number, and calculates the median value of the series. This is where this statistic is different from most statistical filters, which use the mean value. In process control, a frequent use of the median value is in ph, where three transmitters are used and the control signal is the median of the three. Once the median value is calculated, the current value is compared with the median value of the series. This statistic is based on a factor of the median absolute deviation or MAD. A comparison of this is the range in the normal statistical domain is sigma, or standard deviation. The value of the MAD factor is Note that this unit is scaling invariant. The equivalent for 3σ is 3*MAD. If the test point is greater than or equal to 3*MAD, the filtered value is taken as the median value of the sample series. If it is below 3*MAD, the filtered value is taken directly as the value of the point. Three is the normal factor used; however it can be changed depending on the desired performance. There are trade offs when using filters, and this filter is exception. There are two problems with this filter. One is the apparent dead time due to step changes. The filtered value will not change until the median value in the series becomes high enough to shift the median value. For seven points, the filter has an apparent dead time of four sample scans. This might become a problem in some applications. The user should take in to consideration the scan frequency of the analog input hardware as well as any input electronic filters. The second problem is the end effect. The filter needs to be seeded and cannot work unless the series can be established. The MATLAB code for this filter is the following: % x is the process variable signal. 142

143 % xh is the Hampel sample series. % yh is the Hampel filtered value. % i is an index of points in the signal series. % Hampel filter constants MAD = ; K = 3; % For 7 data points in the series % Hampel filter calculation if i<2*k+1 yh(i) = x(i); % the end effects else % Begin the Hampel filter calculation % locate the sample series kk=1; for jj = i:-1:i-2*k+1 xh(kk) = x(jj); kk=kk+1; end Z = median (xh); if abs(x(i)-z)<3*mad yh(i) = x(i); else yh(i) = Z; end end 143

144 The following plot shows the response of this simulated filter compared to a weighted filter. The bottom trace is the unfiltered process variable while the top traces are the EWMA weighted filter and the Hampel filter. Note the spikes generated by the EWMA filter. The Hampel filter removes the spikes, but does experience some dead time in order to see the median value change. The Hampel filter can also serve as a pre-filter to other filters. The following plot shows a Hampel filter together with a self-tuning filter. The self-tuning filter adjusts the weight factor to an EWMA to keep the resulting noise within an expected value. Increasing the controller s rate setting can compensate the added lag. 144

145 This plot shows a Hampel filter together with a CUSUM filter. In this case signals are tested against the Hampel filter "reality check before they are applied to the CUSUM filter algorithm. 145

146 The same test data set when applied to a CUSUM filter without the Hampel filter shows these results. Note the step shifts in the CUSUM output when a spike is sensed, rendering the CUSUM filter almost useless under these conditions. 146

147 Experimental Data Another use of the Hampel filter is data conditioning. In this case a series of experimental data points, say those taken form a pilot plant experiment, that may be used to fit equations. If the number of data points is small, frequently the experimenter will just remove those points before the data is applied to the regression. For large data sets, this filter would be a good choice to remove those points and replace them with ones more representatives of the series. This would help improve the precision of the regression because most regression counts each data point with the same weight. For anyone doing this type of test, an improvement could be made if the outlier point could be fit within a Taylor series of values around the tested data point. This would be more representative value than the median value previously discussed. 147

148 References: Jörg W. Müller, Possible Advantages of a Robust Evaluation of Comparisons, Journal of Research of the National Institute of Standards and Technology, Volume 105, Number 4, July- August 2000, pp. 551 to 555. Ron Pearson, Scrub data with scale-invariant nonlinear digital filters, EDN, January 24, 2002, pp. 71 to 78. R. Russell Rhinehart, Songling Cao, "A Self-tuning Filter", ACOS Newsletter, Instrument Society of America, Research Triangle Park, NC, Summer 1997, pp. 3 to 8. R. Russell Rhinehart, "An on-line SPC-based trigger for control action", Proceedings SPIE - The International Society for Optical Engineering, October 20-21, 1994, Austin, TX, SPIE Vol. 2336, pp. 50 to

149 Chapter 18 Process Simulators Classes and Divisions There are two classes of simulators, ones that require the user to program in FORTRAN, C++, Visual Basic etc. and ones that advertise that these skills are not required. Most of these programs never work the way they should with your process, but usually work well with the sample problems, which are usually very simple or elementary. Why simulate at all? From a control systems engineer's viewpoint, it is helpful to be able to predict the dynamics thereby gaining the knowledge of how loops may behave as well as allowing the simulation to be used as a training tool. The chemical engineers want to have some data to support the plant design and a simulator will help justify equipment design and sizes. I have been asked to sit in on many discussions and vendor presentations about simulators. The subject comes up about what type of physical property database to use or how their product interfaces to the users database or how to enter physical and chemical properties of compounds not in their database. Clearly, this is the single most important factor from the chemical engineering simulation viewpoint. They usually divert their discussion to the DIPPR database while my mind keeps wondering about the dynamics that they say they have, usually as an option. Most of these products require a large cash outlet as well as ongoing customer support from some hot line or service. Control Deficiencies When you use one of these simulators for control, there are some watchouts; does you simulator actually simulate the following: Can the dynamics simulate true deadtime? This is important because if it weren't for deadtime, most process control engineers would be out of a job. The control blocks should emulate real time as much as possible and therefore need deadtime. If your simulator does not do deadtimes, do not give up, it must do first order filtering. Just add multiple first orders in series, which looks like a first order with deadtime. This may not be sufficient, as I will explain later. Noise simulation: This is necessary where analytical control is being implemented, noise needs to be filtered which adds lag to the process. The simulator should be able to add Gaussian noise with an adjustable standard deviation. This is very important for analytical data. Remember if the process model is only 85% accurate, it is good enough for process control. Frequently other engineers are very possessive and not willing to let others see the model because if is not accurate enough. For control purposes, accuracy is not required, just some overall dynamic behavior. The difference of 10% one way or another usually doesn't effect control simulations. Remember the objective of the simulator is to show the approximate behavior, and test various control strategies. 149

150 Simulated Physical Properties This is the major watch out one should have with commercial packages. In order for the simulator to produce good results, you need a good estimate of the physical properties. How do they get these properties in their database? They perform regressions on experimental data or they use some equations based on molecular structure. If the data is experimental, what data did they use? Over what range was the data regressed? Frequently the data entered is only based on a few points and well outside the range where you may want to run your simulation. A good example of this is formaldehyde and water solutions. An Actual Example In order to minimize the size of a surge tank, a commercial package, with dynamic properties, was used to simulate a process chilled cooling system using a mixture of ethylene glycol and water as the cooling medium. Forty percent of the system capacity is a batch process so there was some concern that a large surge tank is in place in order to allow the chiller to maintain the utility at the desired temperature. LOADS COMPRESSOR tower water FREON CONDENSER TC HEAT EXCHANGER Figure 1 Chilled Water System Specifications: 150

151 Outlet Temperature Cooling Media Flow Rate Cooling capacity Piping -4 degf EG-H2O solution 600 GPM 146 Tons 1000 feet 6" SCH40 A commercial simulator was used to test the effect of various size surge tanks on dynamic response of the chiller's outlet temperature controller. The first problem was the apparent inability of the simulator to calculate the viscosity of the glycol and water mixture. The simulator gave a viscosity several times the viscosity given by the vendor of the ethylene glycol and water solution. The density given was also in error. I question how these packages simulate liquid mixtures. Once the simulation was configured, it showed that there was no control problem and that the return temperature changed instantaneously and as a result no surge capacity was required! This, of course, cannot be. The simulation failed to show the effect of the installed deadtime due to the piping. This turned out to be a very important criterion, because the liquid in the piping acted as surge capacity. Piping should be considered both as a delay line and as surge. Consider the following: The pipeline, 1000 feet in length (500-foot supply and return branches) of 6" SCH40 pipe contains 1.5 gal/foot. When flowing at 600 GPM or 6.6 feet/second, the total delay per branch would be 500/6.6 or about 75 seconds. With a sample time of 5 seconds this would be 75/5 = 15 pipe segments with 500/15 = 33 feet/segment which is feet/segment * 1.5 gal/foot = 50 gal/ segment. In this case, it became necessary to simulate the pipeline as a series of 50 gallon tanks, the idea that deadtime can be simulated as a series of first order lags. Once this change was made, to the simulation, the simulator showed the first order effect, but still failed to show the effect of true deadtime. The system was finally simulated in EXCEL to control the integration scan time, which was necessary to see the effect of the piping deadtime. Once the simulation was complete, it demonstrated that there is sufficient reserve of coolant in the supply and return piping to eliminate the surge tank. The following plots show the correct results of the simulation. Notice the dead time between the load temperatures. 151

152 EG-H2O Chiller Temperatures Deg F -2 Tsp T load T return T chiller Time, min Process and Chiller Loads Pcnt p load c load Time, min This simple simulation demonstrates the potential problems with commercial process simulator packages. 152

153 Integration Algorithms So how can you integrate with a spreadsheet? I ll bet it is too complicated. Writing differential equations is not a very complicated exercise. The integration algorithms are found in most college math texts or on the Internet. Writing a differential equation is just a matter of writing a difference equation and solving it with an algorithm. Remember, difference equations first, then given to solve through the algorithm. Integrators come in two varieties, relative to step size, variable or fixed. Examples of variable sized are Gear s Stiff and Runge-Kutta-Fehlberg. These algorithms reduce the integration interval to minimize the error. There is the Simpson s rule that states that the error in an algorithm is related to the size of the integration interval raised to the power of the number of evaluations. Variable size algorithms keep reducing the interval until the error is less than that specified by the user. These algorithms are frequently used by those who are making a space shot or in determining the reaction rate constants for some process chemistry. They are of little use for control simulations because in control, fixed intervals are required. Even if the process is static, control must continue and mixing different algorithms is seldom worth the effort. The Runge-Kutta level 4, meaning four levels or intermediate solutions per iteration, is the best for most control purposes. Even a simple Euler algorithm can give good results. To write a differential equation, just remember you only need to write the difference, which is the input minus the output. Just remember solving a differential equation required the initial value, so you have to start somewhere. The following is a Visual Basic code for a differential equation program solving a simple pressure control loop using the ideal gas law and the Universal Gas Sizing Equations. In this case, a tank is blanketed with nitrogen. The nitrogen is supplied through a regulator upstream of an orifice plate. The tank is vented through a control valve. x is a three element array, x(1) = mass in the tank, x(2) = valve time constant, x(3) = integrated error term. x is set to the initial condition values. The differential equations solve for a new x term based on the differences. In this example, it is best to determine the mass in the tank by assuming an initial pressure. Runge-Kutta level 4 integration example first set the existing variables to a xnew For j = 1 To ssv xnew(j) = x(j) Next ' begin the four step process For j = 1 To 4 ' calculate the initial mass in tank p=nrt/v P_tank = (xnew(1) / MW) * R_gas * t / vol ' calculate the change in pressure ' first we need the outlet flow, n_out dp = P_tank - p_atm If (dp > P1_orifice - p_atm) Then dp = P1_orifice - p_atm 153

154 End If If (dp < 0#) Then dp = 0# End If Qout = Cg_valve(Index) * P_tank * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_valve) * ((dp / P_tank) ^ 0.5)) Qout = Qout / minperhr n_out = Qout * spgr / 13.1 ' then calculate the flow across the orifice plate, n_in dp = P1_orifice - P_tank If (dp > P1_orifice - p_atm) Then dp = P1_orifice - p_atm End If If (dp < 0#) Then dp = 0# End If Qin = Cg_orifice * P1_orifice * _ ((520 / (spgr * t)) ^ 0.5) * _ Sin((59.64 / C1_orifice) * ((dp / P1_orifice) ^ 0.5)) Qin = Qin / minperhr n_in = Qin * spgr / 13.1 for x(1), the mass difference is the inlet minus the outlet for x(2), the first order lag simulating valve travel for x(3), the integration of the control error x_dot(1) = n_in - n_out x_dot(2) = (1 / tau_v) * (u(index) - xnew(2)) x_dot(3) = (Psp(Index) - P_tank) These are the integration equations If j = 1 Then For i = 1 To ssv k1(i) = step * x_dot(i) xnew(i) = x(i) + k1(i) / 2 Next End If If j = 2 Then For i = 1 To ssv k2(i) = step * x_dot(i) xnew(i) = x(i) + k2(i) / 2 Next End If If j = 3 Then For i = 1 To ssv k3(i) = step * x_dot(i) xnew(i) = x(i) + k3(i) Next End If If j = 4 Then For i = 1 To ssv k4(i) = step * x_dot(i) x(i) = x(i) + (1 / 6) * (k1(i) + 2 * k2(i) + 2 * k3(i) + k4(i)) ' Calculated next state Next End If Next ' calculate the new outlet pressure by calculating the mass in tank p=nrt/v P_tank = (x(1) / MW) * R_gas * t / vol 154

155 Using the Control System as a Simulator In many cases where the user is only interested in simulating hydraulic or thermal systems, or where chemical reactions are simplified or ignored, the control system itself can be modified to provide the simulated process. The following example illustrates this. Assume a heat-jacketed vessel is cooled by using an internal cooling coil. The temperature is controlled by the amount of cooling water through the coil and the heat is controlled to keep the flow it a high enough value it facilitate good heat transfer. Modifying the control program can simply be done adding the required function blocks to calculate the heat transfer. The cooling heat value can be subtracted from the heating heat value and be totalized. The resultant total functions as an integrator, which is the heat value in BTU/minute, This can be converted to a temperature reading. In the simulation blocks the following functions are simply calculated: The cooling flow, F_COIL, is equal to K*(TV-104) where TV-104 in percent. The heat transfer coefficient, U_COIL, is equal to a K 0 + K 1 *(TV-104). The coil outlet temperature is calculated by a heat balance across the coil is equal to the heat flowing through the coil: Q_COIL1 = U_COIL * A *( (TI-104R) (TOUTCOIL + Tincoil) /2 ) = F_COIL * (TOUTCOIL Tincoil) Solving the above for TOUTCOIL: TOUTCOIL = (U_COIL * A ((TI-104R) (Tincoil/2) + F_COIL*Tincoil) / (F_COIL + U_COIL*A/2) The heat transferred through the coil, Q_COIL1, is equal to F_COIL*(TCOILOUT Tincoil) / 60. Tincoil is a constant of DegR. The electrical power percentage, P-104, is converted to heat in BTUs. This value is as lagged by a first order lag equal to the thermal time constant across the jacket, tau. Q_ELECT = K*(P-104)* (1.0 - e -t/tau ) The Q_COIL is a lagged value of the calculated Q_COIL1. Once the electrical heat and cooling heat values are calculated, the subtracted element,, subtracts the cooling heat from the electrical heat. This heat value is then totalized. The controlled variable, TI-104, is finally calculated in degrees C. The temperature in degrees R, TI- 104R, is calculated also. 155

156 Figure 2 Controller for Simulation 156

157 Figure 3 Simulation Equations Developed form the Control System s tool kit 157

158 Chapter 19 Environmental Temperature and Humidity Control There appears to be renewed interest in temperature and humidity control for plant sciences. This chapter will address some techniques for good control of the growth environment. Many of the techniques described in this report can be used in dryer control. In order to gain a clear understanding of some techniques, the user is encouraged to consult the psychometric chart. The chart displays the phase conditions of water vapor in air. The chart will provide visibility of underlying phase changes. An understanding of the unit operations occurring on the processed air as well as units of measurement is articulated on the chart. The air temperature is the also called dry bulb temperature. This is the temperature of the stable air water vapor mixture. The dew point temperature is a measurement of the temperature where condensation begins to form as the water is condensed from the wet air. The wet bulb temperature is the temperature at which adiabatic heat is transferred during the drying of a solid or humidification of air. For a dryer, moisture in the solid is transferred to the air. The air will gain moisture while the solid looses moisture, therefore or humidification of the air occurs. This is the same effect if water is sprayed into the air stream. This process will occur at a constant wet bulb temperature. The dry bulb air temperature will decrease during this process and be lower exiting the dryer or chamber. Relative humidity is the ratio of the water vapor pressure at the dew point to the water vapor pressure at the dry bulb temperature. This ratio is usually expressed as a percent. This ratio is multiplied by 100 to obtain the percentage reading. The first step is to consider what type of inlet air is required. In many applications, cool dry air is supplied to a test growth chamber. This can serve as an entry point in the system. The air will enter the system at a given temperature and humidity. Energy sources Heating the air can be accomplished by using an electric heater. In this case, the heated air will exit the heating plenum at a lower relative humidity, because increasing the temperature non- adiabatic will not change the moisture in the air. If steam is used to humidify the air, the temperature will increase as well as the humidity. If, on the other hand, water is injected in the air stream, the temperature will decrease while the humidity will increase. This will occur along the constant wet bulb temperature. Temperature Instruments The preferred method of temperature measurement is with either a thermocouple or an RTD. Many years of experience showing the superiority of the RTD compared to thermocouples. The RTD based on nickel wire resistance, detects temperature on the sheath and is accurate within degree C. 158

159 A thermocouple on the other hand is a tip sensitive element. It is accurate within degree C. In areas that are close to heat or light sources, make sure the element is not placed in a dead spot in the chamber or zone. Shade the element from the sun. Humidity Instruments Several years ago, the only type of humidity instrument available was a coil that changed shape as the humidity changed. These were very unreliable. Another humidity instrument used P 2 O 5 conductivity, as the humidity in the air increased; the P 2 O 5 would become phosphoric acid and increase conductivity. This probe is subject to frequent regeneration. Sometimes the P 2 O 5 would dissolve away from the electrodes. Chilled mirror dew point sensors measure the dew point by controlling the temperature where it a reflective surface begins to fog, by definition this is the dew point. These instruments needs frequent cleaning in dusty environments. Within the last few years a new design a new design has emerged. This is based on solid-state thin film polymer, a capacitive element, moisture absorbs in the polymer and the electrical capacitance changes, which is measured by the electronic circuits. This instrument has an accuracy of + - 2%. These instruments are quite reliable in dusty environments, however they can be permanently damaged if operated at sustained humidity above the rated specification, typically 95%. Another early method of measuring the amount of moisture in air is the wet bulb temperature. A sling psychomotor can measure this temperature. A small cloth sock is placed on the end of a mercury thermometer. This device is slung through the air and the temperature is reduced due to the water evaporative cooling. An inexpensive wet bulb temperature device can be fabricated by using a thermocouple mounted above a cup of water. A paper towel can be folded around the tip of the thermocouple and allowed to form a wicking action with the water. A small fan can move the air around the wetted element. This design was tested and worked for several hours. The water needs to be replenished periodically. 159

160 The water temperature should be equal to or higher than the ambient temperature. If the water temperature is colder than the dew point temperature, then this method will measure the dew point temperature because moisture in the air will condense on the wick. Wet Bulb Temperature Measurement 3/8" wide paper towel strip; 1" from water surface 4" desk fan PARAGON Industries low speed Williams - Sonama Roasting Thermometer Wet Bulb experiment This set up was run for several hours, the capullary action in the paper towel allowed the wet bulb temperature to stabilize. 060 ambient air at 69 degf Cup of water Paper towel; Coronet Dura Fiber Other materials tested: Surgical gause did not support the capullary action Cotton strip is to heavy. Sensor and Moisture Injection Location Make sure that there is adequate airflow around the temperature and humidity elements that they are not in a dead volume in the chamber. Follow the humidity or dew point temperature s operational manual. If the instrument is not mounted in a flowing stream, it will not be responsive to the surrounding conditions. One way to avoid this problem is to mount the temperature and moisture measurement probes in a small white box that has a small electrical enclosure fan to move enough air to insure good response. The box should be white and insulated to avoid heating. Atomization of water in a flowing stream is a complex process. While the overall mass and energy balances follow simple engineering calculations, the transport of water mist to vapor is not trivial. It is recommended that the user seeks out spray vendors and work closely with them for the 160

161 design in question. One way to improve the mass transfer of water into air is to heat the water before it is injected. Plant Physiology For environmental chambers used to grow plants, light becomes an important variable. Biologists are concerned about the spectral response of plants. Special lights have to be used to accommodate the correct spectrum. Different types of lights, incandescent as well as high intensity discharge or special fluorescent lights may be required. The lights should be timed to correspond to day night 24 hour cycle. The plant s DNA will trigger premature flowering if the lights are turned on even for a short period of time during the night cycle. When light is turned on a plant, it begins its transpiration cycle. The plant will begin to release water from its leaves. It is important to operate the chamber at the proper humidity to avoid having the water remain on the leaves. Because of the transpiration process, the plant variability makes it is very difficult to apply feed forward control to the temperature and humidity control loops. Temperature and Humidity Control Interaction As can be seen with the aid of psychometric chart, temperature and humidity are interactive variables. Increasing the temperature will cause a decrease in humidity. For most enclosures, modulating the heat input controls the temperature. Humidity is controlled while adding steam or water in the fan box. Assume electrical heat is used. Refer to the chart below, assume the air enters at 60 degrees F and 50% relative humidity, point 1 and is heated by an electrical heater to 95 degrees F the relative humidity will be reduced to 15%, point 2. However the dew point temperature will remain constant at 41.3 degrees F. 161

162 In the drying or the air humidification with water vapor processes, the wet bulb temperature remains constant while the humidity increases and the temperature decreases. This process is shown as the line between points 2 and 3. On the other hand, if steam is used to humidify the air, the temperature is increased instead of decreased. This is because the steam has higher heat content than the air. This is shown in the following diagram. 162

163 If electrical heat is employed to increase the temperature, there is no change in the dew point temperature. That is, the dew point temperature is the same at point 1 as it is at point 2. One way to decouple the interaction between temperature and humidity is to control the dew point temperature instead of the humidity. The dew point temperature set point can be calculated by knowing the humidity and the temperature. In most cases the users are interested in controlling humidity rather than dew point. The humidity is calculated as a ratio of partial pressures: RH 100* p = (1) p w o w p w is the water vapor pressure at the dew point temperature and p o w is the water vapor pressure at the dry bulb temperature. The water vapor pressure can be calculated through the exponential equation: = * *exp t p (2) Where t is in degrees F and p is in psia. Since the humidity is a ratio of the partial pressures, the dew point controller set point can be calculated as a fraction of the above equation solved in 163

164 reverse. The above equation was solved in reverse by using the Excel solver routine. The dew point temperature equation can then be calculated as: t *exp((( RH * *exp( /( t ))) / ) (3) dp = db Where RH is the relative humidity set point and t db is the dry bulb temperature. The dry bulb temperature set point should be the actual dry bulb temperature. This calculation is valid between the range of 35 and 110 degrees F. In this manor, the humidity is controlled at the actual temperature. The temperature controller will then control at the proper set point which will control be an input to the humidity controller s set point. Both loops need to be in automatic for this method to work properly. Attempting to operate either loop in manual will result in an unstable system. If the user has employed a humidity instrument instead of a dew point temperature, the above equation can be used to calculate the dew point signal except the relative humidity term in the above equation is the normalized ( 0 to 1.0) relative humidity signal. Controlling dew point in either case will result in decoupling the interaction and will result in more stable control. A diagram of the resulting control system is shown below. The linearization function block is used to compensate for the non-linear characteristics of the electrical heater. The low signal selector is used to prevent setting the dew point temperature controller s set point above the required set point. The purpose of this control design is to control the humidity at the correct value independent of the temperature. A change in heat will not affect the absolute moisture value. If a disturbance to the system increases the moisture, the temperature will be reduced. This reduced temperature will lower the dew point controller s set point, which will lower the water flow to the system. In this way the control technique will decouple the temperature and humidity interaction. 164

165 In the above case, it is assumed that any make up air be dry. Frequently this is not the case it Humidity Control by Dew Point Temperature Dry Bulb Temp RH f(rh,t) Calculated Dew Point Controller PV RH SP < low select f(rh,t) Calculated Dew Point Controller SP P I Dew Point Temperature Controller Dry Bulb Temp SP Temperature Controller P I Water Spray valve or pump f(x) Linearization Equation in function block Electrical Heater t dp = db * exp((( RH * * exp( /( t ))) / ) may be desired to control the temperature and humidity in an enclosure by re-circulating a portion of the wet air in the system. Because the re-circulated air has high humidity, it is not possible to have exact humidity control with that design. As a result, reset should not be used in the humidity or dew point controller. An example of this is shown below. By controlling inlet airflow and humidity by venting a portion of the outlet air and mixing the remaining air with fresh air will result in an unstable control system. This is shown through the use of a psychometric chart program from Akton Associates, Martinez, CA Because some of the values are close to others, not all point numbers are displayed on the chart. The results of two of these simulations is shown below: 165

166 Process Report 1 W t rh v h td tw Vtot m ma mw lbm/lbm F % ft^3/lb Btu/lb F F ft^3/hr lbm/hr lbm/hr lbm/hr * 65* * * * 9845* * 82* * * 82* * * 50* * * 84.1* * * 105* * Process Report 2 W t rh v h td tw Vtot m ma mw lbm/lbm F % ft^3/lb Btu/lb F F ft^3/hr lbm/hr lbm/hr lbm/hr * 65* * * * 9845* * 82* * * 82* * * 50* * * 84.1* * * 105* * Air properties are shown as points on the chart. In the case of Process Report 1: Point 1 is the hot air entry point. Point 2 is the air outlet point and assumes that the inlet conditions cause a water addition of 1.04 pounds per hour. Point 3 shows this water loss leaving the system. Any more or less water leaving would result in an imbalance of the drying conditions. Point 4 is the portion of the outlet air re circulated. Point 5 is shows the properties of the fresh air make up stream. Point 6 shows the fresh air makeup mixed with the re circulated air. Point 7 shows the properties of the heated air stream. Note that for all practical purposes, this system results in a balanced design for Process Report 1. For Process Report 2, assume that the inlet conditions will only release 0.6 pounds per hour to the air instead of the 1.04 pounds per hour in report 1. As previously stated, from a mass balance viewpoint, 0.6 pounds per our must leave the system. For this case, in order to obtain 105 degf air at 65% relative humidity, more total air flow is required. The control structure has conditional stability. There is only one stable point of operation. This is quite different from a stable multivariable control system. In that case, there is structural stability. In this case, the volume flow rate of the recycled air is defined because the exhausted air is defined by the amount of moisture added to the air. This fixes the amount of fresh air mixed in the inlet to obtain the desired humidity. The total mixed rate will most probably not be that set by the airflow control, which will cause instability. Even though this will occur, using this system will result in an oscillation of the inlet humidity. With mild tuning settings, this oscillation should be small and not affect the process. 166

167 Wet Bulb Temperature Regressions If the wet bulb temperature is used to measure humidity instead of a humidity or dew point sensor, the dew point temperature can be calculated from the wet bulb and dry bulb temperatures. This can be accomplished by linear regression techniques. The relative humidity can be calculated as: 2 2 rh = * tw 6.385* t * t * tw 0.093* tw* t (4) Where rh is the relative humidity, tw is the wet bulb temperature and t is the dry bulb temperature in degrees F. The dew point temperature can be calculated by modification of the exponential relationship as shown in equation 3 from the previous section. t dp = db *exp((( RH * *exp( /( t ))) / ) 167

168 Chapter 20 Neural Networks When neural networks came on the industrial scene in the 1980s, they were viewed as a panacea for all the difficult on unsolvable control problems through the ages. However, when these problems were undertaken, few successes occurred. This gave them a bad name, and they still suffer the effects of this initial trial. The objective of this chapter is to give the reader a brief understanding of what they are, how to developing a network as well as a perspective in the form of an anatomy of an application. There are many excellent references describing the detailed network structure and mathematics. I strongly advise the user to study these. Just what is a neural network? Neural networks are computer programs that model the functionality of the brain. As with other programs they have inputs and outputs however they process the data differently. They have an analog to the operation of the fundamental cellular unit in the brain called the neuron. There are estimates of as many as 100 billion neurons in the human brain. They are often less than 100 microns in diameter and have as many as 10,000 connections to other neurons. Each neuron has an axon that acts as a wire for all connections to the other cell's neurons. The neurons have input paths that are called dendrites that gather information from these axons. The connection between the dendrites and the axon is called a synapse. The transmission of signals across the synapse is chemical in nature and the magnitude of the signal depends on the amount of chemicals (called neurotransmitter) released by the axon. Many drugs work on the basis of changing those natural chemicals. The synapse combined with the processing of information in the neuron is how the brain's memory process functions. In computers or artificial neural networks, the neuron's analogy is called the processing element or PE. The PE has many inputs either from input data or other PE elements. The inputs to the PE are weighted similar to the synaptic strength and are summed. The result of this summation is processed by a transfer function or a threshold function before it is passed to the output path. The output path is then passed to other inputs or to an output node. These PEs are organized in layers. These layers are grouped into input, output and hidden. Neural networks are different from artificial intelligent or AI systems. AI systems are rule based and as a result need a human expert to work with the system to input the rules. Neural networks learn by processing the data without rules. This input process is called training. Examples of known behavior are presented to the system and computations adjust its junction weights to the required behavior. Obviously someone knowledgeable in the simulated process is necessary to input the data. The compilation of this data is called learning or training instead of programming. The network converges to a point. Testing this network against known data is called recall. Because neural networks do not have rules i.e. not rule based, they cannot explain how they 168

169 arrived at a stated answer. There is a hidden danger in applying bad data to a system that has learned good behavior; it can unlearn. It has no way of knowing that the data it is learning with is bad or not as accurate or valid as it learned before. Perhaps another way to describe a neural network is that it is a non-linear regression. Input data values are applied to a series of functions. The weights of these functions are adjusted to minimize the error between the network s output value and the output data corresponding the input data. Each data input and output point is scaled, that is it is normalized and centered on zero with a standard deviation of one. This is done to insure that each data point is compared to the other data points with the same reference. Types of Networks and Uses The topology of the inputs outputs, and PEs, their connection weights and learning rules are what defines the network. The network is the collection of inputs, outputs and PEs. They are defined as layers, the input and output layers are the points where data is entered and outputs leave. The processing elements or PEs are layered in what is called hidden elements. These are layered parallel to the input and output elements. The connections between the elements have varied strength and form the analogy to the synapse strength in the brain. The network structure actually describes a complex matrix mathematical equation. An example of the network is shown below in figure 1. The u values are the scaled input values. Yhat is the scaled output value. The circles are nodes. The loan node in the upper middle is a constant of one. Single constant values are used to bias the results if necessary. 169

170 Figure 1 Example of a Neural Network The inner connecting lines correspond to weights or values that are multiplied by the input value or the intermediate node value. Solid lines are positive while negative values are dotted. The sum of these weights times the input values (or hidden values) are then processed through a transfer function, commonly some exponential function. This function can even be a linear. In that case the network becomes a linear regression. So for the above example, there are a total of 19 weights that have to be selected. A never-ending amount of the literature on neural networks describes the mathematical way these weights are selected, the number of network layers, as well as the type of function used for each node. There is a great deal of similarity between training neural networks and optimization problems. After all, the design of the neural network is an optimization problem, searching for the best design to minimize the error between the actual value and the output. The literature contains examples of many different applications in a wide variety of uses. Some of these are electrocardiograms (EKG) noise cancellation, speech recognition, sonar signal processing. There has even been an application of a stock market predictor. In the process industries, one of the frequent applications is soft sensors. The concept is that if many physical measurements about the process are known the value of an unmeasured variable 170

171 can be computed with a neural network. This unmeasured value can be an analytical measurement, such as the chemical analysis of a power plant stack. There are many documented applications of successful soft sensor applications. The analytical instrument is rented, installed on the plant stack. Next a large amount of data is taken over several operational conditions. This data is then used to develop and train a neural network to model the analytical instrument. Back Propagation Network Back propagation is a calculation method made to select the size of the weights in the network. It is just one of several, but the one frequently described in control literature for network training. This network works on the basis of updating the weights between the inputs, PEs and outputs by the error; the difference between the output of the network and the desired output. It assumes that all PEs are responsible for the error. This error is then propagated backward through the network and new weights are calculated. There can be several hidden layers, but in most cases one or two are used. A summary of the calculations is presented here. Detailed discussion is available in several of the sources in the bibliography. The output of an element x in layer s with weight w is given the sum of the input elements: X S = S S 1 f ( ( W * U )) = f ( I ) Where s-1 is the output of the layer before s. I is the input to the PE. The PE processes the input to some function such as a hyperbolic tangent: f ( x) = 1 2 exp(2 * x) + 1 Processing the changes in weights depends on a global error E: E = 0.5* ( d o) 2 Where d is the desired output and o the actual output. The error passed back through the network at a particular element is: d( E) e = d( I ) Where d is the partial derivative. The new weight of each PE is calculated as: 171

172 W [ new] = W[ old] + ( lcoef * e * x) + a * delta( W ) Where lcoef is the learning coefficient for that particular element, delta(w) is the past change in weight, and a is an acceleration term. a and lcoef are values less then one. When designing these networks using back propagation method, the size of the step taken to get to the minimum point is important. If it is too large, the network will not find the lowest error point. It is too small, the search will take a very long time to execute. There are several variations to this network. One is to implement different error function. Another is to use different transfer functions within the PEs. These are hyperbolic tangent; tanh and the sin function. There are several different learning rules that can be selected. The delta rule is based on reducing the error of the net's output based on the desired output by variation of the input weights as just described. Hebbian learning rule works on the basis that the input weight is increased if that input produces the desired output. This is analogous to how the brain learns. While I can find no reference to this in the literature, it appears that the delta rule with acceleration method is similar to the Wegstein method used to solve recycle problems in chemical engineering problems. Other Learning Methods One of the most frequent methods to train, another way to say regress, a neural network, is the Marquardt method. This method makes use of two other methods to optimize data sets, the steepest descent and the Newton method. Both these methods are considered classical mathematical methods for data regression and optimization. The steepest decent method uses the first order derivative of the transfer function to determine the direction to move. The Newton method uses the second derivative function to calculate the change in weights. The Marquardt method takes advantage of both these methods. The farther away the solution is from the solution the steepest decent method will perform fastest. Yet when the weights are closest to the point, the Newton method will approach the solution the fastest. Marquardt s method computes the change in weight values based on a combination of these factors. Using both these methods for neural network training in concert, Marquardt method will compute the network much faster than the back propagation method. Marquardt is mentioned in many texts on design optimization. The author recommends the reader to become familiar with the Marquardt method if they will be involved in any optimization problems. Network Pruning The use of a minimum amount of weights to describe a functional relationship is the same principal that applies to neural networks as it does to linear regression techniques. This concept 172

173 should definitely be considered if the data set is small. If a large network is used to train a small data set, the network just learns the data set and not the underlying mathematical relationship. In neural network lexicon this is called over training. Pruning methods start with a trained network and remove a weight and retrain the remaining network, usually with a second data set that is different than the first set. The pruned and retrained network is then checks the change in error due to removed weight. This sequence is repeated until the error begins to increase, at which time the pruning algorithm stops. I recommend that pruning be done on all data sets taken from experimental data. For networks derived from computational methods, that is where a neural network is used to describe the results form a complex simulation or calculation, pruning may not reduce the size of the network since all input variables are used to define the network. Network Development Just how do you go about developing a network? The first step is to organize the data, usually in an EXCEL spreadsheet. I then visually remove entries that have empty data variables. Next I check the minimum, maximum and mean of each data variable. It is important to train the network with the data set that contains the full range of each variable. The network will not be accurate if the tested variables lay outside the training data envelope. One of the main points of opposition is that they dismiss known first principal methods. This statement is true when considering the network itself, which is a mathematical relationship that would precisely resemble the scientifically derived equations only by accident. However the user should consider known principals when selecting the inputs to the network. Do not use variables that contain redundant information. As an example, assume the user is developing a network to model a drying process of a complex solid. Input variables such as air temperature and humidity should be incorporated, as they are logical variables that are known to affect the drying process. Adding wet bulb temperature as an input would serve no useful purpose since the wet bulb temperature has a known relationship to the air temperature and humidity. Once all the data have been checked and measured separate the data in two or three groups. I use two groups if the data set is small compared to size of the network. Three sets are generally used if you use one of the pruning algorithms. One set, the largest, perhaps two-thirds to three-quarters the size of all the data, is used to train the network. The other two sets are used to test and prune the network. It is very important that the data points in test sets are within the values used to train the network. The training set must contain the minimum and maximum points! Before I begin the training, I check the population of the data variables. This can be accomplished by plotting a histogram for each input variable over the trained set. If too many data points are the 173

174 same, the network will do a great job learning that one point. This is because the least error squared is weighted heavily at the one point, repeated many times. Next each data input and output point is scaled, that is it is normalized and centered on zero with a standard deviation of one. This is done to insure that each data point is compared to the other data points with the same reference. This is true on matter what algorithm is used to train the network. Rule one in applying neural networks is a simple one. Develop a linear regression first. In many applications, the linear relationship will produce a better correlation that a neural network. One can easily test this by using a simple regression equation of the data and examining the correlation coefficient. If the linear relationship does not produce a good fit, then a neural network should be developed. For large data sets with many inputs, I generally use the back propagation algorithm. If the data is taken from a simulation or a small data set, I use the Marquardt algorithm. Another problem that can prevent the network from providing a reasonable relationship is the inclusion of an outlier in the data set. The training including outliers will force the network to a point not properly representing the behavior. One technique I use to remove the outlier is to provide a reality check part way through the training. This should be done about one third into the training iterations. The check is to examine the residuals, or differences in error between the training results and the actual data. Data points are removed from the data set if they are outside some bound, usually three standard deviations. I personally believe this is important for large data sets, several thousand points or more, of experimental data. Manually generated data numbers can frequently be entered wrong. Some data points are abnormal for an infinite number of reasons. Within some uses of statistics, the outliers become a major concern. Drug discovery is very interested in outliers. Outliers are studied more intensively that the normal cases. For industrial applications I do not believe there is a problem with discarding outliers from a training set. Concept can be used for linear regression techniques also. Once the training is done, I check the network with the test data. If the network appears reasonable it should be pruned if there is enough data points to do this if there are an excessive number of weights. The Anatomy of a Neural Network A given laboratory process uses a non-specific analyzer to analyze the concentration of one of the impurities. For high values of the impurity, a simple graph was used to correlate the instrument signal to the concentration. However at lower concentrations, this relationship did not correlate. Because the process is very complex it was postulated that a neural network could be developed to improve the correlation by adding other process input signals, such as temperature, 174

175 pressure, level flow rates etc. together with the analyzer signal to develop the model. This example is an example of a soft sensor application. In this particular case the number of data points was limited. The data was separated into two groups, a training set and a test set. This training data set consists of 137 entries while the test set consisted of only 8 data entries. There were 5 process data points plus a constant to make a total of 6 input points to the network. The output is the impurity concentration in parts per million exiting the process. The test set was not part of the training data set in order to preserve the validity of the test. The data points were recorded when the process reached steady state. This is very important if when the network is used to train a dynamic system, otherwise historical data should also be included, which can result in a large model. The data was regressed to a single hidden layer hyperbolic nodes neural network using the Levenberg-Marquardt method. The data was regressed using an algorithm available over the Internet and written in MATLAB. Figure 2 shows the test result of the first regression and figure 3 shows the result of the training set. The initial training gave poor results because there were two points where the impurity analysis was zero. These points were deleted from the data set. While the results from that set appear to be good, R-squared over 0.9, the network was over trained that explains the poor performance in estimating the high concentration. Figure 4 shows the diagram of the network, consisting of 28 weights. This is far to many weights for such a small data set. An algorithm provided in the neural network package that "prunes" the network was then used on the first network. This method trims the size of the network and tests it against both the training and test set to obtain the best fit. The results of this pruning session are shown in figures 5, 6 and 7. The network did have difficulty determining the exact concentration at very high levels. This is because there are not many points at this level to train. The final algorithm only uses the nonspecific analyzer signal and one other process signal. The other node is a constant. A way to obtain the confidence of the network is to prepare an EXCEL spreadsheet that performs the same calculation as the neural network. This way the user can input several what if scenarios and observe the behavior. In actual practice, once the users began to be aware of the effect of the other signal, they recalibrated the non-specific analyzer. This required the data gathered after the calibration change could not be combined with the old data. When the new data was analyzed, a simple linear regression was used to calculate the impurity concentration. One way the old data may have been used with the new data would be to introduce an input to the network 1 for the old data and +1 for the new data. The network would be able to train with both sets. Automatic Control Method Caution should be exercised if this regression network is used to control the impurity concentration in the process. This is because the other process signal is used as input in the 175

176 concentration equation. Before this signal is introduced to the regression equation, a series of first order lags should be applied to the signal. These lags are equivalent to the residence time of the equipment and the non-specific analyzer signal lag. The neural network impurity concentration output would serve as the input to a controller. That controller's reset setting would be equivalent to the total contributed lag of the process input lags. Shinskey describes this technique for inferential moisture controls where the implied moisture is a calculation based on the inlet temperature, which is manipulated to control the moisture. A diagram showing the control function blocks is shown in figure 8. Figure 2 Test Result of the First Regression 176

177 Figure 3 Training Set Results 177

178 Figure 4 Diagram of the Network 178

179 Figure 5 Test Data Results from Pruned Network 179

180 Figure 6 Pruned Network 180

181 Figure 7 Result of the Training Set with the Pruned Network 181

182 Process Lags Instrument Lag Process Signal f(t) f(t) f(t) non-specific analyzer signal f(x) Neural Network Impurity Setpoint P I PI Controller, I term equal to three input lags Impurity Controller Using Neural Network Manipulated Variable Figure 8 Neural Network Connections to PI Controller References: B. Soucek, Neural and Concurrent Real-Time Systems, The Sixth Generation, New York, New York: John Wiley & Sons, 1989 R. Colin Johnson, Chappel Brown, Cognizers Neural Networks and Machines That Think, New York, New York: John Wiley & Sons, 1988 Steven F. Zornetzer, An Introduction to Neural and Electronic Networks, Academic Press, Inc.,San Diego, CA., 1990 John Hertz, Anders Krogh, Richard G. Palmer, Introduction To The Theory of Neural Computation, Redwood City, CA: Addison-Wesley,1991 Russell Eberhart, Roy W. Dobbins, Neural Network PC Tools; A Practical Guide, San Diego, CA.: Academic Press, Inc.,

183 Neural Computing,Reference Guide, Using NWorks, NeuralWare, Inc. Pittsburgh, PA, 1991 (Technical Manuals With NeuralWare Explorer Program) Eugene L. Zurch, Data Acquisition and Conversion Handbook, Mansfield, MA: Datel Intersil, 1979 Ramchandran, S; Rhinehart, R. R., "Do neural networks offer something for you?" InTech November 1995, p 59. MATLAB Neural Network Toolkit, Technical University of Denmark, Department of Automation, Marquardt, Donald W., "An Algorithm For Least-Squared Estimation of Nonlinear Parameters", J. Soc. Industrial Math. Vol. 11, No. 2, June, Hassibi, B., Stork, D. G., "Second Order Derivatives for Neural Network Pruning: Optimal Brain Surgeon", NIPS 5, Eds. S. J. Hansen et al., San Mateo, Morgan Kaufmann, Shinskey, F. G., Energy Conservation Through Control, Academic Press, New York, Reed, Russell D.; Marks II, Robert J., Neural Smithing, A Bradford Book, MIT Press, Cambridge, Massachusetts,

184 Chapter 21 Notes on Instrument Design Introduction This chapter presents some of the watch outs and problems I have experienced with instrument design. There are many handbooks on instrument design that contain a variety of notes and descriptions of various instrument. The following comments are referenced to the author s experiences. Rule one Make sure you know your process. Communicate this information accurately and effectively to the manufacture or their representative. Remember they want to see you succeed with their instrument just as much as you do. They do not want to sell you an instrument that is not right for the application. They know if it doesn t work you will be dissatisfied and not want to use their instrument again. I have found that when I spend the time and effort to communicate the process conditions to an instrument manufacture, I am rewarded for my efforts. Following the installation instructions will also help with a successful startup. The author has spent many nights in far away places simply following the instructions on startups where they were not done in the first place. Power and Current Sensors Give consideration to the frequency response of current and power sensors. They will not read accurately outside their advertised range. This becomes a problem when measuring the current to adjustable speed drives. These drives vary the frequency to adjust the speed of the motor and can operate outside the envelope of many current and voltage sensors. The typical frequency range of these sensors is 47 to 63 Hz while the range of the adjustable drive may be 10 to 80 Hz. A frequent application of these sensors is on pump motors to detect a no flow condition. For small power motors, current sensors may not be sensitive to detect the no flow point. Electrical power is proportional to the square of the applied voltage and as a result, the no load point can be difficult to repeat. Another reason may be that the pump is too large for the application. In these cases, a power sensor is required. Before installing a three-phase transmitting wattmeter, one should consider the cost of installing two single-phase wattmeters. The circuit measures the current through two legs and measures the voltage relative to a common phase, C phase as shown below. This design may be cheaper to install. 184

185 A phase B phase CT1 CT2 V1 M V2 C phase Two Single Phase Watt Meters Measurement of Three Phase Circuit The two-watt meters measure power of phase A and B relative to phase C. Adjustable Speed Drives There is a misconception with adjustable frequency drives that they provide better resolution than control valves. This is not always the case. The digital to analog converter in the drive electronics has a quantiziation error, which is proportional to the number of bits in the converter. An actual application of this is shown below. The histogram shows effect of quanitization error. This plot has two nodes because of the resolution on the circuitry. The positive displacement pump curve has a slope of 0.1 gal/rpm flow. The motor synchronous speed is 1800 rpm. The adjustable frequency AC drive specification has 514 frequency divisions for the published resolution. The following MATLAB calculation shows this effect. resolution=514; f=60; Hz poles=2; speed_reducer=7.65; density=9.25; lb./gal The two nodes have peaks at: delta_mass= ; delta_mass delta_mass = delta_flow=delta_mass/density delta_flow = delta_speed_pump=delta_flow/0.1 delta_speed_pump = rpm delta_speed_motor=delta_speed_pump*speed_reducer delta_speed_motor = rpm Assume drive is calibrated for 0 to 60 Hz. Speed resolution is: sync_speed=f*60/poles; 185

186 sync_speed/resolution ans = rpm Which agrees with data histogram plot. Much better resolution could be accomplished with a control valve with positioner and a centrifugal pump. Histogram Of Flow Controlled by a Variable Speed Controller Filled System Pressure Transmitters Filled system diaphragm transmitters are used for corrosive and slurry applications. These diaphragms are connected to the transmitter by capillary tubing. The whole volume is filled with a liquid fill, usually a silicone or fluorinated chemical. This chemical must be compatible with the process fluid. For oxygen or chlorine service, the fill must not contain any oil or oil based chemicals. Consideration should be made to the internal displaced volume of the transmitter as well as the diaphragm. Every pressure transmitter has some volume displacement, however small. The diaphragm must be capable of flexing this volume. If the transmitter company fabricates the filled system, they have most likely seen the problem. Teflon diaphragms flex more and should be considered if the volume displacement is high, common on older transmitters. Newly designed transmitters use silicon piezoelectric technology which require approx in3 displacement, rather than bourbon tube and bellows force balance methods which have volume displacements, around 0.5 in3. An alternate is to fabricate a short length of pipe between the instrument and the process filled with the chemical fill material, which would be inert to the 186

187 process material. Many years ago this is how standard brass tube instruments were used for chemical service. Temperature differences between the high and low side capillary tube can cause the instrument to read incorrectly. Purge Pipe Level Transmitters Perhaps the most common level transmitter is a purge pipe. This instrument makes use of a differential pressure transmitter measuring the difference between the back pressure created through a gas bubbling out of a pipe inserted in the tank and the tank s head space. Most of the problems with these instruments are as a result of improper installation. Many newer types of level instruments, such as radar and ultrasonic, are used where purge instruments fail to perform. Many of these installations are not necessary. Proper installation requires that: The pipe, typically 1-inch schedule 40, must have a slot, or preferably several slots, at the end of the pipe. The idea is to sparge or create small bubbles of gas at the end of the pipe. If a large bubble occurs, the pipe will tend to plug because when the bubble collapses, the liquid enters the inside of the pipe and solids build up there. An older instrument publication detailed a short length of a larger diameter pipe at the end of the purge pipe with several ¼-inch slots. The gas flow should be flow controlled to the pipe. This should be done with a constant flow controller or regulator rather than a needle valve. Without a flow controller, the needle valve will act as the only restriction and as the level increases, the flow will be reduced. Make sure the flow regulator can compensate for variable downstream pressure variations. This is what will be measured. For aqueous slurry applications, a dry purge gas will cause caking across the end of the purge pipe. This is because the gas will dry out the slurry at that point. One way to prevent this is to purge a small quantity of water and mix it in with the purge gas. The moist gas will prevent the caking. Placement of the low-pressure port is important too. It must measure the head space and not the outlet pressure piping. Frequently the off gas line pressure is made because no nozzles are available on the tank. This example shows the problem with this method. Assume a 6-inch schedule 10 pipe with a vapor flowing at 100 feet per second outlet velocity. A sudden contraction is assumed to be the only restriction. From the CRANE manual: Y=1; d=6.357; K=0.78; V=5; vel=100; A=0.2204; w=vel*a/v w = dp=27.67*k*v*(w/(0.525*y*(d^2)))^2 dp = inches of water This difference is enough to cause false readings, premature alarms and interlock trips. 187

188 Temperature Measurement Elements: For most process measurements, RTD (Resistance Temperature Detector) or TC (Thermocouples) elements are used. These are installed with thermowells and mounted on process vessels or piping. In general, thermocouples are more rugged and less accurate than RTD elements. An ANSI standard details thermocouples and their errors. Thermowells: Thermal elements of both types use thermowells to protect the element from the process stream. Thermowells contribute the major time lag in the temperature control system, on the order of minutes in some cases. To improve the heat transfer, the recommended bore of the element is inches for RTDs and inches for thermocouples. Thermocouples are tip sensitive, therefore important that the element be in contact with the bottom of the well, usually spring loaded. RTD elements are stem sensitive and therefore they should be as close as possible to the side of the well. Tapered or step down type thermowells improve response time. It is generally practiced that the element and the well be purchased as a prefabricated assembly. Thermocouples generally have a faster time constant than RTD elements, however newer designed thin film RTDs have improved the response time. Metal sheathed elements are a design of thermoelements that incorporate a thin walled metal tube, less than ½-inch diameter, around the RTD or TC. These elements screw directly into a pipefitting. These elements have rapid thermal response and little heat conduction error. Errors: The errors resulting from installation effects accumulate in a square root of the sum of squares of each error can reach five times the error of the element itself. A summary of these errors is as follows: Heat Conduction: Heat conduction is the error due to the temperature at the tip of the well being different than the mounting surface, usually the ambient. Heat then travels through the well to the ambient. This error is a function of the thermodynamic properties of the material measured as well as the well construction. In general, the thinner the element, the more accurate the measurement. An Excel spread sheet is included to show the conductive error with the dryer elements in question. This spreadsheet also calculates the time constant. The well should be in a free flowing stream and not coated with material. Heat Radiation: In combustion heat sources, radiation error can contribute several degrees. For combustion heat sources, it is best not to allow the element to be within direct sight of the flame. Velocity Error: If the velocity becomes very high, approaching Mach one, the velocity causes an increase in temperature due to compression heating. Recommendations: A thermocouple transmitter acts as an electrical isolator as well as linearizes the thermocouple signals and generates a control signal, 4 to 20 MA, to A/D (analog to digital) converter. A transmitter should be used if the input accuracy of the thermocouple input is as poor as specified in the control system s documentation. Single Point Ultrasonic Level Instruments 188

189 Be sure to pay attention to the temperature when specifying these types of instruments. Many of these use sensitive crystals to generate and detect the ultrasonic signal. It has been my experience that sometimes the upper temperature limit may be lower than the normal process operating temperature. I was once asked to investigate why one of these instruments failed. After interviewing the operators I learned that it failed after the first time the probe sensed the level. After consulting the instrument data sheet I also learned that the temperature was well above the maximum specified temperature. The diaphragms are usually thin, so material of construction sould be given extra consideration. Pressure Transmitters There are some notable application problems I have frequently observed with these instruments. The first is over pressure due to transient pressure surges. Differential pressure transmitters specify a static over pressure value which may be exceeded if the instrument is not piped properly. The second is the material of construction of the oil fill. If the instrument is used in an oxidizing environment the liquid fill must not react with the process material. This reaction can cause an internal process fire. Other problems with differential pressure transmitters have been: With filled systems the static pressure difference must take into account the density of the fill. Make sure the oil fill will operate properly over the temperature range. When measuring a vapor or gaseous and vapor mixture stream, mount the pressure transmitter above the process connection. If the transmitter is mounted below the take off point the vapor may condense in the sensing line. In many cases this additional head of condensed liquid is greater than the maximum calibrated span of the instrument. In many cases it may requiring mounting the transmitter on the next floor level. I have personally observed this problem in many plants. 189

190 Pressure Transmitter Mount above the process connection An alternate way to avoid the problem is to purge the sensing line. Purge gasses are not well accepted by environmentally conscious chemical engineers. Purge gasses are very often a source of vapor losses and must be reported to the EPA as part of the permitting process. Some companies prohibit the use of purge gasses and invent very cleaver ways to keep the level of inerts low exiting the process. Vacuum Applications Instruments installed in vacuum applications should by piped with piping systems designed for vacuum service. Certain types of compression tubing fittings only work under pressure and not vacuum. Electrical Noise Instrument engineers frequently come across the problem of electrical noise in the instrument control system. The following example is typical of the problem. The problem occurred when attempting to start up a small humidity controlled dryer. Water was pumped to a spray nozzle, the speed of the pump controlled the amount of water added. The humidity probe had a dual sensor, temperature and humidity elements in one device. The sensor used one of the newer capacitive polymer elements. A frequent problem with these elements is should the element become saturated with water, the signal will hold its value for some time. In several cases, the probe never dried out and was discarded. The problem became evident when the motor speed increased; the humidity increased and finally held at a steady value even though it was obvious that much more moisture had been added to the air. A quick call the manufacture s hot line advised me to move the sensor downstream and avoid a sample directly in the spray path. This advice was tried and the sensor increased slowly and then held value at some point after startup. Is there any other way this could happen? Yes, there is. Electrical noise could cause the instrument to read in error, or in severe cases, cause the signal to drive full scale in either direction. I started up the system again and this time when the probe froze, I removed it from the sample line and waved it in the air. The probe did not respond to ambient conditions. Then I shut 190

191 the pump off and it responded correctly. The culprit was electrical noise from a very small adjustable speed drive. Electrical noise from adjustable speed drives is very common in industrial plants. Many manufactures recommend that transformers be installed. The following instruction is taken from a Rockwell Automation manual for a ¼ to 2 HP 115/230 VAC DC3E adjustable speed drive: A good reference on proper wiring and shielding techniques appeared in the IEEE transactions several years ago. I highly recommend it for your reference. Klipec, Bruce E., Reducing Electrical Noise in Instrument Circuits, IEEE Transactions on Industry and General Applications Vol. IGA-3, No. 2, March/April Klipec s recommendation is to use twisted shielded cable, use aluminum Mylar shields, run instrument and power cables at right angles. Even in these times when good design practices are taken by instrument and control manufactures, it still takes a vigilant effort on the part of a control engineer it insure proper wiring techniques. Sensor Placement Where should I place process sensors? Where sensors are placed relative to the process is very critical because it can effect the dynamics. There are two dynamic effects, process dead time and process time constant. Sensors should be placed so as to minimize these two effects. Dead time is generally referenced to transportation time. There is dead time if the sensor is located downstream of the process, which is transportation dead time. This could be as simple as the time it takes for the process to flow to the sensor, or it could be a rather complex dead time as is present in a stirred tank reactor. The sensor should be placed as close to the process as possible. This is not a hard fast rule; there are times that this may be a poor location if the sensor would not represent the true reading because of interference. In a large tank, the sensor should be located close to the heating element. This is to minimize overshoot due to the long time constant. Time constant is the first order effect, as an example volume divided by flow. This is also called lag. There is some misunderstanding within the process community about these terms. In general, lag can be controlled easier than dead time; it is best to minimize process lag so that the dynamics will be faster. However, if the process has a lot of dead time, introduction of process lag will actually help the process. An example of this is ph control. There the ratio of dead time to 191