Level Process Control. Penn State Chemical Engineering

Transcription

1 Level Process Control Penn State Chemical Engineering Revised Spring

2 Table of Contents LEARNING OBJECTIVES... 3 EXPERIMENTAL OBJECTIVES AND OVERVIEW... 3 Pre-lab study... 3 Experiments in the lab... 4 Calculations in the lab... 4 THEORY... 5 Background... 5 PID Controller... 7 Ziegler-Nichols Tuning... 9 Additional Theory Topics: (These are important learning points for prelab, prelab quiz, conducting the experiment and for writing the report. Also make sure to watch the video.) PRE-LAB QUESTIONS (to be completed before coming to lab) EXCEL PREPARATION (Excel spreadsheet to be used for data processing in the lab must be prepared before coming to the lab for the experiment) DATA PROCESSING KEY POINTS FOR REPORT REFERENCES APPENDIX A: Process Control Characteristics APPENDIX B: Wiring and Connections Check APPENDIX C: Familiarization with Operation APPENDIX D: Level Calibration Procedure APPENDIX E: Experimental Procedure APPENDIX F: Opening Data in Excel

3 LEARNING OBJECTIVES 1. Conceptually understand the process control principles using proportional only (P) and proportional-integral (PI) algorithm. 2. Understand the difference between positive and negative feedback control and determine which control mode you need to use to keep the tank level constant. 3. Tune a P and PI controller to keep a fluid level constant in a continuously draining tank with inlet flow rate control using the empirical Ziegler-Nichols tuning method for a simple first order system. 4. Study the effect of proportional band and integral time on controller response in a first order system (level control). 5. Use the observations made from the P and PI control operation to design an effective process control algorithm to reach the set point without overshoot or offset. EXPERIMENTAL OBJECTIVES AND OVERVIEW In this experiment, a proportional-integral (PI) controller will be used to control the water level in a continuously draining tank by adjusting the inlet flow water valve. The Ziegler-Nichols method of tuning the controller will be used to tune a proportional and proportion-integral controller for the process and an algorithm will be designed to reach the setpoint without significant overshoot or offset. The level control of a continuously draining tank is a simple first order system. Pre-lab study: 1) Study the PID control principle and the Ziegler-Nichols closed-loop tuning method 2) Run a Mathematica simulation program (on Angel) to understand the effect of proportional gain (K c ) in P-control and the integral time ( I ) in PI-control of a simple first order system (level control). 3

4 Experiments in the lab: 3) Configure the process control unit (wire connections and water level calibration) 4) Run the unit in positive and negative control modes the controller is set to direct action to observe what will happen under positive control. Determine which control mode should be used to keep the fluid level in the tank constant at the set (desired) level. 5) Determine the Ziegler-Nichols tuning parameters. In this part, the behavior of the system will be observed as the proportional band (PB = 100% / K c ) is changed between 5% and 0.05%. The results are then used to determine the ultimate proportional band (PB u ), the PB at which the water level oscillations around the set point are constant. The PB u data will be used to determine the ultimate time period (t u ). Then, PB and I for P- and PI-control can be determined from the empirical Ziegler-Nichols correlations based on the PB u and t u values determined for this system. 6) P-control observe the effect of PB on the controller response of this first order system. Three PB values will be tested: PB determined by Ziegler-Nichols tuning (PB ZN ), that PB multiplied by 4 (larger than PB ZN ) and the same PB divided by 8 (smaller than PB ZN ). 7) PI-control observe the effect of I on the controller response. Three integral times will be tested: t izn determined by ZN, 4 t izn (larger than t izn ) and t izn 2 (smaller than t izn). 8) Based on what you learn from the P-only and PI-control experiments, determine the best control process (either one of them, or combination of them) to reach the set point without overshoot and offset as quickly as possible. Run the system with your method to confirm the performance of your designed control method. Calculations in the lab: 9) Plot the experimental data in a format that compares the data and reveal the trends clearly. 4

5 THEORY Background Process control involves the regulation of processes with the goal of holding process variables constant over time in order to maintain safe, steady-state, and reliable plant operation. In this particular experiment, a level controller is utilized to control the liquid level in a tank. The flow system is shown in Figure 1. Do not copy LC Process Tank Control Valve Pump Reserve Tank Figure 1: Flow system PFD of liquid level control in a tank Water is pumped from the lower reserve tank to the process tank at the top of the unit. The inlet flow rate to the process tank is regulated by a control valve as to maintain the required water level in the process tank. The process tank water level is measured by means of a float sensor. Water is drained by gravity flow through a pipe at the bottom of the process tank. The opening of the drain pipe valve is Ao. The inlet flow rate varies by means of the controller and is a function of the opening. The outlet flow rate (Fout) is dependent on the drain opening size (Ao) and the water level in the tank (h) by the Torrichelli s law Fout Ao 2gh (1) where g is the acceleration due to gravity. 5

6 The control algorithm can be represented in Figure 2. h sp Set Point Comparator Load V o _ + _ Controller Valve + Process e(t) h m Measured Variable Measuring Element Figure 2: Block diagram of the control algorithm h Controlled Variable Do not copy The set point, h sp, is the desired value of the controlled variable, h, which is the fluid level in the tank. The load (or disturbance) refers to a change in any variable that may cause the controlled variable of the process to change. In our experiment, the difference between the inlet and outlet flows of the process tank is a load variable, V o. For the present experiment, the measuring element that returns the measured value of the controlled variable, h m, is simply the float sensor mounted on the side of the process tank. A controlled change in the set-point, moving the set-point from the current value to a new value, is referred to as a step-change. The control system depicted in Figure 2 is referred to as a closed-loop system or a feedback system since the measured value of the controlled variable, h m, is fed back to a device known as a comparator. In the comparator, the measured value of the controlled variable is compared with the set point value. If there is any deviation between the measured variable and the set point, an error, e(t) = h sp h m, is generated. This error enters a controller, which in turn adjusts the valve on the control element (inlet flow valve in this experiment) in order to return the controlled variable to the set point. The arrangement of the control system in Figure 2 is often described as negative feedback. Negative feedback ensures that the error, e(t), is used to adjust the valve so that the tendency is to reduce the error. For example, assume that the system is at steady state and that h = h m = h sp. If the out flow is suddenly changed, then h and h m would start to deviate from h sp, which in turn would cause the magnitude of error to become larger. Then the controller adjusts the valve and thus input flow to the 6

7 tank so that h approaches h sp, in other words, e(t) becomes zero. In actuality, all of the components operate simultaneously comprising a complex series of events 4. (pp 53-58) Positive feedback also exists, which is inherently unstable. In this case, the error is maximized rather than reduced. Positive feedback systems are almost never utilized in control systems; however, they may arise naturally in more complex systems. PID Controller A PID controller is a device that employs each of the three basic feedback control modes: proportional (P), integral (I), and derivative (D). The control element (control valve in this system) response for the process may be directly proportional to the error itself (P), proportional to the cumulative (integral) error (I), proportional to the instantaneous change (derivative) of the controlled variable (D), or a combination of the above (PI, PD, PID). The selection of a controller type (P, PI, PD, PID) is intimately related to the model of the process to be controlled. A non-zero value of the error, e(t) = h sp h m, initiates the controller action (regulation of the valve position, in our case). The controller output signal, C(t), depends on the deviation or error variable, e(t), and the PID control algorithm is given by equation 2. 1 t 1 C( t) Co Kc e( t) e( ) d D I 0 de( t) dt (2) where C o is the controller offset (value of the output signal when e(t) = 0), K c is the proportionality constant (or gain), τ I is the integral time, and τ D is the derivative time. By selecting these parameters properly, the controller may be tuned to a pure P, I, or D controller or a combination of these. The two most commonly encountered controllers that will be analyzed in this experiment are the P and PI controllers. 7

8 The proportional gain, K c, is simply defined as the ratio of the change in output to the change in input. If K c is large, then the controller response upon a small error is large. As K c is lowered, the controller response to a given error becomes smaller. In some controllers, such as the one used in this experiment, the gain is expressed in terms of the proportional band: PB(%) (3) K c The proportional band (PB), integral time (τ I ), and derivative time (τ D ) are the three tuning parameters of the PID controller used in our experiment. The proportional-only (P) controller produces an output signal that is proportional to the error. The basic expression for P-only control is as follows: 1 C( t) K e( t) (4) c C o With proportional-only control, the controller will not bring the process tank level to set point without a manual adjustment to the controller offset; therefore, the tank level will be offset from set point (you will see this in the lab experiment). If offsets can be tolerated, the use of a proportional controller may be sufficient; however, it will not eliminate the steady state errors that occur after a set point change or load disturbance. The addition of integral control to a P-only control eliminates the offset and the controlled variable returns to the set point. The expression for a PI controller is as follows 1 : 1 C( t) K c e( t) t I 0 e( t) dt C o (5) Integral control depends on the integral of the error signal over time. Since the control response is not instantaneous (requires integrating the error signal over a certain period), the PI control initially overshoots the set point and oscillates around it (with progressively less overshoots) until finally settling at the set point (you will observe how this behavior depends on the I setting). As a general rule of 8

9 thumb, a PI controller with a decay ratio (the ratio of the second overshoot to the first overshoot) of ¼ or less is often considered good control. The Mathematica program demo PID Control mvh of A Tank Level (source) shows how a system similar to our system might behave under P, PI, and PID control. Ziegler-Nichols Closed-Loop Tuning Ziegler and Nichols developed an empirical method for tuning P, PI, and PID controllers back in the 1940 s. This tuning method uses the rule of thumb that a PI controller with a decay ratio of ¼ is considered good control. The Ziegler-Nichols (ZN) tuning method helps determining the process parameters. In the closed-loop ZN method, the P only control is repeated with increasing controller gains (decreasing PB) until a stable oscillation is achieved. This is known as the ultimate proportional band (PB u ). The oscillation period at this specific controller PB is called the ultimate time period (t u ). Decreasing the PB beyond the PB u would result in a loss of control of the system. Thus, the PB u indicates the lowest PB at which there is some control of the system remaining. Using the measured PB u and t u for a system, the ZN tuning method uses an empirical formula to provide reasonably good tuning for the controller. Table 1 details the tuning parameters of the closed-loop Ziegler-Nichols method. Table 1: Ziegler-Nichols tuning parameters Controller PB τ I τ D P 2PB u Do not copy PI 2.2PB u t u / PID 1.7PB u t u / 2 t u / 8 Using the ZN parameters will usually give pretty good control to the system. The limitation of using ZN is that the ultimate PB must be determined first, which is not always feasible. 9

10 Additional Theory Topics: (These are important learning points for prelab, prelab quiz, conducting the experiment and for writing the report. Also make sure to watch the video.) Basic elements of a feedback controller Positive and negative feedback Direct action and reverse action Capacitance and dead time Controller response terms: overdamped, critically damped, and underdamped Overshoot Decay ratio Ziegler-Nichols closed-loop tuning method Set-point change Load disturbance They can be found in: Svrcek, Mahoney, Young. A Real-Time Approach to Process Control. 2 nd ed. Wiley, West Sussex, England, [TS156.8.S ] Chapters 3, 4, and 5. pp ,

11 PRE-LAB QUESTIONS (to be completed before coming to lab) 1. Do literature search on the closed-loop Ziegler-Nichols tuning method. Understand the ultimate proportional band (PB u ) and ultimate time period (t u ). Describe how these parameters will be determined in the experiment. 2. Explain dead time and capacitance as they relate to control. Which one should be minimized as much as possible? (The book by Svrcek 4 has a nice explanation). 3. Use the Mathematica dynamics program found on ANGEL, PID control of tank level demo (mathematica), to see the level output for a set point change in level for P control and for PI control. A description of what you are seeing is included under the demo, within the file. a) What happens as you increase K c for a P controller? (Note: to operate only the P portion of the controller, you must turn off the Integral and Derivative portions. Do this by setting the integral time constant as large as possible (should be at 10 when first start program) and the derivative time constant to zero.) Kc Tank level at t=20 sec Offsett (difference between set point and actual level) Approximate time for curve to start to flatten out b) Sketch the liquid level in a tank experiencing setpoint change with P control with low Kc and again with high Kc. Make sure to indicate the setpoint and clearly indicate the differences in response. 11

12 c) What happens as you change τ I for a PI controller? (Note: set proportional gain to 1.0 and then vary the integral time constant.) τ I (sec) 1 st overshoot max peak height Period of oscillation and number of oscillations Time to steady state (sec) , d) Sketch the liquid level in a tank experiencing a set point change with PI control with low τ I and again with high τ I. Make sure to indicate the setpoint and clearly indicate the differences in response. 4. What are the objectives for this experiment? 5. Explain what data you will collect, how you will collect it, and what you will use it for. EXCEL PREPARATION (Excel spreadsheet to be used for data processing in the lab must be prepared before coming to the lab for the experiment) 1. Prepare a data processing excel spreadsheet to be used for the data processing in the lab. All calculations will be done in excel. a. Prepare a header section with your names and group ID. b. Prepare a units section where you show unit conversions. Make it so that you can reference the appropriate cell when a certain conversion is needed in later calculations. c. Show all needed formulas from the pre-lab calculations clearly explained in text boxes. d. When using your spreadsheet in the lab, make sure that you use cell references when using previously calculated values or constants (instead of copying them); this will 12

13 update the entire spreadsheet if/when a mistake is found early in the spreadsheet. (no work required for 1.e) 2. Make a graph showing a set-point of 40 mm over 300 sec. 3. Make a graph showing a set-point change from 40 mm to 60 mm at 20 seconds into the 300 sec run. DATA PROCESSING 1. Plot your data from the negative vs. positive control experiments. Show the set-point as well as the negative and positive control regimes. 2. Plot the tank level and valve opening versus time for all PB s of the P-only control tests used to determine PB u. 3. Determine PB u and t u from the appropriate plots in #1. Calculate the Ziegler-Nichols tuning parameters for P-only and PI controls. 4. Plot the tank level versus time for the Ziegler-Nichols PB for P-only control (PB ZN ), 4PB ZN, and PB ZN /8. What are the offsets at these PB settings? Make sure to clearly indicate the set point in these plots. If possible, put all 3 plots on a single graph. 5. Plot the PI control data for the τ IZN value suggested by the Ziegler-Nichols method, 2τ IZN, and τ IZN /2 while holding PB at the value suggested by the PI ZN method. Calculate the decay ratio for each integral time setting (ratio of (second peak height minus set point) to (first peak height minus set point)). Make sure to clearly indicate the set point in your plots. Plot your graph(s) so that they are easy to compare to each other. 6. Demonstrate the performance of your optimum control to reach the set point without overshoot and without offset by plotting the data as a function of time. KEY POINTS FOR REPORT See the separate file on ANGEL for the key report questions for level and temperature control. 13

14 REFERENCES 1. Coughanowr. Process Systems Analysis and Control. 2 nd ed. McGraw-Hill, New York, Perry. Perry s Chemical Engineering Handbook. 7 th ed. McGraw-Hill, New York, Ziegler-Nichols PID Tuning, available via: 4. Svrcek, Mahoney, Young. A Real-Time Approach to Process Control. 2 nd ed. Wiley, West Sussex, England, APPENDIX A: Process Control Characteristics PID 1 Screen Control Mode Auto/Manual Represents two different types of control. Automatic Control Changes the valve position based on PID parameters. Manual Control Allows the operator to control the valve manually. Bumpless Transfer A start-up procedure used to gradually bring a control loop into service. Since this process has such a quick response time, the effects of bumpless transfer seem minimal. On smooth initial transition. Off unstable behavior is sometimes observed. Direction Dictates whether the output from the controller decreases or increases with increasing process variable. Depending on which you pick, along with the type of control element you have (direct or reverse acting), the control will become either negative or positive feedback. For this process, reverse acting works best and results in negative feedback. (pp in Svrcek et al.) Set Point Reverse As the level increases % open decreases. Direct As level increases % open increases. Allows one to adjust the set point (level in the tank). For purposes of this experiment, a local set point can be used. The set point has a range of 0-100mm. Local Control from a local location. Remote Control from a remote location (set point calculated by another controller) commonly used in cascade control. PID Controller 1 Parameters Allows one to adjust the parameters in the control algorithm. Proportional Band : range % Integral Time : range seconds Derivative Time : range 0-10 seconds Automatic Control Output Displays how the new value of valve % open is calculated. Controller Offset A bogus value calculated by the computer. Set this value to zero. 14

15 PID Output The output as calculated by the controller based on the control algorithm parameters. Manual Control Indicates the manual valve setting. Controller Output Displays the position of the motorized valve. Process Variable Level of liquid in the tank relative to the calibration 15

16 APPENDIX B: Wiring and Connections Check 1. Ensure that the coiled, black wire leading from the pump is connected to the 240V ~ output on the side of the PCT Ensure that the level conditioning module is inserted into signal conditioning channel 2. (Picture not shown) 3. Ensure that the brown, green, and white cords from the process tank level sensor are inserted into channel 2, inputs Ensure that the IFD3 Interface Console switches are in the normal mode and I/O port positions. 16

17 5. Ensure that the black cord of the PCT12 Mk2 is connected to the other 240V ~ output on the side of the PCT Ensure that the gray cord is connected to the 24V ~ on the side of the PCT10 to the 24V ~ IN connection of the PCT12 Mk2. 7. Ensure that the other gray cord is connected to the other 24V ~ on the side of the PCT10. Do not connect the other end to anything at this point. This is the cord that is used to control the solenoid valves. 8. Ensure that the red wire is connected from signal conditioning channel 2, 4-20mA to PCT12 Mk2 input Ensure that the black wire is connected from signal conditioning channel 2 right side output to PCT12 Mk2 input 1. 17

18 10. Ensure that the motor positioner wire is connected from the motor positioner output on the PCT10 to the face of the PCT9 valve motor input. 11. Ensure that the red wire is connected from the PCT12 Mk2 output 1 to the motor positioner 4-20mA connection. 12. Ensure that the black wire is connected from the PCT12 Mk2 output 1 to the motor positioner input. 13. Ensure that the red and black wires are connected from the Voltmeter (V) to the signal conditioning channel 2 red 0-1V and black output. 18

19 APPENDIX C: Familiarization with Operation 1. Look at the diagram on the front panel of the PCT-9 module. 2. Ensure that nothing is connected to the sol1, sol2, and sol3 inputs on the PCT9 front panel. 3. The valve motor on the front panel should have a connection. This wire carries the instructions from the computer controller to the motor control valve. This valve controls the inlet flowrate into the process tank while the system is under computer control. 4. Ensure that valves V3 and V4 are closed, and that the rubber stopper is secured in the hole connecting the tanks. Refer to the diagram on the PCT9 front panel. 5. Ensure that the reserve tank drain valve V5 is closed. This is the large orange valve behind the unit. Twist the orange knob GENTLY to the right to check. Fill the steel reserve tank in the bottom of the PCT9 module with water until the level is about half way from the top if it is not already full. 6. Double click on the PCT-Win icon. Click OK. Select Exercise G - PID control of level using motor valve. Click OK. 7. Cycle power to the PCT10 module by switching the main supply switch on the upper right side of the face of the unit. You will hear the pump start. Allow the pump to warm up for about 5 min. 8. Select the PID 1 tab from the top menu. Set the motor valve to 100% open by double clicking the area, changing the value, and pressing enter. 9. Open the flow meter valve so the water flow rate is 3000 cc/min. The process tank will fill up and eventually overflow through the overflow tube. 10. Open V4 to manually drain the tank down to about 40 mm absolute height. 11. Note that the tank fills as soon as V4 is closed again. We can stop the flow in two ways. a. Manually: by setting the motor flow rate to 0% (or some other small value). Try this now and then drain the tank back to 40 mm. Note: 0% closes the valve almost the 19

20 entire way, but not completely. You may see a small increase in level with V4 closed and flow rate set to 0%. b. Using solenoid 1: solenoid one is either open or closed. When nothing is connected to solenoid 1, it is open. When the gray plug is inserted, the signal send through it closes the solenoid and thus prevents flow into the tank. Try this now by following the procedure below. i. Set the motor valve back to 100%. ii. Plug the connector (gray) into sol 1. Notice that flow into the tank stops. iii. Drain the tank down to 40 mm level by opening and closing V4. iv. Play with the tank height using sol 1 until you are comfortable with it. 12. We will also be using Solenoid 3 in this experiment. This valve is wired oppositely from sol 1. When nothing is attached solenoid 3 is closed. When the gray connector is plugged in, the solenoid is open and will drain the tank. Explore this now by moving the connector from sol 1 to sol 3. You can also change the motor valve % opening and use V4 to drain the tank. Play around with the connections until you are comfortable with the operation. Fill and drain the tank several times using the different options available. 13. Unplug the gray connector and return the motor valve to 0%. 20

21 APPENDIX D: Level Calibration Procedure 1. Ensure that nothing is connected to the sol1, sol2, and sol3 inputs on the PCT9 front panel. 2. Set the motor valve to 100% open by double clicking the area, changing the value, and pressing enter. 3. Verify that the flow rate is 3000 cc/min. If not, adjust so it is. Checking the Zero 4. When the level in the tank reaches 45mm, close the motor valve by plugging the gray cord into sol1. Reduce the level to 40mm by draining some of the water with valve V4. This level will become the zero point for our level control. 5. Look at the level gauge on the monitor and verify that the level value fluctuates between -1 to + 2 on the indicator. If fluctuations are outside this range, call a TA over to help calibrate the unit. Calibration is done on the Level Conditioning Module, shown below, using the zero calibration point. Note, the level conditioning module is fragile and only the instructor or TA should do any needed calibration. (Level Conditioning Module) Checking the Span 6. Remove the gray cord from sol1 and allow the tank to fill to 145mm then re-insert the cord to stop the flow. Reduce the level to 140mm by draining some of the water with valve V4. 7. Check the value on the level gauge indicator. The value should fluctuate between 98 and 100 mm on the indicator. Note: If the value reads 100 mm, the level indicator is out of range. If this is the case, take a look at the voltmeter on the PCT10 panel. If it reads between and V, the span is fine. If the span is out of range, call the instructor or TA over to calibrate the system. 8. Drain and refill the tank as necessary to ensure the level indicator is accurate. 9. Set the motor valve on the computer to 0%,drain the tank, and connect the gray cord to the sol 1 input on the PCT9 front panel. 21

22 APPENDIX E: Experimental Procedure Note: When changing a blue highlighted parameter, double click in the area, change the parameter, then press enter. The parameter will not be changed unless you press enter. 1. Ensure that the gray connector is connected to sol 1 input on the PCT9 front panel. (Leave the valve motor connection connected.) 2. Ensure that valves V3 and V4 are closed, and that the rubber stopper is secured in the hole connecting the tanks. Refer to the diagram on the PCT9 front panel. 3. Go to the Option menu. Select Exercise G, PID control of the level using the motor valve. Click OK. 4. Go to the PID 1 screen by clicking the button at the top of the screen. Ensure that the parameters in the Control Mode are in the following settings. Manual Control, Bumpless Transfer On, Direction Reverse. Ensure the parameters in Set Point are in the following settings. Source Local. 5. Plug the gray cord into sol3. This will open the process tank outlet drain valve. 6. On the PID 1 screen, set the Manual Control Setting to 100% open and ensure that the flow rate still reads 3000 cc/min on the flow meter. If not, adjust the flow rate so that 3000 cc/min are delivered at 100% valve open. 7. Go to the Timer screen and set the sample time for 300 seconds (the sampling interval should remain at 1 second). 8. First, we will observe the system response for negative vs positive feedback control. Go to the PID 1 screen. Set the Proportional Band to 5% and the Set Point to 50 mm. Ensure that the water level is between the zero and 100 mm full level (tape indicators). * Note: this 50 mm refers to the 50 mm in reference to the set zero (tape label on the tank). 50 mm tank level is equal to 90 mm from the bottom of the tank (ruler). 40 mm from bottom of tank is set as the zero level of the tank. All level measurements during the remainder of the experiment refer to the measurements on the tape on the tank. If this is confusing, please ask the TA to clarify. 9. Switch to Automatic Control in the Control Mode and immediately set the Controller Offset to 0. Click Start Sampling. 10. Collect the data for about 100 sec in the Reverse Direction in Control Mode (which is the negative feedback control); then switch to Direct Direction (which will result in the positive feedback ). 11. Watch how the tank level changes during the negative and positive feedback control. Notice that the PI output continues to change to maximize the error during the positive feedback. 22

23 12. Save your data. Go to File>>Save. Select the D drive and save the file as xxx.dat. (xxx refers to your filename and can be no more than 8 characters long) This will network your file so that you can pick it up in the 480labfiles folder on the black computer. Refer to Appendix F for directions on how to open your files in Excel. Plot time on the x axis and mm on the y axis. 13. Determine which feedback mode must be used to reach and keep the tank level at the value negative control or positive control. 14. Return to the PID 1 screen. You will now proceed to determine the Ultimate Proportional Band (PB u ), the point at which the system reaches sustained oscillations of the valve and thereby water level in the tank. Choose the Direction in the Control Mode (reverse or direct depending on your decision in step 12). Read through the procedure steps before starting. 15. Set the Proportional Band to 5% and the Set Point to 40 mm. Ensure that the water level is approximately 40 mm (tape indicators). 16. Switch to Automatic Control in the Control Mode and immediately set the Controller Offset to 0. The level should settle at about 36 mm on the screen for the Process Variable Water Level. Click Start Sampling. You can watch the oscillations on the output bars and you should watch the water level and valve % open on the Graph screen. 17. Every 100 seconds decrease the PB. You can fit three PBs into each data file. You can watch the timer of the run at the bottom of the PID screen. The change will go into effect when you hit enter. Keep track in your notebook of when changes are made. Run at the following PB: 5%, 2 %, 1%. After 1%, decrease in 0.1% increments down to 0.4%. You are looking for the point where the system reaches a sustained oscillation. This should occur at a PB of about %. You will notice the valve will open and close repeatedly. Watch as the flow on the flow meter repeatedly increases and decreases. Finally, run at a PB of 0.05% as a comparison of too low a PB. Monitor the tank level and valve opening in the graph display page (hit the GRAPH tap at the top menu bar) during the operation (right after hitting enter). The graph will automatically display the tank level data during the operation. You need to add the valve opening data to the graph. This can be done if you click the CONFIGURE tap at the right side of the screen. 18. When the timer runs out (300 sec), the program will prompt you about your data. Click OK. (you will have room for 3 PB values for each sampling run). 19. Immediately go to File>>Save. [same as step 12] 20. Repeat steps until you have collected all the required data. While saving the data, the water level will deviate from the 40 mm mark. Manually return the water level to 40 mm before resuming with more data collection. 21. Set the Manual Control Setting to 0% and set the control mode to Manual. 23

24 22. Unplug sol 3 and plug in sol 1. Make sure the level of the water in the tank is between 0 mm and 100 mm. 23. Graph all the collected data. Show both level and valve opening. Also show the level set-point. Too small a proportional band will have growing or maxed out oscillations; too big a proportional band will have shrinking oscillations. Use your best judgment to determine the PB u. You will find that there are 2 or 3 plots that may be possible PB u s. Keep in mind that you should look at tank water level AND the valve % open data. When the valve is oscillating between 100% open and 0% open, the level oscillations will max out and may not grow anymore, yet the system is unstable and out of control at this point. If this is not clear, please ask the TA to clarify. ** When PB is larger than PB U, the control response (valve opening) is small; when PB is smaller than PB u, the control response continuously oscillates between two extreme conditions (min & max). The PB u value can be determined from the onset of the steady oscillation behavior. 24. Rerun the two most promising PB u runs from the previous steps for a full 300 seconds of data each to get better data and verify your choice of PB u. Remember to plug in sol3 connection and return the manual setting of the flow rate to 100%. Then bring the water level to the set-point of 40 mm before starting automatic control again. 25. Unplug sol 3 and plug in sol 1 while you analyze your data. Make sure the level of the water in the tank is between 40mm and 140 mm. 26. For your determined PB u, determine the ultimate period t u (time to go from peak maximum to maximum or minimum to minimum). This is best done by averaging over a larger sampling area (count the number of maximums in a certain time period). t u should be approximately 5-10 sec. Record your PB u and t u. 27. Use your ultimate proportional band data to calculate your ZN parameters for P and PI control and proceed to test them (following procedure below). 28. On the PID 1 screen, set the Manual Control Setting to 100% open and ensure that the flow rate still reads 3000 cc/min on the flow meter. 29. Switch the gray cord from sol 1 to sol Click the Timer tab. Set Elapsed Time to 300 for the P and PI runs. 31. Go to the PID 1 screen. Set you ZN parameters for P Control. Set the Set Point to 40 mm. Switch to Automatic Control and immediately set the Controller Offset to 0. Allow the system to reach steady state. The tank level should settle at a little below 40 mm Process Variable Water Level. 32. Click Start Sampling. After 20 sec, change the Set Point to 60 mm. Observe. Go to the Graphs window to see your data being collected. Adjust the scaling if necessary, but make sure to include the ramp up from 40 to 60 mm set point change. 33. When the timer runs out, the program will prompt you about your data. Click OK. 24

25 34. Immediately go to File>>Save. [same as step 12] 35. Go back to the PID 1 screen. Change the Set Point back to 40 mm. Allow the tank level to settle as before. You may speed this up by manually manipulating the level. 36. Repeat steps for P control using a PB 4 times that used initially for the ZN response and also 1/8 times that used for the ZN response. (Note: you are now examining the general response of control systems to changes in PB. These two runs are not using ZN parameters.) 37. On the PID 1 screen, set the Manual Control Setting to 100% open and ensure that the flow rate still reads 3000 cc/min on the flow meter. 38. Set your ZN parameters for PI Control. Click Start Sampling. After 20 sec, change the Set Point to 60 mm. Observe. Go to the Graphs window to see your data being collected. 39. When the timer runs out, the program will prompt you about your data. Click OK. 40. Immediately go to File>>Save. [same as step 12] 41. Go back to the PID 1 screen. Change the Set Point back to 40 mm. Allow the tank level to settle as before. You may speed this up by manually manipulating the level. 42. Repeat steps two more times, but now change the integral time to 2 times the integral time used for the ZN response and to ½ the integral time used for the ZN response. Keep your PB the same as for the ZN PI run. (Note: you are now examining how integral time affects PI response, and the parameters are no longer ZN parameters.) 43. Now you know how P-only and PI-controls work. Let s use your knowledge to design the optimum control process which will allow you to reach the set-point without overshoot and offset. Run the tank level control system to test the optimum process that you designed and check the performance of your method. 44. Save and plot your optimum control data. 45. You are finished. Ensure that your data looks as you would expect. If not sure, verify with the TA or instructor. Click the Exit Tab and exit the program. Turn off the main PCT10 power source. 46. Drain the top process tank with valve V4. Close the water flowmeter valve. 25

26 APPENDIX F: Opening Data in Excel 1. Open Excel. 2. Go to File>>Open. 3. Switch from All Excel Files to All Files and open your.dat files. 4. A Text Import Wizard will now appear. 5. Choose Delimited>>Next. 6. In Delimiters, check Tab and Comma>>Next. 7. Click Finish. Click OK 8. You will only need 3 columns of data, Units, mm, and % open. Units = Time (sec). mm = Calibrated Tank Level. % open = valve % open. The rest of the data can be deleted if you wish. 9. Copy your data into your spreadsheet workbook to fully analyze. 26