CONTROL VALVE FROM CONTROL LOOP THEORY PERSPECTIVE: An overview

Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 CONTROL VALVE FROM CONTROL LOOP THEORY PERSPECTIVE: An overview Anna Veneroni SIMECO S.p.A. 1

INTRODUCTION SUMMARY: 1. The valve as control loop element - Pressure regulation for gas - Flow regulation for liquids 2. Characteristic of the valve - Inherent characteristic - Installed characteristic 3. The gain of a control valve in a loop 4. Regulator synthesis and tuning Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 2

1 THE VALVE AS A REGULATION ELEMENT Gas pressure regulation loop Control loop principles EXAMPLE: FEEDBACK CONTROL LOOP FOR PRESSURE REGULATION OF A VESSEL PRESSURE CONTROLLER a feedback controller that acts on the control valve according to the Set Point and to the actual pressure in the vessel REGULATION VALVE Suppose that the pressure in the vessel decrease as a disturbance effect The controller takes action in order to guarantee a proper pressure value in the vessel (direct action) The valve opening (h) decreases The valve flow capacity Cv(h) decreases The outlet flow rate Q decreases The net quantity of gas in the vessel increases and therefore also the pressure in it increases (with T and inlet flow almost constant) The pressure increase due to the control loop action that allows to restore the pressure value at the desired Set-Point. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 3

1 THE VALVE AS A REGULATION ELEMENT Liquid flow regulation loop FLOW CONTROLLER REGULATION VALVE Control loop principles THE VALVE AS THE DISSIPATIVE ELEMENT IN A HYDRAULIC CIRCUIT In a hydraulic circuit with a flow rate control loop, suppose to have a flow rate decrease due to a disturbance effect. The regulator action opens the valve in order to restore the flow rate value in the circuit to the Set-Point. As effect of the controller, the flow rate decreases, the output of the controller increases (reverse action) and the valve opening (h) increases. Cv(h) of the valve Cv(h) increases Variable electrical conductance (NOT linear) Conductance increases Δp 3 decrease ΔV 3 decreases Q increases I increases Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 4

1 THE VALVE AS A REGULATION ELEMENT Reference Hydraulic Model a b p 1 Valve Pressure Profile Low q (the valve is nearly closed) p 1 = P Source p piping a p 2 = P Receiver + p piping b p 2 Δp is concentrated on the valve p 1 High q (the valve is nearly open) p 2 Δp is distribuited on the lines Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 5

2 INHERENT CHARACTERISTIC DEFINITION OF THE FLOW COEFFICIENT Cv The Cv coefficient defines the normalized volumetric flow rate which is referred to the following conditions: Differential pressure between upstream and downstream of the valve = 1 psi The fluid is water at a temperature between 5 and 40 (ρ=1000kg/m³) The unit of measure for the volumetric flow rate is gmp (1gal=3,785l) C v = q v p (cv) p ρ ρ 0 p (cv) is the static pressure drop, equal to 1 psi p is the static pressure drop expressed in psi Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 6

2 INHERENT CHARACTERISTIC Cv calculation ANSI/ISA 75.01.01 2002 (60534-2-1 Mod) Flow Equations for Sizing Control Valves Fourth Printing: 15 August 2005 Sizing equations for incompressible fluids (Chap. 6 ANSI/ISA 75.01.01 2002 (60534-2-1 Mod) Turbulent Flow Non choked flow Applicable if P < F LP F 2 P (P 1 F F P V ) Eq. 2 C = Q ρ 1 /ρ 0 N 1 F P P Choked flow Applicable if P F LP F 2 P F 2 L (P 1 F F P V ) Eq. 4 C = Q N 1 F LP ρ 1 /ρ 0 P 1 F F P V Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 7

2 INHERENT CHARACTERISTIC Cv calculation Sizing equations for compressible fluids (Chap. 7 ANSI/ISA 75.01.01 2002 (60534-2-1 Mod) Turbulent Flow Non-choked flow Applicable if x < F γ x TP Eq. 11a C = Q N 9 F P P 1 Y MT 1 Z x Choked flow Applicable if x F γ x TP Eq. 17a C = Q 0.667N 9 F P P 1 MT 1 Z F γ x TP Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 8

2 INHERENT CHARACTERISTIC INHERENT CHARACTERISTIC The inherent characteristic is the relation between the flow rate and the stroke of the valve keeping constant the composition, the temperature, the pressure upstream and downstream of the valve. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 9

2 INHERENT CHARACTERISTIC INHERENT RANGEABILITY The inherent rangeability of a valve is typically used during the sizing or during the operating verifications. It is the range in which both the prescriptions on the slope of the characteristic curve and the tolerance on the Cv values are applicable. It does not represent anyway the effective flow rate capacity of the installed valve. R = Cv max Cv min h: 100% h: 5% IEC 60534-2-4 Industrial-process control valves Part 2-4: Flow capacity - Inherent flow characteristics and rangeability: ø =Cv/Cvmax It collects all the criteria that shall be applied from the vendors to define the correct Cv of a valve. The valve must operate in an appropriate range, with a declared tolerance. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 10

2 INHERENT CHARACTERISTIC INCREASE OF THE INHERENT RANGEABILITY USING TWO VALVE IN PARALLEL Applicative example: «Thermal recovery MHC-TAME» for Sarlux In order to increase the total thermal efficiency of the refinery, two new heat exchangers have been installed on an existing etherification plant. Their function is to heat the etherified gasoline feed in a column using as hot fluid the GAL available from the near plant MHC. The GAL flow depends on the operating conditions of the plant MHC. For this reason the existing heat exchangers, which works with low pressure steam, shall continue to work though with a higher range, extending it to low flows. This condition allows to maintain Set-Point temperature at the column feed, even if GAL flow rate decreases (for any reason), in order to optimize the low pressure steam usage. A new and smaller valve has been added in parallel to the existing regulation valve E-10 (FV-017, globe equi%, 12") dedicated to the regulation of the inlet steam flow rate to the heat exchanger. This new valve is dedicated to the low flow rate regulation (FV-301, globe equi%, 6"). Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 11

2 INHERENT CHARACTERISTIC INCREASE OF THE INHERENT RANGEABILITY USING TWO VALVE IN PARALLEL N 2 valves equi% in parallel: FV-017: 10000 25000 Kg/h FV-301: 1340 10000 Kg/h Pre-existing Installed in order to increase R Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 12

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 2 INHERENT CHARACTERISTIC INCREASE OF THE INHERENT RANGEABILITY USING TWO VALVE IN PARALLEL Process conditions at switch point: Q=10000Kg/h Pin =3,5barg Dp =0,5bar Valve opening and Cv at switch point: ET-FV-017 Cv =393,1 h=37,3% ET-FV-301 Cv =403,4 h=94% Split range value during valve opening: 35% Split range value during valve closing: 40% 2000 1800 1600 1400 1200 1000 800 600 400 200 0 Cv FV-017 Cv FV-301 The valves shall be controlled with a split range. The switch point is selected in order to obtain the extended curve, with continuity of solution for both the operating valves FV-018 and FV-302. Moreover, it is necessary to enter a value of hysteresis in order to avoid flow rate oscillations around the switch point value and consequently an alternate usage of the two valves FV-018 and FV-302. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 13

2 INSTALLED CHARACTERISTIC INSTALLED CHARACTERISTIC The installed characteristic is the relation between the valve stroke and the related flow rate in a system composed by the valve and the hydraulic circuit in which the physical properties such as temperature and fluid composition are kept constant. The installed characteristic is affected by the operating pressure condition of the hydraulic circuit Pressure trend on flow rate for typical processes: Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 14

2 INSTALLED CHARACTERISTIC INSTALLED CHARACTERISTIC FOR A LINEAR INHERENT CHARACTERISTIC D c = P P t Note: If the valve resistance decreases in comparison to total resistance in the system, Dc decreases. Therefore the flow rate regulation is similar to an onoff regulation. 5 Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 15

2 INSTALLED CHARACTERISTIC INSTALLED CHARACTERISTIC WITH AN EQUIPERCENTAGE INHERENT CHARACTERISTIC D c = P P t Note: Decreasing Dc, the equi-percentage inherent characteristic becomes a linear installed characteristic and the minimum controllable flow rate increases. 5 Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 16

2 CARATTERISTICA INSTALLATA Comparison between main characteristics If Q = Q max and p valve > 40% p tot, the linear inherent characteristic allows to obtain the maximum level of linearity in the installed characteristic. If Q = Q min and p valve < 25% p tot, the equi% inherent characteristic allows to obtain the maximum level of linearity in the installed characteristic. Valve with high values of specific C v (as rotary valves) can be more easily influenced by the line effects than globe valves. This is because the rotary valves have a lower p (5 10 times smaller) at the same flow rate. 5 Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 17

2 INSTALLED CHARACTERISTIC Kg/h Block diagram in figure represents the correspondence between the valve regulation signal (which comes from the regulation loop) and the flow rate in the hydraulic circuit. Kg/h FC regulator output Kg/h Flow Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 18

2 INSTALLED CHARACTERISTIC How to obtain the valve installed characteristic during engineering: 1- Through suitable calculation software for valve sizing E.g.: flow rate regulating valve for low pressure steam Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 19

2 INSTALLED CHARACTERISTIC How to obtain the valve installed characteristic during engineering: 2 Using datasheet information and valve inherent characteristic E.g.: Flow rate regulating valve for liquid (poor amine) With a spreadsheet in Excel it is possible to verify the installed characteristic of the valve. The initial data involved in the calculation are the following: - Liquid density - Pressure value upstream and downstream of the valve in both conditions of maximum and minimum flow rate. - Inherent characteristic declared in vendor datasheet Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 20

1200 1464 1728 1992 2256 2520 2784 3048 3312 3576 3840 4104 4368 q [Kg/h] Knowing upstream and downstream valve pressure in both conditions of maximum and minimum flow rate, it is possible to select the most appropriate pressure trend between typical ones and interpolate the datasheet pressure values accordingly. 7,00 6,00 5,00 4,00 3,00 2,00 1,00 0,00 36 35 34 33 32 31 30 29 28 Dp/q 36 35 34 33 32 31 30 29 28 pin pout 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 h [%] 2 INSTALLED CHARACTERISTIC How to obtain the valve installed characteristic during engineering: Here below are visible the inherent characteristic and the Δp= p in p out trend entered in calculation sheet: Cv/h Inherent characteristis Cv Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 21

0 3,45 6,9 10,35 13,8 17,25 20,7 24,15 27,6 31,05 34,5 37,95 41,4 44,85 48,3 51,75 55,2 58,65 62,1 65,55 69 72,45 75,9 79,35 82,8 86,25 89,7 93,15 96,6 2 INSTALLED CHARACTERISTIC How to obtain the valve installed characteristic during engineering: How to calculate the installed characteristic: - Select a q value in the range - Read the corresponding p value from plot p/q - Calculate Cv from the equation C v = q v 0,865 P ρ/ρ0 q [Kg/h]/ h [%] Caratteristica Installata Q 5000 4500 4000 3500 3000 - Read the corresponding valve stroke value h from inherent characteristic - Plot (q, h) - Select another q value in the range and repeat the steps The installed rangeability is: D c = 0,31 2500 2000 1500 1000 500 0 R = Q 100% Q 5% = 5000 300 = 16.6 D c = P P t Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 22

INSTALLED RANGEABILITY 2 INSTALLED CHARACTERISTIC R = Q max Q min The installed rangeability is the actual relation between maximum and minimum flow rate that valve can adjust during service. INSTALLED GAIN G inst = dq p dh The installed gain is the relation between flow rate variation and the corresponding valve stroke variation. This ratio correspond to the installed characteristic slope. Note that, if the installed characteristic is linear, the gain is constant. A too high gain value could cause high relative errors on flow rate variation (ΔQ ɛ ) due to relative errors on the valve stroke value (h ɛ ). ΔQɛ = G * Δhɛ Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 23

3 VALVE GAIN IN A CONTROL LOOP Introduction to the control theory. MODEL LINEARIZATION AROUND THE OPERATING POINT If we consider a process operating plant in stationary conditions we can assume that: the pressure drop of the valve (Δp(t)) is constant, the valve flow rate (Q(t)) is constant and equal to its nominal value Q and therefore the valve stroke is equal to the corresponding h in valve installed characteristic. In these conditions, if the flow rate has very small variations around the nominal value, the installed characteristic of the valve can be approximated to the straight line with the same slope of the installed characteristic in that point. The valve model Q(t) = Q c inst (h t ) Can be approximated by linearization around every equilibrium flow rate point, Q + δq t = h + G inst h + δh t Applying Laplace Transform On linearized system: Q s = G inst h h s Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 24

3 VALVE GAIN IN A CONTROL LOOP ACTUATOR STEP RESPONSE If the controller output u(t) has a step change from the nominal operating condition, the valve stroke does not reach the new required position instantaneously. We have to take into account the actuator and the positioner dynamics. Typically this control action follows a 1 order dynamic (as for the capacitor regulation in the RC circuit). Therefore, the dynamic of the valve regulation can be approximated to a I order dynamic system which DTF (Dynamic Transfer Function) is the following: F att s = 1 1 + τs The valve stroke is limited between 0 and 100% and the actuator speed is limited too. Hence, we must introduce saturations (NON-linearity) in control loop: Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 25

3 VALVE GAIN IN A CONTROL LOOP THE TRANSFER FUNCTION FOR THE FLOW CONTROL LOOP Assuming: F trasm = F elepos =1 F attuat = 1 Q max 1 1+sτ G inst = installed gain of the valve Neglecting the saturation non-linearity Note: the process control systems are digital controllers. For the purpose of this discussion, we can neglect this fact and dealing with analog controllers. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 26

4 REGULATOR SYNTHESIS GENERAL THEORY CONSIDERATION FOR REGULATOR SYNTHESIS Even if the installed characteristic is nearly linear, the control valve is always a non-linear system. This is basically due to the control valve Cv max limitation. This behavior can be modeled by a saturation. This non-linearity can be approached using the non-linear control theory. For historical and practical reasons in the process control it is widespread the usage of linear controllers. So the regulator synthesis is the construction of a proper Controller Transfer Function. In addition, it is a very common practice to use standard Controller Transfer Functions (typically PID regulators) and to define their parameters by tuning. Then, the actuator saturation is managed taking into account «ad hoc» techniques called ANTI WIND-UP. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 27

4 REGULATOR SYNTHESIS PID CONTROLLER PID controller is the most common controller used in process control. PID regulators combine 3 actions: K p PROPORTIONAL ACTION: proportional to the error K d DERIVATIVE ACTION: proportional to the derivative of the error K i INTEGRAL ACTION: proportional to the integral of the error PID t = K p e(t) + K d de(t) dt t+t + K i e t dt t Appling Laplace transformation: PID s = K p + sk d + K i s We set K d =0 because flow rate measures are affected by noise. So we can use PI controller. PID s = K p + K i s = K p T i (1 + T i s) s Note: Refer to the bibliography for more complex forms and PID implementations in process control systems. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 28

4 REGULATOR SYNTHESIS CONSIDERATIONS ON THE GAIN OF THE INSTALLED VALVE In order to identify the right parameters of the PID controller to guarantee the stability of the process, it is necessary that the parameters of the process transfer function are almost constant. The maximum variation of the process gain (ratio valve flow rate/controller output) must be limited. Empirical value: max 4:1 If the gain exceed this empirical value, will be necessary have a PID regulator with variable parameters to ensure a robust control. Anyway, for the valve system is required that G inst (q(t)) is as much as possible constant. For this reason the valve gain is required to be within a specific range. For example 0,75 3 or 0,5 2 that comply to general rule: G inst max G inst min < 4 Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 29

4 REGULATOR SYNTHESIS LOOP GAIN AND TRANSFER FUNCTION Q(s)/Q0(s) L s = G inst Q max K p T i (1 + T i s) 1 + τs s F s = L(s) 1 + L(s) = (1 + T is) αs 2 + βs + 1 Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 30

4 REGULATOR SYNTHESIS THE STATIC GAIN OF THE SYSTEM Q(0)/Q0(0) F s = (1 + T is) αs 2 + βs + 1 F(0)=1 From a mathematical point of view s=jω=j2πf where f is the frequency. So, if the signal frequency f goes to zeros the transfer function F(s) goes to one. If f 0 then F(s) 1 In time domain, for a Set-Point step variation, after a theoretically infinite time period, Q(s)= Q 0 (s), so the error between the Set-Point and the process variable (i.e. the flow rate) is zero. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 31

4 REGULATOR SYNTHESIS REGULATOR TUNING PI s = K p T i (1 + T i s) s If the time constant of the actuator t is available, it is possible to choice T i =t L s = K (1+T is) 1+τs s = K s F s = 1 1+Ts in which in which T = 1 K K = G inst Q max K p T i Hence, F(s) results to be a low-pass filter with gain=1 and critical pulsation: ωc = 2π T (Hz) It is possible to choose K p in order to force the desired critical pulsation w c and the response time of the system, of course, within the actuator valve and process limit. Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 32

4 REGULATOR SYNTHESIS TUNING METHODS FOR PID CONTROLLER A ) Tuning methods based on the experimentally process open loop response to Set-Point step variation If the process response can be approximated to a I order system, we can use: Tangent method Areas method Ziegler-Nichols in open loop Cohen-Coon Internal Model Control (IMC) B ) Tuning method based on the experimentally closed loop response analysis on the system Ziegler-Nichols in closed loop Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 33

BIBLIOGRAPHY Bibliography: Béla G. Liptàk, Instrument Engineers Handbook - Process Control and Optimization - 4 th Edition, CRC Press Taylor & Francis Group, 2006 P. Muroni, Valvole di regolazione per processi industriali - GISISERVIZI.srl, Milano, 2001 METSO, Flow Control Manual 6 th Edition, METSO AUTOMATION INC., Vantaa, Finland, 2011 F. G. Shinskey: Process Control Systems 4 th Edition, McGraw-Hill,1996 P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di controlli automatici 3 Edizione - McGraw-hill, 2008 ANSI/ISA-75.01.01-2012 (60534-2-1 MOD) Industrial-Process Control Valves - Part 2-1: Flow capacity - Sizing equations for fluid flow under installed conditions IEC 60534-2-4, Industrial-process control valves - Part 2-4: Flow capacity - Inherent flow characteristics and rangeability, Edizione 2.0, 5/13/2009 Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 34

THANK YOU FOR YOUR ATTENTION Simeco S.p.A. Via Romilli, 22-20139 Milano (Italy) tel. +39.02.99298.1 fax +39.02.56.91.424 www.simecomilano.it Automation Instrumentation Summit Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni Simeco S.p.A. 35