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Integrating stiction diagnosis and stiction compensation in process control valves
16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering W. Marquardt, C. Pantelides (Editors) © 2006 PubHshed by Elsevier B.V.
Integrating Stiction diagnosis and Stiction Compensation in Process Control Valves R. Srinivasan^* and R. Rengaswamy^^ ^Honeywell Inc, ACS Labs, Phoenix, USA. ^Dept of Chemical Engineering, Clarkson University, NY 13676, USA Limit cycles caused due to valve non-linearity such as stiction can be eliminated with proper valve maintenance. Since valve maintenance is usually scheduled during production stops and with production stops scheduled typically once every six months to three years, the loss of product quality and energy loss during this intermediate period can be quite high. Stiction compensation algorithms can mitigate this problem to a large extent. In this paper, an optimization based approach for stiction compensation much in the sprit of predictive control strategies is proposed. 1. Background It has been reported that 20% to 30% of all control loops oscillate due to valve problems caused by static friction [1]. Oscillations lead to poor end product quality and wastage of energy. Hence, reliable diagnosis of valve stiction by itself will have a large economic impact. Valve maintenance, usually taken up during production stops, can reduce the static friction forces and lead to an improvement in loop performance. However, normal production stops are typically between every six months to three years. The loss of product quality and energy loss during this intermediate period can be quite high. Stiction compensation algorithms can mitigate this problem to a large extent. Two basic approaches to stiction compensation, namely dithering and impulsive control have been reported in the literature [2]. A good overview on stiction compensation in electromechanical systems can be found in Armstrong et al. (1994). Unfortunately, pneumatic valves that constitute 90% of actuators employed in a control loop filter such high frequency dither signal, making dithering technique ineffective. Similar drawback exists with impulsive control technique. Kayihan and Doyle [3] and Hagglund [4] have addressed stiction compensation algorithms for pneumatic control valves. The approach of Kayihan and Doyle [3] assumes that all the valve parameters such as mass of stem, stem position, stem velocity etc, are known a priori. Such detailed parameter values may not be available for all valves . Hagglund [4] proposed a novel *This work was done when the first author was a graduate student at Clarkson University ^Corresponding author: [email protected].
1233
1234
R. Srinivasan and R.
Rengaswamy
K Figure 1. Knocker Pulse
approach where a knocker signal is added to the control signal for stiction compensation. This is probably the best available current approach for stiction compensation. 1.1. Hagglund's Technique In Hagglund[4] technique (termed as 'knocker') short pulses are added to the control signal in the direction of the rate of change of the control signal. However, there is a need to tune three parameters that characterize the short pulses (see Figure 1): amphtude (a), pulse width (T) and time between each pulse (/z^). It was shown in our earlier work [5] that the 'knocker' performance was influenced by the pulse parameters. A brief summary of our past work is given in the next section. 1.2. Previous work[5] In our earlier work[5], we proposed a framework and a design procedure to automate these knocker parameters based on a stiction severity measure. This framework which integrates stiction diagnosis and stiction compensation tasks was shown to reduce the output variability by at least 6-7 times. However, it was pointed out that the reduction at the output variability was achieved at the cost of an aggressive stem movement. The 'knocker' in order to eliminate the output variability, shifted the variability to the stem, causing the stem to move aggressively. Such an aggressive stem movement is not preferred as it may wear the valve quickly. Hence, a design strategy for compensating stiction should ideally meet the following requirements: • Less aggressive stem movement (or valve movement) • Reduced Output variability • Less energy in the signal that is added to the control signal In this work, a novel design strategy that attempts to meet these requirements is proposed. The proposed method is devised based on the physical understanding of the stiction phenomenon and uses the stiction severity. 2. Proposed approach for stiction compensation 2.1. Problem setup Figure 2 shows the block diagram of a control loop in the presence of stiction. Valve dynamics are observed only after the start of the stem movement; stiction phenomenon, if present, will precede the valve dynamics. Also, it was discussed in [6,5] that a simple stiction model given by Equation 1 will be adequate under closed loop conditions. The simple stiction model is given
Integrating Stiction Diagnosis and Stiction
Compensation
1235
Identified Linear dvnaiiiics SP V
Controller
OP
Valve
Sliction V
Controller
Non-lineai' element
(+W
Figure 2. Process control loop in presence of sticky control valve.
Stiction Non Linearity
Plant
Figure 3. Process control loop with a compensator.
below^: X{t):
x[t-\) u{t)
if\u{t)-x{t-l)\ otherwise
(1)
Here x{t) and x{t — 1) are present and past stem movements, u{t) is the present controller output, and W is the valve stiction band. The stiction model given by Equation 1 coincides with the industrial procedure used for measuring stiction and the readers are referred to [6] for a detailed discussion on the applicability of this simple model for modeling stiction. For processes other than flow loops, the identification of the plant's linear dynamics includes the valve dynamics (that occur due to stem and plug movement, see Gp in Figure 2). This is because the flow through the valve, which is an intermediate variable, is usually not measured. In view of this assumption and combined with the fact that the stiction phenomenon precedes the stem movement, the stiction nonlinearity and the plant dynamics can be represented in separate blocks. This is depicted in Figure 3. Here ysp is process set-point (SP), y is process output (PV), e is the error (SP - PV), m is the controller output, f^ is the compensator output, u is the additive signal (m + fk) that is the input to the valve and x represents the predicted stem position obtained using the stiction model. 2.2. Problem formulation The requirements of an ideal stiction compensator can be translated into a meaningful objective function and realized using an optimizer. A possible objective function is: min J - XIISEY + X2Var{X) + X3<^{X)
(2)
Fk
Here, an optimization formulation that minimizes the objective function J over a defined prediction horizon is posed for designing the compensator signal (Fk). The first term in the objective function J is the integral square error (ISEY) of PV (with respect to set point), the second term addresses the valve stem variability Var{X), and the third term includes valve aggressiveness ((|)(X)). F and X are vectors obtained over a defined prediction horizon (p). A,i, A,2 and A-3 represents either the cost associated for maintaining the product quality or the penalty for each term
1236
R. Srinivasan and R.
Rengaswamy
in J. A compensating signal that minimizes J is the best possible signal that will meet the requirements of an ideal compensator. However, formulating such an objective function requires several assumptions to be made. These assumptions are listed below: 1. The plant model Gp is available. 2. The controller (G^) structure and its parameters are available. 3. Stiction is already detected. 4. Stiction severity measure d is ascertained a priori. With these assumptions, the optimization formulation is formally stated as: minJ
-
XxISEY + X2Var{X) +
'k2>
(3)
Uk-i = GcCk-i+fk-i
(4)
ek = ysp-Jk x{t) = ^{u{t),x{t-l),d)
(5) (6)
{ypred)k
=
GpXk-l
(7)
{ypred)k+p
=
GpXk+p-l k+p Y. {{ypred)i-ysp? i=k+l
(8)
ISEY
Var{X)
=
= variance{xi),i = k-{-l....{k-^p-l)
^{X) = 100* ( 1 - - ^ ) , p-l X
=
{Xk,Xk-\-l,....:Xk+p-l)
Fk
=
{fk,fk+\i'-"ifk+m-\)
(9)
(10) (11)
where, p is the prediction horizon, m is the control horizon, x denotes the predicted stem movement using the nonlinear transformation 9{^ (simple stiction model given by Equation 1) and Ut is the total number of switches in the signal between Xt and Xt^p. The stem aggressiveness denoted as (|)(X), is computed as a signal friendliness factor (see [7] for definition). The friendliness factor for the stem denotes how fast the stem changes, a value of (|) ?^ 0 indicates that the stem changes its position at every time instant and a value (j) ?^ 1 indicates that the stem changes it position only at few time instances over the time duration considered. At every time instant, a set of 'm' compensator moves are computed and similar to the MPC concept, only the first compensator move is added to the PID controller output. Since, the stiction model fA^is discontinuous and the stem friendliness factor ((|)(X)) does not have a closed form, an approximate numerical approach is used to solve the above nonlinear optimization problem. 3. Simulation results 3.1. Simulation example Consider a closed loop process with ^ , , 0.009U-i-h0.0082z-2 ^ ^ ^ 16-27.53^-1 + 11.81^-2 ^^(^^^l-1.724z-i+0.748z-i ^^^^^ ^ T^F^
^^'^
Integrating Stiction Diagnosis and Stiction
Compensation
^/WVVVV---=Tr^ Compensation started at time = 120 seconds
jlj
1237
""•
Compensation started at tinfe t = 120 S(
set-npint Runi Run 2
Umm^ 9 (sacs)'w
toJ ^"rimo (secsy^
^^^
I ^"^imefsecsy^
Figure 4. Results for optimization approach for compensation, (a) Process output and (b) ControUer output. The compensation started at time 120 seconds
Figure 5. Results for optimization approach for compensation, (a) Compensator signal, (b) Valve input obtained after addition of compensating signal to controller output and (c) Stem position.
sampled at every second. The loop oscillates due to the presence of stiction. The stiction is simulated using the simple stiction model given by Equation 1, with a stiction band d = 0.5. 3.2. Results Two simulations were performed to highlight the usefulness of the optimization approach. The optimization approach used the 'fmincon' algorithm of the MATLAB optimization toolbox used. The parameters for both the simulations are given in Table 1. Figures 4 and 5 show the comparison of the results obtained for the two simulations. It is seen that, based on the penalty imposed for each term in the objective function, the duration for the process output to reach its set-point varies. Also, the amount of variability and stem friendliness factor varies based on the weights of X.
Table 1 Parameters used in the simulation for the Optimization approach. Parameters Prediction horizon (p) Control horizon (m) ^1
y^i
h
Runl 40 2 100 0 0
Run 2 40 2 0 100 100
3.3. Discussion It was seen that the optimization approach has parameters that need to be tuned to attain efficient stiction compensation. Two main drawbacks are seen with the optimization approach:
1238
R. Srinivasan and R.
Rengaswamy
1. As the objective function (Equation 3) is non-smooth, the optimizer was not able to attain the global minimum; instead a local solution was obtained. This is evident from Figure 4, where for both runs, the process output failed to reach the set-point. This is because the stem position did not move to the correct steady state value, instead moved the stem close to it with an offset. Also the objective function values obtained for the various compensating signals (simulated as a grid of values for the next two moves) showed that the objective function is generally non-smooth but convex. 2. When the optimization approach was tried on an experimental level system at Clarkson University, the Simulink interface could not solve the optimization formulation between each iteration, due to real-time issues. Alternate non-gradient based optimization techniques that use function evaluation such as DIRECT (Divide RECTangle method). Implicit filtering can be studied to overcome the real-time issues. 4. Summary In this paper, a model based optimization approach for stiction compensation was presented. The optimization approach was observed to provide more trade-off than the 'knocker' approach. Preliminary studies suggest that the model based compensation method can be an useful strategy for stiction compensation. Further analysis of the effect of model plant mismatch, incorrect stiction measure, real time issues on the proposed stiction compensation approach needs to be done before these methods can be implemented online. REFERENCES 1. L. D. Desborough and R. M. Miller. Increasing customer value of industrial control performance monitoring - honey well's experience. Arizona, USA, 2001. CPC-VI. 2. B. Armstrong-Helouvry, R Dupont, and C. C. De Wit. A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica., 30(7): 1083-1138, 1994. 3. A. Kayihan and F. J. Doyle. Friction compensation for a process control valve. Control Engg. Practice, 8:799-812, 2000. 4. T. Hagglund. A friction compensator for pneumatic control valves. Journal of Process Control, 12:897-904, 2002. 5. R. Srinivasan and R. Rengaswamy. Stiction compensation in process control loops: A framework for integrating stiction measure and compensation. Accepted for publication in Industrial and Engg. Chemistry Research, 2005d. 6. R. Srinivasan, R. Rengaswamy, S. Narasimhan, and R. M. Miller. Control loop performance assessment 2: Hammerstein model approach for stiction diagnosis. Industrial and Engg. Chemistry Research, 44:6719-28, 2005b. 7. S. Narasimhan, R. Srinivasan, and R. Rengaswamy. Multi-objective signal design for plant friendly identification. 13th IFAC Symposium on System Identification, 2003.
Integrating Stiction diagnosis and Stiction Compensation in Process Control Valves R. Srinivasan^* and R. Rengaswamy^^ ^Honeywell Inc, ACS Labs, Phoenix, USA. ^Dept of Chemical Engineering, Clarkson University, NY 13676, USA Limit cycles caused due to valve non-linearity such as stiction can be eliminated with proper valve maintenance. Since valve maintenance is usually scheduled during production stops and with production stops scheduled typically once every six months to three years, the loss of product quality and energy loss during this intermediate period can be quite high. Stiction compensation algorithms can mitigate this problem to a large extent. In this paper, an optimization based approach for stiction compensation much in the sprit of predictive control strategies is proposed. 1. Background It has been reported that 20% to 30% of all control loops oscillate due to valve problems caused by static friction [1]. Oscillations lead to poor end product quality and wastage of energy. Hence, reliable diagnosis of valve stiction by itself will have a large economic impact. Valve maintenance, usually taken up during production stops, can reduce the static friction forces and lead to an improvement in loop performance. However, normal production stops are typically between every six months to three years. The loss of product quality and energy loss during this intermediate period can be quite high. Stiction compensation algorithms can mitigate this problem to a large extent. Two basic approaches to stiction compensation, namely dithering and impulsive control have been reported in the literature [2]. A good overview on stiction compensation in electromechanical systems can be found in Armstrong et al. (1994). Unfortunately, pneumatic valves that constitute 90% of actuators employed in a control loop filter such high frequency dither signal, making dithering technique ineffective. Similar drawback exists with impulsive control technique. Kayihan and Doyle [3] and Hagglund [4] have addressed stiction compensation algorithms for pneumatic control valves. The approach of Kayihan and Doyle [3] assumes that all the valve parameters such as mass of stem, stem position, stem velocity etc, are known a priori. Such detailed parameter values may not be available for all valves . Hagglund [4] proposed a novel *This work was done when the first author was a graduate student at Clarkson University ^Corresponding author: [email protected].
1233
1234
R. Srinivasan and R.
Rengaswamy
K Figure 1. Knocker Pulse
approach where a knocker signal is added to the control signal for stiction compensation. This is probably the best available current approach for stiction compensation. 1.1. Hagglund's Technique In Hagglund[4] technique (termed as 'knocker') short pulses are added to the control signal in the direction of the rate of change of the control signal. However, there is a need to tune three parameters that characterize the short pulses (see Figure 1): amphtude (a), pulse width (T) and time between each pulse (/z^). It was shown in our earlier work [5] that the 'knocker' performance was influenced by the pulse parameters. A brief summary of our past work is given in the next section. 1.2. Previous work[5] In our earlier work[5], we proposed a framework and a design procedure to automate these knocker parameters based on a stiction severity measure. This framework which integrates stiction diagnosis and stiction compensation tasks was shown to reduce the output variability by at least 6-7 times. However, it was pointed out that the reduction at the output variability was achieved at the cost of an aggressive stem movement. The 'knocker' in order to eliminate the output variability, shifted the variability to the stem, causing the stem to move aggressively. Such an aggressive stem movement is not preferred as it may wear the valve quickly. Hence, a design strategy for compensating stiction should ideally meet the following requirements: • Less aggressive stem movement (or valve movement) • Reduced Output variability • Less energy in the signal that is added to the control signal In this work, a novel design strategy that attempts to meet these requirements is proposed. The proposed method is devised based on the physical understanding of the stiction phenomenon and uses the stiction severity. 2. Proposed approach for stiction compensation 2.1. Problem setup Figure 2 shows the block diagram of a control loop in the presence of stiction. Valve dynamics are observed only after the start of the stem movement; stiction phenomenon, if present, will precede the valve dynamics. Also, it was discussed in [6,5] that a simple stiction model given by Equation 1 will be adequate under closed loop conditions. The simple stiction model is given
Integrating Stiction Diagnosis and Stiction
Compensation
1235
Identified Linear dvnaiiiics SP V
Controller
OP
Valve
Sliction V
Controller
Non-lineai' element
(+W
Figure 2. Process control loop in presence of sticky control valve.
Stiction Non Linearity
Plant
Figure 3. Process control loop with a compensator.
below^: X{t):
x[t-\) u{t)
if\u{t)-x{t-l)\ otherwise
(1)
Here x{t) and x{t — 1) are present and past stem movements, u{t) is the present controller output, and W is the valve stiction band. The stiction model given by Equation 1 coincides with the industrial procedure used for measuring stiction and the readers are referred to [6] for a detailed discussion on the applicability of this simple model for modeling stiction. For processes other than flow loops, the identification of the plant's linear dynamics includes the valve dynamics (that occur due to stem and plug movement, see Gp in Figure 2). This is because the flow through the valve, which is an intermediate variable, is usually not measured. In view of this assumption and combined with the fact that the stiction phenomenon precedes the stem movement, the stiction nonlinearity and the plant dynamics can be represented in separate blocks. This is depicted in Figure 3. Here ysp is process set-point (SP), y is process output (PV), e is the error (SP - PV), m is the controller output, f^ is the compensator output, u is the additive signal (m + fk) that is the input to the valve and x represents the predicted stem position obtained using the stiction model. 2.2. Problem formulation The requirements of an ideal stiction compensator can be translated into a meaningful objective function and realized using an optimizer. A possible objective function is: min J - XIISEY + X2Var{X) + X3<^{X)
(2)
Fk
Here, an optimization formulation that minimizes the objective function J over a defined prediction horizon is posed for designing the compensator signal (Fk). The first term in the objective function J is the integral square error (ISEY) of PV (with respect to set point), the second term addresses the valve stem variability Var{X), and the third term includes valve aggressiveness ((|)(X)). F and X are vectors obtained over a defined prediction horizon (p). A,i, A,2 and A-3 represents either the cost associated for maintaining the product quality or the penalty for each term
1236
R. Srinivasan and R.
Rengaswamy
in J. A compensating signal that minimizes J is the best possible signal that will meet the requirements of an ideal compensator. However, formulating such an objective function requires several assumptions to be made. These assumptions are listed below: 1. The plant model Gp is available. 2. The controller (G^) structure and its parameters are available. 3. Stiction is already detected. 4. Stiction severity measure d is ascertained a priori. With these assumptions, the optimization formulation is formally stated as: minJ
-
XxISEY + X2Var{X) +
'k2>
(3)
Uk-i = GcCk-i+fk-i
(4)
ek = ysp-Jk x{t) = ^{u{t),x{t-l),d)
(5) (6)
{ypred)k
=
GpXk-l
(7)
{ypred)k+p
=
GpXk+p-l k+p Y. {{ypred)i-ysp? i=k+l
(8)
ISEY
Var{X)
=
= variance{xi),i = k-{-l....{k-^p-l)
^{X) = 100* ( 1 - - ^ ) , p-l X
=
{Xk,Xk-\-l,....:Xk+p-l)
Fk
=
{fk,fk+\i'-"ifk+m-\)
(9)
(10) (11)
where, p is the prediction horizon, m is the control horizon, x denotes the predicted stem movement using the nonlinear transformation 9{^ (simple stiction model given by Equation 1) and Ut is the total number of switches in the signal between Xt and Xt^p. The stem aggressiveness denoted as (|)(X), is computed as a signal friendliness factor (see [7] for definition). The friendliness factor for the stem denotes how fast the stem changes, a value of (|) ?^ 0 indicates that the stem changes its position at every time instant and a value (j) ?^ 1 indicates that the stem changes it position only at few time instances over the time duration considered. At every time instant, a set of 'm' compensator moves are computed and similar to the MPC concept, only the first compensator move is added to the PID controller output. Since, the stiction model fA^is discontinuous and the stem friendliness factor ((|)(X)) does not have a closed form, an approximate numerical approach is used to solve the above nonlinear optimization problem. 3. Simulation results 3.1. Simulation example Consider a closed loop process with ^ , , 0.009U-i-h0.0082z-2 ^ ^ ^ 16-27.53^-1 + 11.81^-2 ^^(^^^l-1.724z-i+0.748z-i ^^^^^ ^ T^F^
^^'^
Integrating Stiction Diagnosis and Stiction
Compensation
^/WVVVV---=Tr^ Compensation started at time = 120 seconds
jlj
1237
""•
Compensation started at tinfe t = 120 S(
set-npint Runi Run 2
Umm^ 9 (sacs)'w
toJ ^"rimo (secsy^
^^^
I ^"^imefsecsy^
Figure 4. Results for optimization approach for compensation, (a) Process output and (b) ControUer output. The compensation started at time 120 seconds
Figure 5. Results for optimization approach for compensation, (a) Compensator signal, (b) Valve input obtained after addition of compensating signal to controller output and (c) Stem position.
sampled at every second. The loop oscillates due to the presence of stiction. The stiction is simulated using the simple stiction model given by Equation 1, with a stiction band d = 0.5. 3.2. Results Two simulations were performed to highlight the usefulness of the optimization approach. The optimization approach used the 'fmincon' algorithm of the MATLAB optimization toolbox used. The parameters for both the simulations are given in Table 1. Figures 4 and 5 show the comparison of the results obtained for the two simulations. It is seen that, based on the penalty imposed for each term in the objective function, the duration for the process output to reach its set-point varies. Also, the amount of variability and stem friendliness factor varies based on the weights of X.
Table 1 Parameters used in the simulation for the Optimization approach. Parameters Prediction horizon (p) Control horizon (m) ^1
y^i
h
Runl 40 2 100 0 0
Run 2 40 2 0 100 100
3.3. Discussion It was seen that the optimization approach has parameters that need to be tuned to attain efficient stiction compensation. Two main drawbacks are seen with the optimization approach:
1238
R. Srinivasan and R.
Rengaswamy
1. As the objective function (Equation 3) is non-smooth, the optimizer was not able to attain the global minimum; instead a local solution was obtained. This is evident from Figure 4, where for both runs, the process output failed to reach the set-point. This is because the stem position did not move to the correct steady state value, instead moved the stem close to it with an offset. Also the objective function values obtained for the various compensating signals (simulated as a grid of values for the next two moves) showed that the objective function is generally non-smooth but convex. 2. When the optimization approach was tried on an experimental level system at Clarkson University, the Simulink interface could not solve the optimization formulation between each iteration, due to real-time issues. Alternate non-gradient based optimization techniques that use function evaluation such as DIRECT (Divide RECTangle method). Implicit filtering can be studied to overcome the real-time issues. 4. Summary In this paper, a model based optimization approach for stiction compensation was presented. The optimization approach was observed to provide more trade-off than the 'knocker' approach. Preliminary studies suggest that the model based compensation method can be an useful strategy for stiction compensation. Further analysis of the effect of model plant mismatch, incorrect stiction measure, real time issues on the proposed stiction compensation approach needs to be done before these methods can be implemented online. REFERENCES 1. L. D. Desborough and R. M. Miller. Increasing customer value of industrial control performance monitoring - honey well's experience. Arizona, USA, 2001. CPC-VI. 2. B. Armstrong-Helouvry, R Dupont, and C. C. De Wit. A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica., 30(7): 1083-1138, 1994. 3. A. Kayihan and F. J. Doyle. Friction compensation for a process control valve. Control Engg. Practice, 8:799-812, 2000. 4. T. Hagglund. A friction compensator for pneumatic control valves. Journal of Process Control, 12:897-904, 2002. 5. R. Srinivasan and R. Rengaswamy. Stiction compensation in process control loops: A framework for integrating stiction measure and compensation. Accepted for publication in Industrial and Engg. Chemistry Research, 2005d. 6. R. Srinivasan, R. Rengaswamy, S. Narasimhan, and R. M. Miller. Control loop performance assessment 2: Hammerstein model approach for stiction diagnosis. Industrial and Engg. Chemistry Research, 44:6719-28, 2005b. 7. S. Narasimhan, R. Srinivasan, and R. Rengaswamy. Multi-objective signal design for plant friendly identification. 13th IFAC Symposium on System Identification, 2003.