Reducing wear of sticky pneumatic control valves using compensation pulses with variable amplitude

Preprint, 11th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems June 6-8, 216. NTNU, Trondheim, Norway Reducing wear of sticky pneumatic control valves using compensation pulses with variable amplitude Celso J. Munaro, Gabriel B. de Castro, Filipe Amorim da Silva, Oscar F.B.Angarita, Marcos Vinicios Gomes Cypriano Federal University of Espirito Santo, Vitoria, ES, Brazil (e-mail: munaro@ele.ufes.br). (e-mail: gab.bar.cas@gmail.com ) (e-mail: filipe.amorim.silva@gmail.com ) (email: oscar.molinos@hotmail.com) (email: mvcypriano@gmail.com ) Abstract: The presence of friction in control valves produces limit cycles that reduces the performance of control loops. Once friction is detected, its compensation avoids process stops until the next maintenance stop is performed. Model free methods adding feed-forward pulses to PID controller output have been proposed to reduce the effect of friction. A common drawback in such methods is the increase in the movement of the valve stem. A new method is here proposed to overcome this issue. The amplitude of the pulses vary and becomes zero when a specified limit for the error on the process variable is achieved. Another advantage of this method is its ability to cope with uncertainty in friction, since the amplitude of the pulses pulses vary between limits. The method is illustrated via simulation, and its implementation in a real industrial controller is shown and discussed. Keywords: Friction compensation, nonlinear control, performance monitoring, control valves, PID control. 1. INTRODUCTION The presence of non-linearity in control loops causes oscillations in the process variable called limit cycle. In many cases the corrective maintenance of these equipments is not possible, since the production of the process should stop. The result is the reduction of the overall performance of all control loops that are affected by these oscillations. Friction compensation techniques have been developed to reduce or eliminate oscillations, improving the performance of the control loop until the maintenance can be performed. One of these methods is the knocker, proposed by Hägglund (22). The error is reduced considerably but the valve movement is increased. The Constant Reinforcement method is proposed by Ivan (29). A single constant value is applied every time the control signal changes its direction. Since the energy of the pulses is higher, the valve tends to move more aggressively. To reduce the valve movement, the two-move method was proposed by Srinivasan (28). However, this method requires the knowledge of the value of the pulse to be applied in the second movement to send the valve to the desired position, and this information is hard to obtain with a valve under limit cycle. A method was proposed in Cuadros and Munareto (212) with the same purpose. The pulses applied to compensate stiction were disabled when the derivative of the error was smaller than a threshold, and the integral action was also disabled so that small errors could not bring oscillation back. The last pulse applied before these actions could move the valve and violate the threshold, resuming the pulses. In Arifin (214) the procedure of turning pulses on and off was replaced by application of pulses with amplitude proportional to absolute value of the error. Thus, small errors produce pulses with small amplitudes that are not able to move the valve, that remains in a region of specified error. This method does not work when the amplitude of pulses becomes higher than half the friction and the error keeps increasing proportionally to the amplitude of the pulses. In this situation, the amplitude of the pulses will increase up to saturation and there is no convergence. A new method to overcome these difficulties is proposed here. A search in the amplitude of the pulses is performed and when the corresponding error between process variable and setpoint becomes smaller than a specified threshold the pulses are ceased and the controller action is disabled. Simulations and the application to a real industrial controller illustrates its superiority to other methods. 2. MODEL FREE COMPENSATION OF STICTION The static friction (stiction) model used for simulation was first proposed by Choudhury (25) and then improved by Xie (213). This model uses only two parameters (dead band S and slip-jump J), and requires low computational effort for simulations. Moreover, it was demonstrated in Xie (213) that it can properly represent the behavior of stiction. A well known method that does not require a model for compensation is knocker (Hägglund (22)). Copyright 216 IFAC 389

IFAC DYCS-CAB, 216 June 6-8, 216. NTNU, Trondheim, Norway 1 3 IAE 1 2 1 1.2.4.6.8 1 1 4 1 3 VT 1 2 1 1.2.4.6.8 1 Amplitude of pulses / S Fig. 1. Effect of the amplitude of pulses It consists in the addition of pulses to a PID controller output. These pulses are intended to overcome the existing friction in the control valve. A side effect of their application is an increase in the number of reversals in control valve increasing wear. The choice of the three required parameters for this compensator to improve its performance was discussed in Srinivasan (25). The effect of the amplitude of pulses can be seen in Fig. 1. The upper plot shows the Integral of Absolute (IAE) as the amplitude of the pulses ranges from to S. The abscissa shows the value that is multiplied by S to produce the pulses. N V T = x(i) x(i 1) (1) i=1 The lower plot shows the valve travel, measured using equation 1. One can see that the minimum value of IAE is obtained when the amplitude of the pulses is.5s, as shown in Srinivasan (25). The valve travel increases with the increase in the amplitude of the pulses, and for pulses with amplitude greater than.5s the valve travel tends to increase considerably. The pulses are added to the controller output according to its direction, i.e., if the controller signal is increasing the compensation pulses are added otherwise they are subtracted. Thus, the information of its direction is fundamental for the correct implementation of the method. The use of a filter or the use of a delay of a few sampling times to calculate the direction is advised. If constant pulses are applied (like in Ivan (29)) the conclusions about the effect of amplitude of pulses on IAE and VT are similar. 3. PROSED METHOD The proposed method consists in the application of pulses with decreasing amplitude to bring the process variable to the setpoint within specified limits for the error. The use of a variable amplitude signal to the pulses is twofold: the valve travel is reduced and the possibility of a change in the valve position when the pulses are ceased is reduced. The expected result is the process variable to approach the setpoint, respecting the specified limits for the absolute value of the error, and the pulses to cease, since a dead Fig. 2. Flowchart of the proposed algorithm zone in PID controller is applied to avoid that small errors are integrated and can bring oscillation back. If the process variable exceeds the specified limit, the application of variable compensation pulses is resumed. The proposed algorithm is depicted in Fig. 2. The amplitude of the pulses is given by rs. Each sampling time, the amplitude is reduced by. The parameter r min is chosen.2 and r max is equal to.8. This choices assure pulses with a minimum amplitude (r min S) to have effect on stiction but limited to r max S that does not cause excessive valve movement. The variable LL counts the number of sample times during which the error is smaller than the specified value δ. When LL > Ne, the limit for the absolute value of the error was 39

IFAC DYCS-CAB, 216 June 6-8, 216. NTNU, Trondheim, Norway IAE 5 4 3 PI PI+Variable Ampl. 2 1 PI+knocker 1 2 3 5 4 3 2 1 PI Valve Travel PI+knocker PI+Variable Ampl. 1 2 3 Fig. 3. Integration of proposed algorithm with PID controller Fig. 6. Indices for the simulation comparing three compensation methods 2 1 1 2 94 96 98 1 12 14 16 Absolute value of error.4.3.2.1 94 96 98 1 12 14 16 Fig. 4. Effect of pulses on the error 31 3 δ=.15 δ=.1 δ=.5 SP 29 2 4 6 8 1 12 14 32 3 28 2 4 6 8 1 12 14 32 + 3 28 2 4 6 8 1 12 14 31 MV(Valve movements) 3 29 2 4 6 8 1 12 14 Fig. 5. Simulation achieved and the pulses can cease and the PID action as well. The error is monitored, and if its value is greater than the limit δ the compensation is resumed. The integration of the proposed algorithm with the existing PID controller is shown in Fig. 3. The compensator Fig. 7. PLC and Arduino to emulate control valve 25 2 15 1 5 Response to step input 5 1 15 2 25 3 Fig. 8. Step response of valve+process emulated with Arduino uses the information about error and controller output to generate the pulses. The action to disable the PID controller is implemented according to the existing PID block. The expected effect is that shown in Fig. 3, i.e., to introduce a dead zone before the PID block so that an error smaller than the threshold δ do not produce any action on PID output. 391

IFAC DYCS-CAB, 216 June 6-8, 216. NTNU, Trondheim, Norway 6 4 Response to multiple step input 1 8 6 2 4 2 1 2 3 4 5 6 7 8 9 6 4 2 Valve Signature 1 2 3 4 5 5 1 2 3 4 5 5 1 2 3 4 5 Fig. 9. Response to step and valve signature 6 4 2 5 1 15 2 6 4 2 2 5 1 15 2 Fig. 1. Step response and compensation on instant 8s. 1 8 6 4 2 5 5 5 1 15 2 25 3 35 4 45 5 5 1 15 2 25 3 35 4 45 5 Fig. 11. Compensation for different setpoints 3.1 Choice of parameters The application of the algorithm requires the error specification and two parameters. An estimate for stiction is the amplitude of PID output during the limit cycles. The user must specify the limit δ for the minimum absolute Fig. 12. Test for stiction dependent of position value of the error. A simple way to obtain this value is to use pulses with a constant amplitude of aproximately.5s and to measure the error between the setpoint and the process variable (see Fig. 4). If constant pulses are applied (Ivan (29)), only an estimate for S is required. If knocker is used (Hägglund (22)), the choice of the pulse width and the time between pulses are also required. According to Srinivasan (25), the pulse width is about twice the sampling time, and the time between pulses is about 4-6 times the sampling time of the system. The values of r min and r max are not related to the application, but to the amplitude of S. Thus, the proposed values of.8 and.2 should produce good results in any application. The parameter is related to the settling time of the control loop. The ramp signal should be decreased in a rate that the control loop can react properly. If the inclination is high, the control loop will not be fast enough to respond to pulses during a cycle. On the other hand, if the inclination is low, a long time interval is required to attain the required error, increasing the index IAE. The proposed value for is =.6T s t s (2) where T s is the sampling time and t s is the settling time, which is easily estimated for any control loop. Using this value of, the value r of the ramp will change from r max to r min in t s seconds. The effect of knocker pulses on the error is illustrated in Fig. 4. The constant pulses started on instant 1s, and after 4s the absolute value of the error was smaller than.5. Finally, the second parameter N e must be chosen. This parameter reflects the confidence that, once the absolute value of the error is smaller than δ, after N e it will remain within this limit. A small value for N e can make the pulses start again because the error left the specified bound. A larger value will cause the ramp to keep decreasing, reducing the amplitude of the pulses and its effect on stiction. In addition, the amplitude can restart to its maximum value r max and a new cycle should start. The author s experience has shown that 5 N e 1 produces good results, and its value is not critical. 392

IFAC DYCS-CAB, 216 June 6-8, 216. NTNU, Trondheim, Norway 4. APPLICATION AND RESULTS A simulation was performed to a system given by G(s) = 1.1 25s+1 and a PI controller C(s) =.8+ s. The two parameters model from Choudhury (25) with improvements from Xie (213) was used with S = 3 and J = 1. The sample time was T s = 1s. A uniform random noise with amplitude.1 was added to system output. A knocker compensator with pulse width of 2T s and time between pulses of 3T s was used. The limit for the error was.2. The parameters and N e were 1.2e 3 and 5, respectively. The choice of considers a settling time of 5s. The results from simulation can be seen on Fig. 5. The limit cycles are present until the compensation starts on instant 8s. After approximately 1s the pulses are ceased and the valve stem remains still. The simulation was repeated for 2 different random setpoints and for three situations: PI, PI+knocker, PI+variable amplitude. The indices IAE and VT are measured and plotted via boxplot on Fig. 6. Knocker produces the best IAE with the price of a high valve travel. Valve travel using PI is small, due to limit cycles. However, the IAE is large. The best result considering both indices is the proposed method. A second test was performed using a real industrial controller, the Field Controller Select Freelancer 2 from ABB. The card AI93N for analog input signals and the card AO92N for analog output signals were used. The communication of these cards with the controller is via Profibus D1. Instead of a sticky control valve, a microcontroller (Arduino) was programmed with the two parameters model of stiction, the same used in simulations. This strategy allows testing the compensator for different values of stiction and also, to have different values of stiction according to the position of the stem. An RC circuit produces the dynamics of a flow control loop. The communication between the PLC and the microcontroller is performed using 4-2mA signals. The step response of the valve+process emulated by the Arduino is shown in Fig. 8. A time delay of 1.5s and a time constant of 3.5s were found. The transfer function of valve+process is G(s) = e 1.5s.85 3.5s+1. The valve signature was also obtained, using a model with stiction varying with the valve position (input signal). The applied signals and the valve signature are shown in Fig. 9. For small input values, S = 4. As the input signals approach 1%, the value of S tends to 8. For the first tests, the value of S was fixed in 1 and the value of J in 2. For the tests using PLC, the sampling time was 1s. The specified limit for the error was 1%. The same parameters were used for the knocker, with N e = 1 and = 1e 2 (close to those used for simulations). The value considered in the first tests was S = 1. The result for the proposed method is shown in Fig. 1. The compensation started on instant 8s and and just after 1s was able to stop the limit cycles keeping close to SP (< 1%). A sequence of step changes, from 3% to 8%, and then back to 3% was performed (Fig. 11). Everytime the setpoint changes the limit on the error is violated and the compensation resumes, bringing the error within the limits again. The final test was performed considering that the amount of stiction depends on the input signal (valve position). The value of S in the microcontroller is given by S = 4 +.4U, where U is the input ranging from to 1%. Thus, for = 3, S = 5.2. For = 8, S = 7.2. This behavior is very typical in control valves (see e.g. Mohammad (212), pp.1812). The value considered for the amplitude of the pulses was S = 1. Since the decreasing ramp seeks the amplitude to reduce error, the compensation algorithm performed very well in all operating ranges. 5. CONCLUSION In this work, a new method for stiction compensation using pulses with variable amplitude has been proposed. The method was applied to a simulation example and compared to commonly used methods, produced better results when considering the IAE error and valve travel. The application to an industrial controller was also performed, compensating stiction emulated in a microcontroller. The compensation was applied in a situation were the stiction changes according to valve position, and even in this case its performance was good. Besides its good performance when compared to others, the method can cope with uncertainty in the stiction values. Its implementation in a commercial PLC confirms also its simplicity. REFERENCES Arifin, B.M.S., M.C.C.M.S.S. (214). A model free approach for online stiction compensation. IFAC World Congress, 5957 5962. Choudhury, M.A.A.S., T.N.S.S. (25). A friction compensator for pneumatic control valves. Control Engineering Practice, 13, 641 658. 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