Novel Model-Free Approach for Stiction Compensation in Control

Article pubs.acs.org/IECR

Novel Model-Free Approach for Stiction Compensation in Control Valves Marco Antônio de Souza L. Cuadros,*,† Celso J. Munaro,‡ and Saul Munareto† †

Instituto Federal do Espírito Santo, Campus Serra Rodovia ES-010, Km 6,5, Manguinhos, CEP 29164-231, Serra, Espírito Santo, Brazil ‡ Departamento de Engenharia Elétrica, Universidade Federal do Espírito Santo, Avenida Fernando Ferrari, 514, CEP 29075-910, Vitória, Espírito Santo, Brazil ABSTRACT: Stiction in control valves is a frequent cause of loop performance deterioration. The solution is maintenance, but since plant shutdown to perform this task can take a long time, loop performance improvement through stiction compensation affords increased efficiency and profitability by reducing the necessity for unscheduled plant shutdowns. Non-model-based methods add compensating pulses to the control signal, thereby reducing process variability. However, the current practice of this strategy transfers variability to the control valve stem, degrading this actuator prematurely. In this paper, such methods are analyzed and a new method for reducing both process variability and valve stem actuation is proposed. The essence of this new method is to add the pulses only when they are required for reduction of process error. The compensation algorithm presented can handle set point changes and perturbations as is illustrated via simulation and through application to a pilot plant flow loop. The proposed method’s performance is measured using integral absolute error and valve reversal indexes. It produces better results than similar methods found in the literature.

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INTRODUCTION Oscillations are a common type of plant disturbance and have causes such as aggressive controller action, disturbances, and nonlinearities. The nonlinearities in control valves have a significant role in poor process performance. The valve problem most commonly reported is stiction, which produces limit cycles in process variables, as shown in ref 1, increasing the process variability and thereby worsening performance. Strictly speaking, all control valves are affected by stiction, but while some may have a value that is acceptable, others require maintenance. A Canadian paper mill audit indicated that about 30% of all control loops suffer from these problems.2 A poorly performing control loop can result in a disrupted process operation and degraded product quality as well as higher material and/or energy consumption, in that way decreasing plant profitability.3 The frequency and amplitude of the oscillation depend on the degree of the stiction. When only the dead band is present, oscillation occurs in the case of integrating processes controlled by PI controllers.1 Stiction effects can be eliminated by maintenance, but part of the production line must be stopped for this. Several stiction compensation methods have been proposed to allow continued operation of sticky valves with better performance until the next planned production stop. The literature presents some noninvasive techniques for stiction detection4−8 and quantification9−11 in control loops, using the controlled variable (PV) and the controller output (OP). These techniques are useful for control valve maintenance planning during the regular production stops which typically are required at 6 month to 3 year intervals.12 Once stiction is detected, it is desirable to improve the process performance by applying stiction compensation techniques, in that way prolonging the interval between shutdowns. © 2012 American Chemical Society

Two basic approaches to compensate the effects of stiction in electromechanical systems, called “dithering” and “impulsive control”, were presented in ref 13. The application of dithering in pneumatic control valves does not produce good results, because they filter high frequency signals. Similar difficulties arise with the impulsive control technique. Later Kayihan and Doyle14 proposed a method based on input−output linearization (IOL) and Hägglund15 presented a method called “Knocker”. Subsequently, Ivan and Lakshminarayanan16 proposed a method called “constant reinforcement” (CR) for stiction compensation. This method is similar to backlash compensation as discussed by Hägglund,17 since in both the compensating signal is calculated as the product of a constant and the variation of the signal of the output controller. In the first method this constant is chosen to overcome the stiction, while in the second method it is chosen to overcome the backlash. The term “backlash” in the context of linear motion control valves is interpreted as the dead band. The objective of these methods is to improve the performance of the process variable (PV), but this is achieved at the cost of increasing stem movement, which results in premature valve degradation. Then, Srinivasan12 proposed the two-move method which reduces the transfer of variability of PV to the valve stem. This method is based on the one parameter stiction model. It is revisited in this paper; it is shown here that the knowledge of the steady-state stem position of a control valve that arrives at PV = SP (set point) is not easily obtained. Received: Revised: Accepted: Published: 8465

July 14, 2011 May 25, 2012 May 31, 2012 May 31, 2012 dx.doi.org/10.1021/ie2015262 | Ind. Eng. Chem. Res. 2012, 51, 8465−8476

Industrial & Engineering Chemistry Research

Article

Figure 1. Typical input−output behavior of a valve.

where m is the mass of the valve’s moving parts, x is the stem position, Fpressure = SaP is the force applied by the actuator which depends on the diaphragm area Sa and the air pressure P, Fspring = Kmx that depends on the spring constant Km, and Ffriction is the friction force given by

A compensation procedure that does not require knowledge of the plant, does not result in increased variability in valve stem movement, and which can handle set point changes and disturbances is highly desirable. This paper proposes a procedure which has those characteristics. The paper has been organized as follows: the modeling of stiction is briefly reviewed, followed by a section with a description and comparison of the methods for stiction compensation in pneumatic control valves. The next section describes the application of the proposed method in simulated examples. The validity of the proposed compensation method is then demonstrated by its application in such simulated examples and in a pilot plant. Conclusions are provided in the final section.

2 Ffriction = ⎡⎣Fc + (Fs − Fc)e−(v / vs) ⎤⎦ sign(v) + Fvv

where Fc is the Coulomb friction coefficient, Fs is the static friction coefficient, v is the stem velocity, vs is the Stribeck velocity, and Fv is the viscous friction coefficient. The Karnopp model defines an interval around v = 0, creating a dead zone for |v| < DV, with DV = 0.6vS = 0.000 015 24 m/s.18 The control valve behavior shown in Figure 1 was simulated using the parameters shown in Table 1. The parameters Sa, m, k, and vs were extracted from ref 18, and the parameters Fc and Fs were chosen to obtain a certain level of stiction. The value of the viscous coefficient friction in ref 18 is 612.9; however, Fv was chosen differently from the original value to provide a more realistic time constant of 0.095 s (the time constant is 0.012 s using Fv = 612.9) to the valve. The signature of this valve via simulation is shown in Figure 1, where the parameters S and J (slip jump) are shown. The parameter S represents the behavior of the valve when it is not moving; this feature is present in each reversion of the sticky valve. The parameter J represents the abrupt release of potential energy stored in the actuator chambers due to high static friction in the form of kinetic energy as the valve starts to move.1 These two parameters are related to the data-based model proposed by Choudhury,1 and can be obtained from Figure 1: S = 16% and J = 4%. They are used in the compensation methods addressed in this work. They can also be obtained directly from the model parameters. Since the parameters S and J are commonly used to quantify stiction in the literature, their usual values will be used for simulations and the parameters Fc and Fs that quantify stiction in the Karnopp model will be computed based on these values.

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STICTION MODELING Models based on physical principles as well as empirical or datadriven ones have been proposed to simulate stiction. In a Table 1. Parameters of the Simulated Valve parameter

value

Sa, area of actuator diaphragm (m2) m, mass of moving parts of the valve (kg) k, spring constant (N/m) Fc, Coulomb friction coeff (N) Fs, static friction coeff (N) Fv, viscous friction coeff (N s/m) vs, Stribeck velocity (m/s)

0.064 52 1.361 52 538 320 533 5000 0.000 254

comparison of eight friction models reported in ref 18, it was concluded that the Karnopp model reproduced the expected behavior, mainly stick−slip, of pneumatic control valves. In this paper, the Karnopp model of friction19 is used for simulations. The force balance equation is18 m

d2x = dt 2

∑ forces = Fpressure − Fspring − Ffriction

(2)

(1) 8466

dx.doi.org/10.1021/ie2015262 | Ind. Eng. Chem. Res. 2012, 51, 8465−8476


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Hägglund15 proposed the compensator named “Knocker”, which uses a sequence of pulses of relatively small energy. Pulses of equal magnitude and duration in the direction of rate of change are added to the control signal. The added signal uk(t) is shown in Figure 2 and is given by eq 3; these pulses are continuously applied. It is characterized by three parameters: the time between each pulse (hk), the pulse amplitude (a), and the pulse width (τ). In eq 3 tp is the time of onset of the previous pulse. Hence, the sign of each pulse is determined by the rate of change of the control signal uc(t). Industrial field tests have shown that friction compensation results in a drastic improvement in control performance. However, the Knocker causes aggressive moves of the valve stem.12

METHODS OF STICTION COMPENSATION Different techniques have been recently proposed for stiction compensation in pneumatic control valves. This section briefly

Figure 2. Knocker.

Table 2. Comparison of Stiction Compensation Methods

method

improves performance of PV

IOL Knocker CR two move

× × × ×

reduces variability of valve stem movement

does not require information in addition to stiction

handles SP changes and disturbances

× ×

× × ×

×

⎧ ⎪ a sign(uc(t ) − uc(t p)) t ≤ t p + hk + τ uk(t ) = ⎨ ⎪ t > t p + hk + τ ⎩0

(3)

In ref 16 a method called “constant reinforcement” (CR) was proposed for stiction compensation, which is given by

×

ui(t ) = γ sign(Δu)

describes the methods of stiction compensation in pneumatic control valves commonly found in the literature and provides a comparison of their principal advantages and disadvantages. Kayihan and Doyle14 proposed a local nonlinear control for a process control valve that has been proven to be more efficient than other linear methods such as the PID controller. However, it requires the knowledge of all states obtained through the use of sensors or an observer. An observer requires knowledge of the model parameters, which are usually not available. It is also important to note that this nonlinear method was proposed for implementation in the positioner and not in the loop controller. In the case of rotary control valves, loop controller implementation can provide better results because the variations of valve stem actuation do not necessarily propagate to PV. Since the position sensor is attached to the stem, the presence of backlash in the mechanical couplings can prevent the small movement detected by the sensor from reaching the valve plug, mainly in rotating valves.

(4)

where γ is the estimated stiction and Δu = u(k) − u(k − 1). This compensation is similar to the backlash compensation discussed in ref 17, where the use of derivative of the error (SP−PV) was evaluated. This method also produces a noticeable reduction of PV variability, but at the expense of greatly increasing the variability of the valve stem position. This method adds pulses continuously to the signal control, and there is not a stop condition. Srinivasan12 proposed a method called “two move” to reduce the variability of PV and also the variability of the valve stem position. This is done in two movements: the first compensating signal moves the stem from its stuck position and the second brings the stem to its steady-state position so that PV converges toward SP. However, this method requires knowledge of the value of the control signal to eliminate steady-state error. It so happens that this information is rarely known for a reason such as this: the loop to be compensated is oscillating so that steady-state

Figure 3. Simulation using Knocker. 8467



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Figure 4. Simulations using CR method.

show that the Knocker and CR methods decrease the error of the process variable but produce great variability in valve stem position. However, one can observe that Knocker keeps the valve stem in the same position for a longer period (at t = 168 s) than the CR. During these time intervals the variation in PV is only due to the noise (see t = 168 s in Figure 3). Furthermore, when using CR the results are clearly worse than those obtained using Knocker. This worsening results from the higher amplitude and duration of the pulses which are added to the PI controller signal and which keep the valve moving constantly. Since some error exists, the integral action of the PI controller eventually produces larger variations in the error, although they are always smaller than the amplitude of the error without a compensator. The variability of valve stem movement using the above methods is not only found in simulations. The same effect was observed in ref 9 using Knocker in a real plant, and will be observed later in this study in the use of a flow loop from a real pilot plant.

relationships cannot be obtained and the controller output to make PV converges to SP depends on the process nonlinearities and gain. The presence of disturbances and set point changes will certainly bring the oscillation back after compensation, and the PID controller must bring the process to stationary oscillation for the compensator to be activated again. In Table 2 the compensation methods reviewed above are compared. It can be observed that, although all the methods improve the performance of PV, none of the methods also improves the variability of the movement of the valve stem without requiring knowledge of all states or of the value of the control signal to eliminate steady-state error. The most desirable method would be one having all of the characteristics shown in Table 2. Knocker and CR are simple to implement, failing only to improve the variability of valve stem movement. The application of Knocker and CR methods is shown in Figures 3 and 4 respectively; the lower panels of these figures show the valve stem position (x). The parameters of the simulated valve are shown in Table 1, and the process is given by G (s ) =

1 −0.1s e s+1

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PROPOSED STICTION COMPENSATION METHOD In this section, the analysis of the section Methods of Stiction Compensation will be used to propose a new method that meets all the characteristics shown in Table 2. The essence of the method lies in the fact that when the Knocker or CR compensator is applied, after some time the absolute error is minimum and, if there are no disturbances or set point changes, the compensating pulses are no longer needed. Of course, when these conditions are not met, the compensating pulses should be resumed. The questions posed are the following: (1) How can one detect these conditions? (2) Will the control valve remain in the desired position when the pulses cease? The first question involves a problem inherent to optimization algorithms; i.e., when is the minimum objective function attained? In our case, the minimum absolute error is sought, and the derivative of the filtered error can be used to detect it. If the maximum derivative of the filtered error during a given time interval is less that of a threshold, the minimum absolute error was found and the compensating pulses should stop. In the case of the second question, the amplitude of the pulses must be considered. A single pulse of considerable amplitude can

(5)

with the PI controller given by ⎛ 1 ⎞ Gc(s) = Kc⎜1 + ⎟ Tsi ⎠ ⎝

(6)

with Kc = 1.74, Ti = 1.14 s, and the variance of the measurement noise was 0.2%. Since the measurement noise is inherent to all measured variables, it is added to the process output. The parameters of the Knocker are hk = 0.5 s, τ = 0.2 s, and a = 0.9S/2, according to the suggestions of Srinivasan and Rengaswamy9 and simulations to achieve the best performance for this compensator. In Figure 3 are shown the results of this method; the compensating pulses start at instant 150 s. The parameter γ of the CR method is γ = S/2 as is proposed in ref 16. The results of the application of this method to the same system of Figure 3 are shown in Figure 4, with the compensating pulses also starting at instant 150 s. One can observe that PV moves constantly due to the aggressive control action of the CR compensator. The results 8468



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for the error δ2 is harder to obtain, since it depends additionally on the value the PV converges to; i.e., a change in SP would require estimating a new threshold. The time interval TP is related to the period hk of the Knocker, and was chosen as TP = 4hk, so that the algorithm checks for four pulses to see if the error does not exceed the threshold. The filter for the error is not critical, since it changes the threshold value δ1 but with negligible effect to detect the instant when the error δ2 cannot be decreased. It is proposed to design a second order Butterworth filter with its parameters related to the period of oscillation of PV. In our simulations, filter bandwidth was chosen to be twice the frequency of oscillation. When the PID controller is disabled, its output value remains unchanged, and this also makes the pulses pause, in accordance with eq 3. The error must be greater than or equal to δ2 during the time interval 4Ts to reactivate the PID. This short interval increases robustness to noise, avoiding having the pulses restarting unnecessarily. In the absence of set point changes or disturbances, the controller output could then be kept constant with minimum error. Since this not a realistic situation, the error is monitored, and if its value exceeds δ2, PID controller action is resumed and, as a consequence, the pulses restart. The implementation of the proposed compensator is shown in Figure 6, and is comprised of eq 3 and the algorithm shown in Figure 5. It receives the error and the controller signal to produce the pulses and to enable the PID controller. The action of enabling and disabling the PID controller can be performed, changing its mode to manual. This action can be also replaced by enabling and disabling the PID output dead band. When the process variable crosses the SP (error crosses zero and changes sign) and as long as SP−PV remains in the dead band, the controller output does not change. This a common strategy used to reduce actuator wear resulting from controller signals in response to noise only. However, the proposed scheme is more robust to outliers since the error signal must be greater than δ2 during four sample intervals for the PID controller to resume operation.

Figure 5. Decision flow diagram of the proposed method.

make the valve move too far and increase the error. A closer look at Figures 3 and 4 allows us to conclude that the Knocker is less aggressive than CR, with several pulses being needed for the valve to move. In Figure 3, at instant 168 s the valve stem stops for 7 s. This illustrates a situation in which the pulses could have been stopped and the error would have remained small. This analysis indicates that the Knocker compensator is the best candidate to answer the second question. Based on the arguments above, the algorithm depicted in Figure 5 is proposed. It is assumed that oscillation was detected, its period of oscillation was measured, and the root cause was found to be stiction. The reader is referred to ref 3 for a review of such algorithms. The minimum error that can be attained using Knocker is unknown, but an estimate for the maximum derivative of the filtered error (ef) is easy to set, turning on the Knocker and computing its maximum value after at least twice the period of oscillation of the PV (see Figure 3). This threshold δ1 depends on the designed filter and the level of noise, but the filter suggested will always give the minimum error δ2 that can be attained. To keep the PID controller disabled, the condition “|e| < δ2 during 4Ts s” (Ts is the sampling time) must be true; if it is false, the PID is enabled again. The absolute value of the error is used in this condition to ensure a quick action, and the period 4Ts s is used to avoid transient values of the error from being considered. A limit

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SIMULATION RESULTS The performance of the proposed compensator was measured using two indexes: the number of valve reversals (VR) to evaluate the variability in valve stem motion and the integral absolute error (IAE) to evaluate the performance of the control loop. The index VR is calculated using N

VR =

∑ sign(|W (k) − W (k − 1)|) k=2

(7)

Figure 6. Block diagram illustrating the proposed compensator. 8469



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Figure 7. Simulation results for the stable process with Knocker.

Figure 8. Part of the simulation given in Figure 7.

where W(k) = sign(xf(k) − xf(k − 1)); xf is the filtered signal of the stem valve position obtained using the Butterworth filter and N is the length of data considered. In the first instant when k = 1, the index VR starts with 0; when the direction of the position changes, the index VR is incremented by 1. The IAE is calculated using IAE =

1 T2 − T1

∫T

T2

1

|e(t )| dt

follows the Knocker is activated until instant 250 s, when only the PI controller acts. At instant 300 s the proposed compensator is activated and remains on until the end of the simulation. The performance indexes can be evaluated in this simulation for the PI controller, for the PI controller plus Knocker, and for the proposed compensator, using time windows of 100 s. We can see that it converges quickly to a position of minimum error using the proposed compensator (Figure 8). The minimum derivative threshold δ1 was chosen to be 0.3, TP = 4hk = 2 s, and 4Ts = 0.2 s, so the error must be greater than δ2 for 0.2 s for the compensator to be reactivated. The algorithm computed δ2 = 0.63, the maximum error in the time windows between the instants 306.8 and 308.8 s (Figure 9). When the compensator is turned off, the position of the valve stem is constant (Figure 8 lower panel), so PV variations come from noise only. The CR compensator can also be used with the proposed scheme. A simulation using CR instead of Knocker is shown in Figure 10. In the instant 150 s only CR was used, and in the

(8)

where T2 − T1 is the time interval considered. The parameters for the model valve are shown in Table 1; the process is given by eq 5 and the controller is given by eq 6. The simulation results for the stable process with the Knocker are shown in Figure 7; the lower panel shows the valve stem position. The simulations were initially carried out using the Knocker compensator with a = 0.9S/2, hk = 0.5 s, and τ = 0.2 s. Until instant 150 s the PI controller keeps a limit cycle; in what 8470



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Figure 9. Details of error, filtered error, and derivative of the error (related to Figure 8).

Figure 10. Simulation results for the stable process with CR.

Table 3. Comparison of Performance Indexes only PI

proposed method with Knocker

PI + Knocker

PI + CR

proposed method with CR

J

IAE (%)

VR

IAE (%)

VR

IAE (%)

VR

IAE (%)

VR

IAE (%)

VR

3 3.5 4 4.5 5 5.5 6

1.16 1.36 1.49 1.65 1.62 1.93 2.04

15 19 22 21 21 25 27

0.34 0.36 0.39 0.43 0.38 0.44 0.44

45 45 46 50 34 43 36

0.26 0.22 0.24 0.26 0.30 0.30 0.30

13 9 8 12 11 6 4

0.24 0.28 0.31 0.35 0.38 0.42 0.45

170 174 180 197 198 198 198

0.28 0.37 0.42 0.48 0.48 0.48 0.59

54 57 53 63 65 110 122

instant 300 s the proposed compensator using CR was activated. More time than required with Knocker was necessary to reach

the criteria to stop the pulses, due to the larger variations in PV caused by CR pulses. 8471



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Figure 11. Box plot for the IAE index.

Figure 12. Box plot for the VR index.

Figure 13. Simulation for set point changes and perturbation.

noise was carried out, since the condition |def/dt| < δ1 for 4TP s (Figure 5) to disable PID is affected by noise. Also, as shown in ref 1, as the relation S/J decreases, the frequency and amplitude

In order to analyze the performance of the proposed compensator using Knocker and CR for different stiction parameters, a Monte Carlo simulation for 10 realizations of 8472



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Table 4. Performance with Uncertainty in S

changed the error increases and the compensator is activated. One disturbance of 2.5% was applied as shown in the block diagram (Figure 6) at instant 250 s and produced the same effect, but this was readily handled by the compensator. Since the parameter a depends on S, the effect of the uncertainty of its estimate on the compensator performance has been studied. The effect of parameter a on Knocker performance was analyzed in ref 9. It was shown that a = S/2 produced, in general, the best integrated squared error (ISE) reduction, but the results were very acceptable using values of a from 0.25S to 0.75S. In the case of our algorithm, the value chosen for the parameter a is 0.9S/2 since it reduced the time to achieve minimum process error, thus providing better performance. We will now analyze the effect of the uncertainty in S on compensator performance. To that end, the valve was simulated using S = 16% and J = 4%, but the estimates of S used for tuning the parameter a were 20, 16, 14.4, and 12%, and a Monte Carlo simulation for 10 realizations of noise was carried out. The performance of the control loop using the proposed method for each S estimate is shown in Table 4, where the mean and the standard deviation values of IAE and VR for the 10 simulations for each case are presented. The test used to obtain these results was the same as that shown in Figure 13. The performance indexes using only the PI controller for S = 16% and J = 4 were IAE = 1.37% and VR = 38. One can see that underestimation of S tends to produce better VR indexes and worse IAE indexes. Overestimates in the value of S produce compensating pulses of higher amplitude, increasing the number of valve reversals. However, in all situations the IAE index was improved when compared to that obtained with PI controller, and for all situations where S was underestimated VR was also improved when compared to VR of the PI controller. This analysis indicates that the algorithm works quite well for variations around the correct value of the stiction, but a reduction of this value is advisable when uncertainty is present. Uncertainties about J are not analyzed individually since J is part of S (S = dead band + J). According to Hägglund,15 Srinivasan and Rengaswamy,9 and Ivan and Lakshminarayanan,16 many integrating and selfregulating processes, with or without dead time may, have their performance improved using the Knocker or the CR compensators. The method here proposed introduces a supervisory level to this kind of compensation, disabling the

proposed method estd S

IAE (%)

VR

mismatch (%) in S

20 17.6 16 14.4 12

0.51 ± 0.042 0.38 0.39 ± 0.063 0.45 ± 0.030 0.59 ± 0.11

302 ± 44 160 74 ± 30 26 ± 5 25 ± 14

25 10 0 −10 −25

of the oscillation increase, resulting in larger values for IAE and VR. The parameters for Knocker and CR were the same as those used in Figures 7 and 10, respectively. Table 3 summarizes the results of these simulations. The dead band was 12% for all values of J, so S = 12 + J was compensated by the algorithms. The mean values of IAE and VR for the 10 simulations are presented. As expected, the IAE and VR tend to increase as S/J decreases. However, for PI + Knocker and for proposed method with Knocker, the relation of VR and S/J does not hold. Also, the presence of extreme values of IAE and VR were observed in the simulations. Considering these facts, box plots were used to compare the performances of CR and Knocker and to analyze the effect of S/J. The box plots represent the distribution of IAE (Figure 11) and VR (Figure 12) for different relations of S/J for the five compensation schemes. The proposed method using Knocker clearly produced smaller values for IAE (Figure 11). Also, the effect of the relation S/J on IAE is smaller in this method when compared with the proposed method using CR, the PI controller, or the PI controller + Knocker. The proposed method using Knocker also achieved the best results for the VR index, as shown in Figure 12. The effect of the S/J relation on VR is smaller in the proposed method + Knocker than in PI + Knocker, PI + CR, or proposed method + CR. These results clearly indicate the proposed method using Knocker as the best candidate to reduce IAE and VR indexes, and this scheme referred to as the “proposed method” will be used from now on. The proposed compensator can handle set point changes and disturbances. The simulation for J = 4 has been chosen, and it was carried out for changes in the set point and disturbances, keeping the same simulation parameters, with results shown in Figure 13. The initial set point is 50%, at t = 130 s it then changes to 55%, and at t = 180 s it returns to 50%. Every time the set point is

Figure 14. Pilot plant. (a) Diagram of the flow control loop; (b) control valve; (c) details of the stem packing. 8473



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Figure 15. PI controller applied to the pilot plant.

valve stem packing. The flow transmitter and the I/P transducer work with 4−20 mA signals. The industrial controller CompactRIO from National Instruments was used to control and to monitor all the signals in the pilot plant as well to implement the compensator proposed in this work. The value of S was estimated using the ellipse method,7 yielding S = 16%, which is confirmed by the amplitude of OP in Figure 15. The value of J was estimated using open loop tests; the valve pressure was increased slowly and, using one sensor position installed in the valve stem, the jumps were measured and reported as J, yielding J = 1.2%. The transfer function of the flow process is

pulses and the action of the PID if they are not able to produce better performance. Therefore, this scheme can be implemented in any control loop for which Knocker or CR produces good results, restricted however to stable processes, since the PID output is made constant for small errors (SP−PV).

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APPLICATION TO THE PILOT PLANT The proposed method was also applied to a flow control loop of a pilot plant (Figure 14). Friction was increased by tightening the Table 5. Comparison of Performance Indexes index

only PI

PI + Knocker

proposed method

IAE (%) VR

0.92 45

0.31 454

0.3 78

G (s ) =

1 e−0.05s 0.6s + 1

(9)

The PI controller is given by

Figure 16. Knocker applied to the pilot plant. 8474



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Figure 17. Proposed method applied to the pilot plant.

Figure 18. Details of error, filtered error, and derivative of the error (related to Figure 17).

⎛ 1 ⎞⎟ Gc(s) = 1.3⎜1 + ⎝ 0.62s ⎠

parameters hk = 0.6 s, τ = 0.3 s, and a = 7%. It is possible to see that the joint action of PI and Knocker tends to keep the valve moving, producing small variations in PV. This method decreased IAE when compared to PI only, at the cost of increasing valve motion variability. Finally, the results using the proposed compensator are shown in Figure 17, with TP = 4 s and δ1 = 0.4. The compensation was also enabled at time t = 50 s, and the details of the error, filtered error, and derivative of the error can be seen in Figure 18. After instant 60 s the derivative of the error became smaller than δ1, so at the instant 64 s the PI controller was disabled. The maximum error in the time window from t = 60 s to t = 64 was 0.4%, and the value of δ2 was set to 1.2·0.4 = 0.48. After instant 64 s, the PI controller and the compensator remained inactive until the SP change at instant 100 s. One can see that the same behavior was shown as for the

(10)

To compare the performance of the process using only the PI controller with the Knocker and with the proposed method, three tests with a sampling time of 0.1 s were made at the pilot plant. In all tests, the SP was initially 45%, at t = 100 s SP changed to 50%, at t = 150 s a perturbation was applied by changing the pump speed from 60 to 65%, and finally at t = 200 s the SP returned to 45% again. In the three cases the indexes IAE and VR were measured from t = 20 s to t = 300 s. The results using only the PI controller are shown in Figure 15. One can see that the limit cycle was always present, with a higher IAE and a lower VR (Table 5). The results using PI controller + Knocker are shown in Figure 16. The Knocker was enabled at time t = 50 s with 8475



Article

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other SP changes and for the perturbation. This evidences the gains introduced by the proposed method, clearly shown in Table 5. The IAE, as expected (see Table 3), is slightly smaller than that for PI + Knocker, but VR is much smaller, even though it is higher than with PI alone. The increase in VR comes from the instants when the Knocker is active. If one expects to reduce IAE without the burden of high valve stem motion variability, the proposed method is the best candidate.

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CONCLUSION In this work, a non-model-based method for stiction compensation for control valves has been introduced. The method is based on the Knocker approach with addition of a level of supervision to analyze process error and to interact with a PID controller. The result is a strategy that can reduce IAE and the number of stem reversals of control valves. Simulation studies have shown that the proposed method has better performance for different levels of stiction when compared with the use of PID and Knocker. The method was also applied to a flow loop of a pilot plant and subjected to set point changes and perturbations. The IAE was similar to that of Knocker, but the number of valve reversals was greatly reduced. This method requires only an estimate of stiction for the Knocker pulses and an estimate of the error derivative achievable using Knocker; both are parameters which are easily obtained with online measurements. The proposed method can be applied to a great variety of processes.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Facitec/Prefeitura Municipal from Serra/ ES for partial support.

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REFERENCES

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Novel Model-Free Approach for Stiction Compensation in Control

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