Comparison of Stiction Compensation Methods Applied to Control

Article pubs.acs.org/IECR

Comparison of Stiction Compensation Methods Applied to Control Valves Bruno C. Silva* and Claudio Garcia* Department of Telecommunications and Control Engineering, University of São Paulo, São Paulo, Brazil ABSTRACT: Control valves are common instruments in industrial settings. As with any device with mobile parts, they suffer from the effects of stiction. Normally, a valve in good state of preservation presents low stiction; however, over time, this nonlinearity tends to increase. The presence of stiction decreases the control loop efficiency and can even cause oscillations in the controlled variable. Despite being the best solution, sometimes removing the valve for maintenance is not possible. In this work, two stiction compensation techniques were enhanced (knocker and modified two-move method). Then, they were tested along with other known methods to compensate for stiction effects in the flow control loop of a pilot plant. In addition, a method for estimating the stiction parameters using the same kind of signal as used by most previous compensators (single step) is proposed.

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addition, the constant reinforcement (CR)8 and knocker9 methods were also chosen. These techniques present the disadvantage of inserting abrupt changes in the control signal, reducing the life span of the actuators. To reduce this side effect, a modified form of the algorithm developed by Cuadros et al.10 was utilized with both stiction compensators. The effect of this algorithm with only a proportional−integral−derivative (PID) controller was also evaluated. The last method studied is a variation of the two-move method,11 proposed by Ely and Longhi.12 This modified version of the two-move method and the knocker method were altered by the authors to try to improve the results obtained.

INTRODUCTION Friction is present in every device with mobile parts, such as control valves. Over time, these moving parts deteriorate, increasing the friction magnitude. These valves are frequently found in process industries as the final control element. The static friction (usually referred to as stiction in the literature) inserts nonlinearities in the process, which reduce the control loop efficiency and can even prevent the process variable from stabilizing at the desired value. According to Srinivasan and Rengaswamy,1 20−30% of control loops oscillate due to stiction or hysteresis in control valves. The same work also reported that 90% of these valves have pneumatic actuators. For this reason, this type of equipment was used in this work. The most effective method of eliminating valve stiction is to perform maintenance. However, this would require stopping the process, which is sometimes viable only in programmed situations. Normally, this only happens in periods of six months to three years,1 which means that the valve might need to operate under these poor conditions for a considerable amount of time. With that possibility in mind, stiction compensation methods have been created to eliminate or minimize the effect of stiction on control valves and, consequently, oscillations in the controlled variable. Although stiction quantification is not the focus of this work, it is necessary to set the compensator parameters. The majority of the proposed quantification methods are nonintrusive, meaning that they use historical process data and do not affect the operation of the plant in any way.2−6 However, to achieve a precise estimation of the stiction parameters, the first method proposed by Kano et al.5 is applied, considering the valve actuator pressure and its stem position (instead of the control signal and the controlled variable). This estimation is then refined by a method proposed in this work. Once in possession of the stiction parameters, it is possible to test the compensation methods and compare their results. The first method chosen for this purpose was the one proposed by Mohammad and Huang,7 which is not actually an algorithm but rather a method to find a tuning for the controller that eliminates or reduces the oscillations in the process variable. In © 2014 American Chemical Society

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STICTION The term stiction was defined by Choudhury et al.3 as follows: “Stiction is a property of an element such that its smooth movement in response to a varying input is preceded by [a static part (deadband + stickband) followed by] a sudden abrupt jump called the slip−jump. Slip−jump is expressed as a percentage of the output span. Its origin in a mechanical system is static friction that exceeds the friction during smooth movement.” Figure 1 shows the input−output relationship in a valve with stiction. Point A represents the moment when the valve stem ceases its movement and the input (control signal or actuator pressure) tries to impose a movement in the other direction. Before the stem starts changing its position again, the input variation must exceed the deadband (AB) plus the stickband (BC). Once the static friction is overcome, the phenomenon called slip−jump occurs (CD), which is a small and fast movement. After that, the valve enters a linear phase and remains in this phase until it stops again. If the stem stops moving but the input tries to induce a movement in the same Received: Revised: Accepted: Published: 3974

July 30, 2013 January 28, 2014 February 5, 2014 February 5, 2014 dx.doi.org/10.1021/ie402468r | Ind. Eng. Chem. Res. 2014, 53, 3974−3984

Industrial & Engineering Chemistry Research

Article

values for the proportional gain (Kc) and the integral time (Ti) reported in Table 2. Table 2. Controller Tunings Obtained by the DS Method gasket material

Kc

Ti

teflon graphite

0.6520 0.7564

3.3090 3.6212

Compensation by Controller Tuning. The first method is actually a retuning of the PI controller, based on the linear model of the process plus a nonlinear element to represent the stiction. The closed-loop transfer function (GCL) of the process is given by GCL(jω) =

direction in which it was moving previously, it is only necessary to overcome the stickband, which is followed by the slip−jump. At point E, the stem movement is reversed; therefore, the deadband and stickband (EF) need to be overcome once again. Consequently, there is a new slip−jump (FG ). Stiction Model. There are many stiction models in the literature. According to Garcia,13 the models proposed by Kano et al.5 and Karnopp,14 along with the model called Lugre,15 are the ones that best represent stiction in control valves. In this work, the Kano et al. model is employed, because it is much simpler to use its parameters to tune the stiction compensators. The model has two parameters. The first parameter, S, is the sum of the deadband and the stickband. Considering that both the input and the output are given in percentages, the stickband and the slip−jump have the same magnitude, represented by parameter J. The estimation of these parameters can be found in Appendix A.

A=

B = −3

teflon graphite

0.880 0.933

3.3090 3.6212

0.44 0.44

(3)

Uc U + c cos 2ϕ + 2Uc sin ϕ − 2(S − J ) cos ϕ 2 2 (4)

⎛U − S ⎞ ϕ = sin−1⎜ c ⎟ ⎝ Uc ⎠

(5)

The process oscillates if Gp(jω) Gc(jω) = −1/N(Uc). Mohammad and Huang7 calculated, for some specific cases, how to avoid or minimize these oscillations in the process, by solving eq 1. For a PI controller and a first-order process with dead time, which is the case in this work, the integral time Ti must be greater than the sum of the process time constant τ and its dead time θ to avoid oscillations. Constant Reinforcement. The constant reinforcement (CR)8 method consists of adding or subtracting a constant value to/from the control signal, depending on the direction of its variation, as in the equation

Table 1. First-Order-Plus-Dead-Time Model Parameters of the Process θ

Uc ⎛π ⎞ sin 2ϕ − 2Uc cos ϕ − Uc⎜ + ϕ⎟ ⎝ ⎠ 2 2 + 2(S − J ) cos ϕ

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τ

(1)

where

STICTION COMPENSATION This section describes all of the compensation methods analyzed. All of the techniques studied require the presence of a proportional−integral (PI) regulator to control the process; therefore, it is first necessary to tune this regulator. To solve this issue, the process was modeled as a first-order plus dead time, as shown in Table 1. The direct synthesis

Kp

1 + Gp(jω) Gc(jω) N (Uc)

where Gp is the process linear model, Gc is the controller transfer function, Uc is the magnitude of the harmonic input to the sticky valve, and N represents the stiction17 as in the equation 1 (A − jB) N (Uc) = − πUc (2)

Figure 1. Input−output behavior of a sticky valve.2

gasket material

Gp(jω) Gc(jω) N (Uc)

S sgn[Δuc(t )] (6) 2 uk(t) is the compensator output, which is added to the controller output uc(t). S is the parameter previously estimated. To avoid fast changes due to noise in the process variable signal, the algorithm is updated every 1 s. The control loop structure, when this compensator is utilized, is presented in Figure 2. Hägglund4 proposed this method to compensate for the effects of backlash and presented a second implementation of this algorithm, considering the error signal instead of the direction of the control signal variation uk(t ) =

(DS)16 approach was used to tune the controller, with the desired closed-loop time constant τCL = 5 s. Note that the process is actually nonlinear, because the control valve characteristic is equal percentage and it suffers the effects of stiction; hence, the model obtained is just an approximation and is valid only in the operating region. The model was obtained excluding the effects of stiction. A controller tuning was carried out for each of the control valves, generating the 3975

dx.doi.org/10.1021/ie402468r | Ind. Eng. Chem. Res. 2014, 53, 3974−3984


Article

acceptable error defined for the method, the higher the probability that the control signal will be frozen; therefore, a lower variation of the control signal is expected. However, higher error values are also expected for the controlled variable. In this work, this parameter was approximately one-half of the maximum peak to peak noise variation of the process variable in a static test. The time at which the error must be below the limit to freeze the control signal and the time necessary to unlock this signal were chosen according to the authors of the original method; specifically, the times are 20 and 4 times the sampling time, respectively. Variation of the Two-Move Method. Srinivasan and Rengaswamy11 developed a technique to compensate for stiction by inserting two movements in the valve stem. When the process variable is oscillating near the set point, the valve is moved away from the null error position, and afterward, it is moved to this exact position. The idea is to reach the position where the process variable equals the set point in the valve linear phase; therefore, it is possible to stabilize at that point. This method is called two-move method. However, it is sensitive to perturbations, and it requires knowledge of the control signal amplitude that reaches the null error position. An alternative method based on the two-move method was presented by Ely and Longhi.12 This algorithm input is the controller output, and the output is the signal sent to the control valve, as presented in Figure 3. The current output depends on the difference between the previous output and the controller current output. If this difference is larger than the stickband, the null error position is assumed to be farther than the slip−jump; therefore, the compensation algorithm follows the controller output. If the difference is smaller than the stickband but greater than a process output band (POB), the stem needs to perform a movement smaller than the slip− jump, which is achieved by using the same principle as used in the two-move method. These two movements are represented by the equations

Figure 2. Control loop structure with the CR method.

uk(t ) =

S sgn[e(t )] 2

(7)

In this work, the first implementation is referred to as CR1 and the second as CR2. Knocker. The knocker9 is a compensation algorithm that inserts pulses in the control signal as in ⎧ ⎪ a sgn[uc(t ) − uc(t p)] t ≤ t p + τk + hk uk(t ) = ⎨ ⎪ t > t p + τk + hk ⎩0

(8)

and has the same structure as shown in Figure 2. In this equation, tp is the start time of the previous pulse. Srinivasan and Rengaswamy,1 after a series of experiments, determined that the best parametrization for this method is to use a pulse period (hk) of 5 times the sampling rate and a pulse duration (τk) of 2 times the same rate. The amplitude of the pulse (a) was originally set as one-half the stickband. However, that result was obtained considering a one-parameter model of the stiction,18 which does not consider the presence of the deadband. To compensate for both the deadband and the stickband, the amplitude used herein was S/2. Control Freezing (CF) Algorithm. Cuadros et al.10 verified that the CR and knocker methods insert abrupt changes in the control signal, even if the valve stem is fixed in a position with minimal error. These changes do not actually affect the stem position and are therefore not necessary. With that in mind, they developed an algorithm to stop the action of the controller and the compensation algorithms when the control loop error is stabilized at a small value. This minimizes the variations in the control signal and preserves the valve actuator. Here, a slightly different version of this algorithm is used, to allow it to be applied even without stiction compensation. If the error is below 0.5% for 10 s, the controller stops at its current output, and the compensation algorithm output is maintained at zero, freezing the control signal (the original method uses the error derivative). This allows the method to be used also with a PI controller alone. If the error stays above 0.5% for 2 s, the previous situation is reverted. Those values were chosen for the process studied in this work. Although Cuadros et al.10 did not name this method, this modified version is referred to herein as CF (control freezing). The definition of these parameters is given by analyzing the process behavior. The greater the

First movement CO(t1) = CO(t0) + sgn[uc(t1) − CO(t0)] [|uc(t1) − CO(t0)| + J ]

(9)

Second movement CO(t 2) = CO(t1) − sgn[uc(t1) − CO(t0)]J

(10)

where CO is the compensator output, uc is the controller output, t0 is the time of the first sample before the first movement, t1 is the time of the first movement, and t2 is the time of the second movement. Finally, if the difference is smaller than the POB, the algorithm output does not change. Note, however, that the methods developed by Srinivasan and Rengaswamy11 and by Ely and Longhi12 do not consider the presence of a deadband. To correct this shortcoming, the CR principle is used here in conjunction with the two-move

Figure 3. Control loop structure with the two-move method. 3976



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Figure 4. Results from the set-point tracking experiment with the PI controller tuned by the DS method (low-stiction valve).

To evaluate each method, four performance indexes were used: integral of the absolute error (IAE), a factor related to the stem position variation (Dv), a factor related to the valve actuator pressure variation (DIP), and the rising time (tr). The first index measures the effect of the algorithms on the process error, whereas the next two are used to evaluate the wear on the valve and its actuator, respectively. These indexes were calculated as follows

method. Because the direction of the movement that needs to be induced in the valve is known, it is possible to compensate for the deadband with the equation uk(tk) = CO(tk) + dir

S−j 2

(11)

where dir is the direction in which the stem needs to be moved (1 for positive movements and −1 for negative movements). Ely and Longhi12 also suggested that a dead zone be inserted in the integral action of the PI controller, to avoid changes due to noise in the signal. In this work, in addition to adding this dead zone, the controller is disabled during the two movements to correct the stem position. During the first movement, the process variable is moved away from the set point, which means that, if the controller were operating normally, the integral action would change the controller output and, after the correction of the position, this new output would change the stem position again (even if the process variable reached the desired value). The duration of the first movement of the correction process was set to be long enough for the stem to complete its movement, whereas that of the second movement was set to be long enough for the process to stabilize. This is a disadvantage of this method, because perturbations will not be compensated during the interval mentioned. Unless the process can safely operate without controller action for a few seconds (in this work, both movements occurred in 6 s), this approach cannot be used.

IAE =

1 Δt

∑ |e(k)|

(12)

where e(k) corresponds to the error between the measured flow and the set point in the kth sampling time Dv =

∑ |x(k) − x(k − 1)|

(13)

where x(k) corresponds to the stem position in the kth sampling time DIP =

∑ |P(k) − P(k − 1)|

(14)

where P(k) represents the pressure in the valve actuator in the kth sampling time. The last index (tr) is defined as the mean of the time needed, after each change in the set point, for the process variable to cross the new set point for the first time. Two types of experiments were used to test the methods presented earlier. The first was a set-point tracking experiment, in which the set point received steps with 5% amplitude every 1200 s. In the second type of experiments, there were no changes in the set point, but the perturbation valve stem position was changed every 1200 s. Set-Point Tracking Experiments. The response of the low-stiction valve with only the PI controller tuned by the DS method (see Table 2) is presented in Figure 4, where both the controlled variable (left) and the control signal (right) are shown. The performance indexes are listed in Table 3. The results for the high-stiction valve are shown in Figures 5−11, and the performance indexes are presented in Table 3. The final objective was that the compensation algorithms provide results similar to those obtained by the low-stiction valve. The high IAE value in Table 3 obtained using only the PI controller with the high-stiction valve was due to oscillations in the process. The increase of Ti decreased the oscillation frequency and amplitude, but the system response became slower. The insertion of the CR1, CR2, or knocker algorithm in the control loop increased the quality of most of the performance indexes, specially IAE, which presented values close to those obtained with the low-stiction valve. However, there was a great

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EXPERIMENTAL RESULTS All of the techniques presented in the previous section were tested in a flow control laboratory, created for the purpose of studying the effects of stiction in control valves. In the pilot plant, water is pumped from a water tank through three control valves (one to create perturbations, one with high stiction, and one with low stiction). The plant has a data acquisition board that collects/sends signals from/to the instruments in the process. Among others, measurements of the flow, valve stem position, and pressure in the valve actuator are available. All of the compensators were implemented in Matlab, which operates in real time when receiving/sending data from/to the data acquisition board. The retuning method7 specifies only that Ti > τ + θ, so the experiments were performed with three different values of Ti: the value obtained by the direct synthesis (DS) method (i.e., Ti = τ), Ti = 3(τ + θ) (denoted as I), and Ti = 4(τ + θ) (denoted as II). All of the other compensation methods operate with DS tuning. 3977



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Differently from the results in the previous subsection, increasing the value of the controller integration time did not reduce IAE. Despite decreasing the oscillation frequency, smooth tunings did not reduce the oscillation amplitude, and the high response time also increased this index. Again, the CR1, CR2, and knocker methods decreased IAE at the cost of a large variability in the actuator pressure. However, when the CF algorithm was inserted, the PI controller with DS tuning without compensation had performance close to that obtained with the compensation methods. In this case, the controller was able to bring the process variable close to the set point after each perturbation, and the CF algorithm maintained the process in this condition until the next disturbance. Even though this combination eliminated the process oscillations (Figure 13), the three compensation methods with the CF algorithm were able to reach lower errors before the algorithm froze the control signal, despite providing higher DIP indexes, indicating more wear on the control valve actuator. In this case, the CR2 method presented the lowest IAE of all tests with the CF algorithm. Even though the IAE index with the CR2 method without CF was the lowest, the corresponding Dv and DIP indexes were much higher than when the CF algorithm was used, thus demonstrating once again the benefits of using such a technique.

Table 3. Performance Indexes from the Set-Point Tracking Experiments with the Low- and High-Stiction Valve (Teflon and Graphite Gaskets, Respectively) method

IAE (%)

Dv (%)

DIP (%)

tr (s)

PI (DS) - low stiction PI (DS) PI (I) PI (II) CR1 CR2 knocker PI (DS) + CF PI (I) + CF PI (II) + CF CR1 + CF CR2 + CF knocker + CF two-move

0.4122 1.8996 1.3008 1.534 0.3711 0.3860 0.4215 0.8556 1.1414 1.2718 0.4771 0.4117 0.4169 0.4651

78.41 180.90 101.25 84.54 110.28 122.39 118.69 85.55 89.74 87.31 81.67 100.25 84.79 120.68

148.33 786.86 187.91 163.47 2625.03 3108.35 1736.22 258.83 153.69 139.42 225.42 363.10 228.41 285.31

19.87 24.62 74.50 98.62 13.625 16.87 14.87 38.00 81.88 100.25 14.00 13.50 16.62 13.25

increase in the variation of the valve actuator pressure, meaning that the equipment life span might suffer a considerable reduction. Adding the control freezing algorithm to these compensation methods maintained the good results for IAE, Dv, and tr and decreased DIP compared with the results obtained using only the PI controller. Adding the CF algorithm to the PI controller alone also generated an improvement in the control efficiency. The method based on the two-move method presented indexes similar to those obtained with the CR1, CR2, and knocker with the control freezing algorithm. The CF algorithm also improved the results of the PI controller without compensation algorithms. The cause of this improvement can be visualized in Figure 5. When the controller was operating alone, the process variable was sometimes stabilized at a value close to the set point; however, because of the signal noise or a small offset, oscillations started after some time. When CF was present, the freezing of the control signal prevented oscillations from occurring. Regulatory Experiments. As in the previous experiments, the regulatory experiments were carried out with all of the methods for the high-stiction valve but with only the PI controller tuned by the DS method for the low-stiction valve, to be used as a reference. The results are presented in Figures 12−19 and summarized in Table 4. In this case, because there was no change in the set point, the rising time was not considered.

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CONCLUSIONS Detuning the controller by increasing Ti did not prove to be an efficient solution. The CR1, CR2, and knocker methods presented low IAE values at the cost of very high DIP values, when compared with the PI controllers with different tunings. They improved the performance of the controlled variable but greatly reduced the life span of the valve actuator. The wear on the valve itself, however, did not change much, because, after a low error position was reached, the fast changes inserted by the compensators in the actuator pressure were not sufficient to move the valve stem (because the controller output had small variations). With the aim of reducing the high variability of the actuator pressure, the original CF algorithm was created. The insertion of this algorithm normally caused an increase in the IAE index of the CR1, CR2, and knocker methods, taking into account that it considers a band of acceptable errors. On the other hand, the variability of the control signal was greatly reduced, which caused a significant improvement in the Dv and DIP indexes. In most cases, the insertion of the CF algorithm in the tests with PI controllers alone decreased the IAE as well as the Dv and DIP indexes, as it was able to stop the oscillations of the controlled

Figure 5. Results from the set-point tracking experiment with a PI controller tuned by the DS method, using or not using the CF algorithm (highstiction valve). 3978



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Figure 6. Results from the set-point tracking experiment with a PI controller with tuning I, using or not using the CF algorithm (high-stiction valve).

Figure 7. Results from the set-point tracking experiment with a PI controller with tuning II, using or not using the CF algorithm (high-stiction valve).

Figure 8. Results from the set-point tracking experiment with the CR1 method, using or not using the CF algorithm (high-stiction valve).

Figure 9. Results from the set-point tracking experiment with the CR2 method, using or not using the CF algorithm (high-stiction valve).

variable in most cases. If the process set point was constantly

Overall, when considering all combinations, CR1, CR2, and knocker with CF as well as the two-move method presented results for the high-stiction valve close to those obtained for the low-stiction valve, which was the proposed objective. Despite

changed or there were constant perturbations, the CF algorithm had little effect on the system. 3979



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Figure 10. Results from the set-point tracking experiment with the knocker, using or not using the CF algorithm (high-stiction valve).

Figure 11. Results from the set-point tracking experiment with the two-move method (high-stiction valve).

Figure 12. Results from the regulatory experiment with the PI controller tuned by the DS method (low-stiction valve).

Figure 13. Results from the regulatory experiment with the PI controller tuned by the DS method, using or not using the CF algorithm (highstiction valve).

the controller for short periods of time. The PI controller with DS tuning and the CF algorithm also showed good results in the regulatory case, but not in the set-point tracking case. Based on the experiments performed, we conclude that the first three

providing results similar to those obtained with the other compensation methods (with the CF algorithm), the improved two-move method is harder to implement, and if the modifications proposed here are used, it is necessary to disable 3980



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Figure 14. Results from the regulatory experiment with a PI controller with tuning I, using or not using the CF algorithm (high-stiction valve).

Figure 15. Results from the regulatory experiment with a PI controller with tuning II, using or not using the CF algorithm (high-stiction valve).

Figure 16. Results from the regulatory experiment with the CR1 method, using or not using the CF algorithm (high-stiction valve).

Figure 17. Results from the regulatory experiment with the CR2 method, using or not using the CF algorithm (high-stiction valve).

combinations cited in the beginning of this paragraph are the approaches recommended for dealing with sticky valves. The techniques evaluated here proved to be able to decrease the effects of stiction in the process, without significantly

impacting the wear on the equipment. The best solution is still to remove the sticky valve for maintenance, but these algorithms allow the process to run without great losses until it is possible to do so. 3981



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Figure 18. Results from the regulatory experiment with the knocker, using or not using the CF algorithm (high-stiction valve).

Figure 19. Results from the regulatory experiment with the two-move method (high-stiction valve).

Table 4. Performance Indexes from the Regulatory Experiments with the Low- and High-Stiction Valves method

IAE (%)

Dv (%)

DIP (%)

PI (DS) - low stiction PI (DS) PI (I) PI (II) CR1 CR2 knocker PI (DS) + CF PI (I) + CF PI (II) + CF CR1 + CF CR2 + CF knocker + CF two-move

0.3412 0.7615 0.7766 1.2813 0.3320 0.3188 0.3861 0.4985 1.0513 0.9008 0.4581 0.3508 0.4546 0.4941

63.3858 60.62 61.57 63.85 95.92 80.63 103.56 64.80 61.84 61.04 71.85 64.62 69.16 99.00

120.3635 308.32 121.85 135.43 2688.26 2763.07 1701.75 119.89 132.36 92.39 191.44 240.60 213.42 356.33

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Figure 20. Algorithm to refine the estimation of the parameter S.

APPENDIX A: ESTIMATION OF THE STICTION PARAMETERS The initial estimation of the model parameters was done by the first method proposed by Kano et al.5 The algorithm considers that the stem is static at the time intervals when the change in the process variable from one sample to the next is less than ε. However, only the intervals in which the maximum variation of

Table 6. Refined Estimation of S

S (%)

ρ

teflon graphite

4.14 19.82

1 1

S (%)

number of iterations

teflon graphite

4.90 18.76

4 6

the control signal is greater than εu and the maximum variation of the process variable is less than εy are considered as intervals in which the stem was not moving due to stiction. Finally, the mean of the maximum variation of the control signal in intervals in which the valve was stuck because of stiction is the estimated value of S. The method does not calculate J. The authors also suggested the calculation of the index ρ, which is

Table 5. Results from Kano et al.’s Identification Method gasket material

gasket material

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Figure 21. Input−output graphic of the control valves.

Table 7. Refined Estimation of J gasket material

J (%)

number of iterations

teflon graphite

0.66 1.03

5 5

generate movement in the stem, whereas the opposite must occur in the upper limit. In this work, the value used for H was 20% of the estimation of S obtained by Kano et al.’s method. The value of p represents the present size of the search region, and it is divided by 2 after each iteration. When the search region is smaller than h, the algorithm is stopped. In this work, h = 0.1% was used. The results are reported in Table 6. A visual analysis of the input−output graphs of both valves (Figure 21) leads to the conclusion that the stickband is small, because the slip−jump phenomenon can not be seen. With that in mind, an altered version of the refining method described previously was used to estimate parameter J. The initial estimation was considered to be J = 1.5%, and H = 1.5% was chosen, which means that the search region was from 0% to 3%. However, the step experiment was changed, so that the step was applied in the direction of the last valve movement. The value of h was maintained at 0.1%. This procedure returned the values listed in Table 7. If the valve is operating in a process, it is necessary to estimate the parameters S and J based on historical data, using nonintrusive methods,2−6 employing the control signal (uc) and the controlled variable (pv).

the relation between the amount of time the valve is stationary due to stiction and the total amount of time during which the valve is stationary. The closer ρ is to 1, the higher the probability of the process to be affected by stiction. To change the control valve stem position through electrical signals, a current-to-pressure converter is used. To remove the influence of both the converter and the process dynamics, the method described was applied considering the pressure in the valve actuator and the stem position, instead of the control signal and the process variable. Two valves were subjected to this identification process, one with teflon gaskets (low stiction at ambient temperature) and one with graphite gaskets (high stiction at ambient temperature). Applying this algorithm to the response of these valves to a triangular control signal provided the results reported in Table 5. The values obtained were then refined by the method proposed in the next paragraph. In the beginning of this section, S was defined as the sum of the deadband and the stickband, which corresponds to the maximum possible variation in the valve input, after a reversion in its movement direction, without altering the stem position. To find this value, a step experiment is proposed after a reversal in the valve direction. This test is intrusive and is thus performed if the valve is not in normal operation, that is, if it is in a bench or installed in the process but not actuating in the manipulated variable. It also requires that the stem position and the pressure in the valve actuator be measured. This kind of experiment was chosen because most of the compensators used in this work insert fast changes in the control signal; therefore, the estimation was made with a step signal. Basically, the method aims to find the highest step amplitude that does not change the stem position after a direction change (valve reversal). To make this process faster, the same concepts as employed in a binary search were used, decreasing the search region by half at each iteration. The diagram in Figure 20 shows the refining algorithm. The amplitude of the first step in Figure 20 corresponds to S estimated by Kano et al.’s method. To find S, it is necessary to define a search region and a stopping condition, which are represented by H and h, respectively. The search is conducted between the limits S + H and S − H; therefore, to make sure that the real value for S is within these limits, the step experiment with an amplitude equal to the lower limit must not

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Comparison of Stiction Compensation Methods Applied to Control

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