Control Valve Stiction Compensation - Part II: Performance Analysis of

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 11326−11337

Control Valve Stiction Compensation - Part II: Performance Analysis of Different Stiction Compensation Methods Ahaduzzaman Nahid, Ashfaq Iftakher, and M. A. A. S. Choudhury*

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Department of Chemical Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh ABSTRACT: Control valves are important elements of control loops. Stiction in control valves limits the performance of control loops. It decreases the life of control valves. Minimizing the negative impact of sticky control valves can improve the performance of control loops. This is the second part of a twopart study on control valve stiction compensation. In the first part, a novel stiction compensation method has been proposed. This second part compares the performance of the proposed stiction compensator described in Part I with six other important stiction compensators that have appeared in the literature. The proposed compensator performs better than any of the other six compensators.

1. INTRODUCTION

and critically compares the performance of all these stiction compensation methods. The paper has been organized as follows. Different stiction compensation methods are described in section 2, while section 3 compares the performance of the available stiction compensation methods, using MATLAB Simulink software. Section 4 presents the experimental evaluation of two best methods. Section 5, which is the conclusion of the paper, summarizes the work.

Constrained resources, stringent environmental regulations, and tough business competition have resulted in efficient manufacturing operations, in terms of energy usage, raw material utilization, superior product quality, and plant safety.1 Most of the modern plants are automated to achieve these goals. Control loops are essential elements of automatic process plants. Large-scale, highly integrated process plants include hundreds or thousands of control loops.2 The aim of each control loop is to safely and efficiently maintain the process at the desired operating condition. Poorly performing control loops can cause disrupted process operation, degraded product quality, and higher material and energy consumption.3 Control-loop performance has been an active area of research in academia and industry for the last few decades.4 Control loops often suffer from poor performance, because of process nonlinearity, valve nonlinearity, process disturbances, poorly tuned controllers, and poorly configured control strategies. These problems often surface as oscillation in process variables. Among various valve nonlinearity, stiction is the most commonly encountered one.5 Many methods have appeared in the literature to find the control loops with sticky control valves. Once sticky valves are identified, they are to be sent for maintenance, but that requires shutdown of the plant. An alternative is to minimize or compensate the effect of stiction. Over the last two decades, several stiction compensation methods have appeared in the literature, such as the knocker method,6 the two-move method,7 the constant reinforcement method,8 the improved knocker method,9 the model-free stiction compensation method,10 and the fourmove method11,12. These methods are described briefly in the next section. Part I of this study describes a novel method for stiction compensation.13 This second part of the study analyzes © 2019 American Chemical Society

2. BRIEF DESCRIPTION OF STICTION COMPENSATORS The purpose of control valve stiction compensation is to increase the control loop performance10 and thereby continue production with minimum impact of valve stiction. To deal with the valve stiction problem, the first step is to detect sticky control valves and then quantify the severity of the stiction. Before sending sticky valves for maintenance, stiction compensation can be employed as an attractive alternative until the next shutdown occurs. The important stiction compensation methods appeared in the literature are as follows: • The knocker method by Hägglund in 2002.6 • The two-move method by Srinivasan and Rengaswamy in 2008.7 • The constant reinforcement method by Xiang Ivan and Lakshminarayanan in 2009.8 Special Issue: Sirish Shah Festschrift Received: Revised: Accepted: Published: 11326

January 18, 2019 May 28, 2019 May 28, 2019 May 28, 2019 DOI: 10.1021/acs.iecr.9b00335 Ind. Eng. Chem. Res. 2019, 58, 11326−11337

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Industrial & Engineering Chemistry Research • The improved knocker method by Arumugam et al. in 2014.9 • The model-free stiction compensation method by Arifin et al. in 2014.10 • The four-move method by Bacci di Capaci et al. in 2016.11,12 • The Variable Amplitude pulse method by Arifin et al. in 2018.14 A brief description of the above methods and the newly proposed stiction compensator that was described in Part I of this study13 is provided below. 2.1. The Knocker Method by Hägglund6 (2002). The idea behind the stiction compensation procedure proposed by Hägglund6 is to add short pulses of equal amplitude and duration to the control signal to move the valve from the stuck position. The direction of the pulse signal is dependent on the rate of change of control signal. Each pulse has an energy content that is used to compensate the effect of stiction in control valves. With a lower energy content, the valve will remain stuck. With a higher energy content, the valve slip will be larger than that desired. The input signal to valve, u(t), consists of two terms: u(t ) = uc(t ) + uk(t )

disturbance occurs during that period. According to the authors, two tasks are required: (1) The compensating signal must push the stem to its steady state in a desired number of moves. (2) After the stem is moved to its steady-state value, the compensating signal must be designed such that the stem does not move from this position and remains undisturbed. The two compensating moves (uk and uk+1) for stiction compensation given by the authors are i d u (t ) y uk(t ) = uc(t ) + signjjjj c zzzzuk(t ) k dt {

(3)

uk = |uc(t )| + αd

(4)

uk(t + 1) = −uc(t + 1)

(5)

where d is the stickband (the amount of stiction) and α is a real number that is >1. It can be seen from eqs 4 and 5 that the design of the second move is not dependent on the first move. Finally, the valve input signal is characterized by u(t ) = uc(t ) + uk(t )

(1)

(6) 7

The two-move method claims an improvement over the knocker method6 by reducing the aggressiveness of control valve movement. Instead of continuous stem movements, the approach tries to bring the valve stem to steady state using predefined moves. However, this method requires knowledge of the exact amount of stiction, d, which is equal to the deadband for the one-parameter stiction model. The plant should be stable and the process should not be affected by disturbance or white noise. Therefore, this method may not be feasible for practical applications. 2.3. The Constant Reinforcement Method by Xiang Ivan and Lakshminarayanan8 (2009). Xiang Ivan and Lakshminarayanan8 introduced a compensation method called the constant reinforcement (CR) approach. The CR method is similar to the knocker method,6 but the added signal is a constant quantity instead of a pulse. The compensating signal is a constant reinforcement, added to controller output signal in the direction of the rate of change of control signal. The valve input signal, u(t), is defined as follows:

where uc(t) is the output from a standard controller and uk(t) is the output from the knocker. The output uk(t) from the knocker is a pulse sequence that is characterized by three parameters: the time between each pulse (hk), the pulse amplitude (a), and the pulse width (τ). During each pulse interval, uk(t) is given by

l o o a sign(uc(t ) − uc(t p)) if t ≤ t p + hk + τ uk(t ) = m o o otherwise (2) n0 where tp is the time of the previous pulse. The sign of each pulse is determined by the rate of change of control signal, uc(t). The knocker method6 is considered to be the simplest compensation method. It can achieve reduction in process output variability. This method removes oscillations at the cost of faster and wider motion of the valve stem. Excessive valve stem movements reduce the longevity of the valve, which may lead to frequent maintenance actions and unavailability of the plant. 2.2. The Two-Move Method by Srinivasan and Rengaswamy7 (2008). To avoid the aggressive valve movements of the knocker method, 6 Srinivasan and Rengaswamy7 proposed a two-move method for stiction compensation. The two-move method adds two compensating movements to the controller output in order to make the control valve eventually arrive at a desired steady-state position. They have used a one-parameter model of valve stiction. The one-parameter model of valve stiction does not represent true stiction behavior. It causes valve stem to jump between two positions, one above and another below the steady-state positions. If stiction does not occur and enough time is given to the transients to die out, the process variable, control signal, and valve stem will reach their final steady-state position. From these observations, the authors claimed that, if a compensation signal can be added to force the valve stem to reach its steadystate position, the controller can achieve the desired process variable values, provided no further set-point change or

u(t ) = uc(t ) + α(t ) = uc(t ) + a sign(Δuc)

(7)

where α(t) is the compensator signal. If the controller output is constant, the value of α(t) is zero. The magnitude of the constant reinforcement (a) is dependent on the estimated amount of the stiction, d. However, it cannot minimize excessive valve movements. 2.4. The Improved Knocker Method by Arumugam et al.9 (2014). Arumugam et al.9 proposed a new method for compensating stiction in control valves. This method is also similar to the knocker method.6 However, in this method, sinusoidal signals are considered for stiction compensating purposes instead of pulse signals. The compensating signal, uk, is a sinusoidal signal that is characterized by the following equation: uk = A sin(ωt )

(8)

where A is the amplitude of the sine wave (A = 2a), ω is the frequency of the sine wave (ω = 2πf), and f = 1/T. A and ω are calculated from the oscillatory response of the process output 11327

DOI: 10.1021/acs.iecr.9b00335 Ind. Eng. Chem. Res. 2019, 58, 11326−11337

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Industrial & Engineering Chemistry Research uss = MVss − fd

before compensation. Parameters a and T are the amplitude and period of oscillation of the uncompensated process output, respectively. This method performs better than the knocker method. It can reduce output process oscillation, track set points, and reject disturbances satisfactorily, but it cannot reduce the aggressiveness of the valve stem movement. 2.5. The Model-Free Stiction Compensation Method by Arifin et al.10 (2014). Arifin et al.10 proposed a model-free stiction compensation technique, where the compensating signal is a function of control error. A small error produces little or no valve movement. The signal uk(t) for compensating stiction is calculated following the procedure of the knocker or CR methods.8 The amplitude of the pulse to overcome stiction is a = S/2, where S is equal to the deadband plus the stickband. A signal ec(t) is calculated as the filtered absolute error multiplied by a constant, λ, which lies between 0 and 1. The compensating signal is the product of ec and uk. um(t ) = ec(t )uk(t )

Time interval Tsw in eq 11 does not need to be specific. A safe choice is Tsw ≈ Top, where Top is the average half-period of oscillation of uc. Th should be as small as possible for this case as well. This method was derived from He’s two-parameter stiction model, but only the fd parameter is directly involved into the stiction compensation moves. This compensator performs poorly if the amount of stiction, fd is not estimated correctly. The stiction amount, fd is to be known to estimate steady-state valve positions. 2.7. The Variable Amplitude Pulse Method by Arifin et al.14 (2018). Arifin et al.14 proposed a compensator scheme that minimizes error within specified limits by providing pulses with variable amplitudes. As illustrated by the authors, there exists a pulse magnitude for which IAE is minimum. It is found to be 0.5S, where S is the deadband plus the stickband of stiction. As for valve travel (VT), the authors found that it increases as the pulse magnitude increases. However, there does not exist any optimum pulse amplitude when both IAE and VT are considered. Therefore, this method performs an unidirectional search to determine the amplitude of pulses for the compensator using the following equation:

(9)

The valve input signal is defined as u(t ) = uc(t ) + um(t )

(10)

This method requires specification of many parameters. They are different for different processes. So it is cumbersome to implement in real industrial plants. 2.6. The Four-Move Method by Bacci di Capaci et al.11 (2016). Bacci di Capaci et al.11 proposed a revised stiction compensation technique by introducing some practical simplifications based on the work of Wang et al.15 This method requires four open-loop movements. The valve input signal in this method is defined as l uc,max o o o o o o o o o uc,min u(kTs) = m o o o usw o o o o o o uss n

um(k) = sign(uc(k) − uc(k − θ ))p(k)r(k)

T0 ≤ kTs < T0 + Tsw T0 + Tsw ≤ kTs < T0 + Tsw + Th (11)

where T0 = t0 + θ0 and Ts is the sampling time. The first two moves are same as those reported in the 2015 work of Wang et al.15 When uc increases close to its peak, the controller is switched into open-loop mode at time t0 and uc is set to uc,max. Then, after time interval θ0, uc is enforced to uc,min. If one chooses to impose symmetrical movements to uc, that is, T1 = T2, the steady-state valve stem position becomes MVss =

uc,max + uc,min 2

(12)

The parameter usw can be calculated using the equation usw = uss − βsw (uc,max − uc,min)

(13)

l uc(kTs) o o o − A p sign(error) if T0 < kTs < T1 o o o α o OP(kTs) = m o o uc(kTs) o o o otherwise o o α n

Here, βsw is a coefficient (≥1) that enables the valve to overcome the stickband. If the controller signal, uc(t), is increased first and decreased afterward, the steady-state valve input signal, uss can be computed using the equation uss = MVss + fd

(16)

where uc(k) is the controller output at instant k, θ is the time delay, p(k) is the pulse to be applied, r(k) is a ramp signal with slope, Δr = 0.3/nr, and nr = floor(4τ/Ts). The signal, um(k), calculated using eq 16, is added to the control signal, uc(k). Therefore, the signal sent to the valve is u(k) = um(k) + uc(k). 2.8. The Proposed Method from Part I.13 This section provides a short description of the proposed method appeared in Part I of this paper.13 The proposed compensator receives two signals, namely, a control error signal and a controller output signal. When the error signal crosses a predefined threshold limit, the pulse generator inside the compensator is activated and it generates a predesigned pulse. The proposed stiction compensator calculates either of the two outputs, as shown in eq 17. The second output of eq 17, which is called “reduced control action”, is obtained by dividing the controller output with an appropriately estimated detuning parameter, α. This step is performed to reduce the controller action. The first output of eq 17, which is called “compensator output with pulse”, is obtained by adding a predesigned pulse from the pulse generator to the “reduced control action”. The pulse is added only for a short duration of time, TG, in order to cause the valve slip from its stuck position (refer to eq 17). After time TG, the compensator output switches to “the reduced control action”. The output of the proposed compensator (OP) is calculated as follows:

kTs < T0

otherwise

(15)

(14)

(17)

where fd is the stiction amount in the control valve. Conversely, if the method is implemented in the opposite direction, i.e, uc(t) is decreased first and increased afterward, then uss is defined by the following equation:

where uc is the controller output at time kTs, Ts the sampling time, k any integer, Ap the pulse amplitude, T0 the time when pulse addition is started, T1 the time when the pulse is 11328


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Industrial & Engineering Chemistry Research withdrawn, and α a detuning parameter to reduce control action. The addition of a pulse is started at time T0 when the error crosses a predefined threshold ϵ and continues up to time T1. Therefore, TG = T1 − T0. TG is a specified time duration during which the pulse addition is continued and the compensator produces its first output. In order to add the pulse with the reduced control action, the change of direction of error signal is taken into consideration. The relationship between controller parameter and detuning parameter, α, as derived in Part I of this study,13 is defined as follows: α=

834

{

3τI (τI + 3θ )Kc

− 12

0.3

}

Note that S is equivalent to d or fd for some compensation methods. A white noise sequence with zero mean and standard deviation, σ = 0.01 was added to the process output. The compensator was started at 3001 s and the set point was changed from 10 to 20 at 6000 s for all cases. Each simulation was run for 9000 s. Parameters used in different compensators are listed in Table 1. 3.1. Comparison of Trend Analysis. The trends of the process variable (PV) and set point (SP) for different compensators are shown in Figure 1. As can be seen from this figure, all compensators were able to reduce process oscillations and track the set point successfully. However, oscillation frequency has increased for all of them, except for the Bacci di Capaci et al.11 compensator and the proposed compensator. The Bacci di Capaci et al.11 model can reduce oscillation successfully but it requires a certain time period (1000 s) after the compensator has been activated to calculate its parameters. For this 1000 s, there is no compensation. Moreover, if there is any set-point change or disturbance, oscillation returns for a certain period of time, which is used to recalculate parameters. For the proposed compensator, there is no such problem. The valve stem position (MV), along with the compensator output (OP) data are plotted in Figure 2. It is clearly visible that the first five methods increase the valve movements and cause a significant increase in VT after the compensator is switched on at 3001 s. This will certainly reduce the longevity of control valves. The last two methods, namely, the Bacci di Capaci et al.11 compensator and the proposed compensator, do not increase the number of valve reversals or valve travels. 3.2. Comparison of Performance. Performance of the compensators can be quantified using the criteria of integral absolute error (IAE), process variable variance (σ2), and valve travel (VT). Smaller values of IAE and σ2 mean that the compensator can reduce process oscillation, track set points, and reject disturbances satisfactorily. The valve reversals can be analyzed by calculating VT values. A minimum number of valve reversals results in smaller VT values. Therefore, it is expected that a good compensator should have minimum IAE, σ2, and VT values. These parameters are calculated as follows:

+ (τI

0.7

0.9

+θ )

(18)

The proposed compensator model can mitigate the stiction effect by reducing output process oscillation as well as the number of valve reversals. Note that the requirement of a process model is not essential for the proposed compensator. However, if available, a First Order Plus Time Delay (FOPTD) model of the process is useful for estimating different parameters of the compensator. Otherwise, default parameters can be used.

3. COMPARISON OF DIFFERENT COMPENSATORS BASED ON SIMULATIONS A good compensator should have the properties of oscillation reduction, good set-point tracking, quick disturbance rejection, Table 1. Parameters Used in Different Compensators author(s) of the methods Hägglund6 (2002) Srinivasan and Rengaswamy7 (2008) Xiang Ivan and Lakshminarayanan8 (2009) Arumugam et al.9 (2014)

value of parameters Ps = 1 (1% < Ps < 4%), tr = 1, tp = 2 d = 3 (stiction parameter) α = 3 (stiction parameter)

a and w are calculated from the uncompensated process variable Arifin et al.10 (2014) τe = 1.2, γ = 8 Bacci di Capaci et al.11 (2016) fd = (S − J)/2 = 1 (stiction parameter) proposed compensator α = 10, ϵ = 0.5, Ap = 1

N

IAE =

and minimum valve travel. This section compares the performance of the stiction compensators discussed in section 2, except the method reported by Arifin et al.,14 because it cannot compensate stiction satisfactorily for the process considered below. For comparison, the integral absolute error (IAE), valve travel (VT), and variance of process variable (σ2) have been calculated and compared with each other. Let us consider the following FOPTD process: 50 P(s) = e−10s (19) 100s + 1

∑k = 1 |e(k)| (21)

N N

VT =

∑ |x(k) − x(k − 1)| (22)

k=1 N

σ2 =

∑k = 1 (PV (k) − μ)2 N

(23)

where e(k) is the control error, x(k) the valve position at sampling instant k, μ the mean value of process variable, and N the total number of data points over which the summation is performed. The IAE, σ2, and VT values before compensation were calculated using data for 1001−3000 s, and those values after compensation were calculated using data for 4001−6000 s. The IAE values before and after compensation are shown in Table 2. The percentage decrease in IAE is also shown in the right-most column of this table. The proposed method has the minimum IAE among all compensators. It can reduce IAE by 92.89%, which is the highest among all of the methods.

This process has slow dynamics, high gain, and moderate time delay. Therefore, it is a difficult process from control point of view. The PI controller, based on the IMC method, is 1 yz i zz C(s) = 0.046jjj1 + (20) 100s { k Valve stiction was introduced using the Choudhury et al.2 stiction model, with the following parameter set: S = 3, J = 1.

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Figure 1. Response curve of output process variable (PV) and set point (SP) for different compensator models.

Depending on the valve stem position, VT was measured. The actual VT measurement is cumbersome in actual industrial process plants, because the MV data is generally not available. However, the measurement of VT is possible for simulation studies. The VT values for different compensators are summarized in Table 4. The last column shows the percentage change of VT before and after the compensator. The VT value has increased after starting the compensator for the first five methods. However, for the Bacci di Capaci et al.11 compensator and the proposed compensator, it has decreased. They could reduce the VT values by 50% and 99%,

Table 3 shows the variances of process variables. The minimum variance indicates smaller oscillation in process variables. Before the compensator was started, the variance in PV was 8.29 for all cases. All compensators were successful in reducing oscillations. Although the methods that appeared after the knocker method6 claimed an improvement over the knocker method, the simulation results for the process under consideration do not support this claim. Only the Bacci di Capaci et al.11 compensator and the proposed compensator perform better than the knocker method. 11330


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Figure 2. Response curve of valve position (MV) and controller output (OP) for different compensator models.

respectively, whereas other compensators have increased the VT several times. Excessive valve movements reduce the longevity of the valve. Therefore, implementation of the first five compensators in industry would damage the control valve. However, the latter two can be implemented in industrial plants without the fear of damaging valves. 3.3. A Unified Performance Index. It is convenient for an operator or engineer to use one performance index instead of many, because he/she may need to address hundreds or thousands of control loops. The performances based on IAE, σ2, and VT can be combined to a single unified performance index. The unified performance index (η) can be defined as

η=1−

3

IAEacσac 2 VTac IAE bcσbc 2(VTac + VTbc )

(24)

where the subscripts “ac” and “bc” denotes “after compensation” and “before compensation”, respectively. An index value close to unity indicates good performance while a value close to zero indicates poor performance. The results of Tables 2, 3, and 4 for different compensators are now combined in this unified performance index and are reported in Table 5. The unified performance index in Table 5 clearly shows that the Bacci di Capaci et al.11 compensator and the proposed compensator provide η values close to 1, indicating good compensation of stiction. 11331


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Table 6 shows that all methods exhibit good capabilities in reducing PV oscillation. Most of them cause excessive valve movements, and many of them require a priori process knowledge. Although all of them can track set points and reject disturbances, the proposed stiction compensator outperforms any of the other compensators. 3.5. Comparison of the Proposed Compensator and the Bacci di Capaci et al.11 Compensator. The performance of the proposed compensator and Bacci di Capaci et al.11 compensator, with respect to set-point tracking, IAE, σ2, VT, and η are similar to each other. Their performances are further investigated below. 3.5.1. Set-Point Tracking. This section compares the setpoint tracking performance of the Bacci di Capaci et al.11 compensator and the proposed compensator. For both methods, the compensator was switched on at 2001 s. As can be seen from Figure 3, oscillation returns for ∼1000 s for the Bacci di Capaci et al.11 method when a step change was introduced at 5000 s and 10 000 s. However, for the proposed compensator, oscillation does not come back. The bottom two panels of Figure 3 show the valve movements. It is evident that excessive valve movement does not occur in the proposed method. Therefore, in terms of set-point tracking, the proposed compensator outperforms the Bacci di Capaci el al.11 compensator. 3.5.2. Disturbance Rejection Capability. A good compensator should have quicker disturbance rejection capability. In order to investigate disturbance rejection capability, for both cases, the compensators were switched on at 5000 s and a unit step disturbance was added to the process output at 10 000 s. The PV trends for these two cases are shown in Figure 4. For the Bacci di Capaci et al.11 compensator, oscillation returns and remains for some time before the disturbance can be eliminated. On the other hand, the proposed compensator can quickly reject the unit step disturbance within a short period of time without any return of oscillations. 3.5.3. Performance in the Presence of Error in Stiction Amount. The Bacci di Capaci et al.11 compensator is dependent on the accuracy of the estimated stiction amount (fd). Accurate stiction quantification is an a priori task in their work. If S and J are known, then fd = (S − J)/2. Note that, in real life, it will be very difficult to know the correct values of the stiction parameters and thereby specify fd accurately. Incorrect quantification of the stiction parameters S and J can produce wrong results. To study the effect of wrong specification of fd, simulations were performed using different values of fd for a fixed set of stiction parameters (S = 3 and J = 1). The compensator was switched on at 3000 s for all cases. The value of fd was varied from 0.5 to 2.0 in increments of 0.5. The performance of the compensator is shown in Figure 5. As can be seen, for fd = 1, the performance was good. For other cases, the performance was not satisfactory. Even for the case of fd = 1.5, there is an offset between PV and SP. Therefore, it can be concluded that the performance of the Bacci di Capaci et al.11 is not satisfactory in the presence of error in stiction estimation. On the other hand, for the proposed compensator, there is no requirement of knowing stiction parameters. The performance of the proposed compensator for this particular case is shown in the second panel from the bottom in Figure 6. To analyze the performances of the Bacci di Capaci et al.11 compensator and the proposed compensator in the presence of varying amounts of stiction, simulations were performed.

Table 2. Integral Absolute Error (IAE) Data for Different Compensators IAE author(s) of the method Hägglund6 (2002) Srinivasan and Rengaswamy7 (2008) Xiang Ivan and Lakshminarayanan8 (2009) Arumugam et al.9 (2014) Arifin et al.10 (2014) Bacci di Capaci et al.11 (2016) proposed compensator

before compensator

2.596

after compensator

decrease in IAE (%)

0.772 1.032

70.20 60.24

2.092

19.41

1.164 2.141 0.359 0.184

55.14 17.52 86.16 92.89

Table 3. Variance of Output Process Variable σ2 Data for Different Compensators σ2 author(s) of the method

before compensator

Hägglund6 (2002) Srinivasan and Rengaswamy7 (2008) Xiang Ivan and Lakshminarayanan8 (2009) Arumugam et al.9 (2014) Arifin et al.10 (2014) Bacci di Capaci et al.11 (2016) proposed compensator

8.29

after compensator

decrease in σ2 (%)

0.737 1.401

91.07 83.10

5.934

28.42

1.740 5.818 0.620 0.074

79.02 29.81 92.53 99.11

Table 4. Valve Travel (VT) Data for Different Compensators VT author(s) of the method

before compensator

Hägglund6 (2002) Srinivasan and Rengaswamy7 (2008) Xiang Ivan and Lakshminarayanan8 (2009) Arumugam et al.9 (2014) Arifin et al.10 (2014) Bacci di Capaci et al.11 (2016) proposed compensator

1.60

after compensator

decrease in VT (%)

64.29 58.52

−3924.30 −3554.60

230.81

−14313

40.76 203.72 0.80 0.01

−2445.50 −12622 49.93 99.17

Table 5. Comparison of the Unified Performance Index author(s) of the method

performance index, η

Hägglund6 (2002) Srinivasan and Rengaswamy7 (2008) Xiang Ivan and Lakshminarayanan8 (2009) Arumugam et al.9 (2014) Arifin et al.10 (2014) Bacci di Capaci et al.11 (2016) proposed method

0.704 0.597 0.169 0.551 0.169 0.849 0.983

3.4. Summary on the Performances of the Compensators. The performances of the seven stiction compensators have been summarized in Table 6. Four criteria have been used: (1) reduction of PV oscillations, (2) reduction of valve movement, (3) process knowledge requirement, and (4) setpoint tracking and disturbance rejection. 11332


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Industrial & Engineering Chemistry Research Table 6. Performance Evaluation of the Stiction Compensation Methodsa Sec.

author(s) of the method

reduction of PV oscillation

reduction of valve movement

no a priori process knowledge requirement

set-point tracking and disturbance rejection

1 2 3 4 5 6 7

Hägglund6 (2002) Srinivasan and Rengaswamy7 (2008) Xiang Ivan and Lakshminarayanan8 (2009) Arumugam et al.9 (2014) Arifin et al.10 (2014) Bacci di Capaci et al.11 (2016) proposed method

√ √ √ √ √ √ √

×× ×× ××× ×× ××× √ √

√ × × × × × √

√ √ √ √ √ √ √

Legend of symbols in this table: ×, no/low; × ×, bad; × × ×, very bad ; √, yes/good.

a

Figure 3. Comparison of set-point tracking capability between the Bacci di Capaci et al.11 and the proposed compensator for step up and step down.

amount for all simulations was SD = 2, J = 1. The stiction compensator was switched on at 3000 s for both cases. For the Bacci di Capaci et al.11 compensator, fd was varied from 0.5 to 2.0 in increments of 0.5. Results are shown in Figure 7. Clearly, the performance of this compensator is not satisfactory. The poor performance is probably because this method was developed using a one-parameter stiction model, which does not represent the real stiction behavior. On the other hand, the proposed compensator was applied for the same case of nonhomogeneous stiction parameters. The results are shown in Figure 8. The performance is clearly satisfactory.

Figure 6 compares the performances of the Bacci di Capaci et al.11 compensator and the proposed compensator in the presence of varying amount of stiction when the stiction parameters [S, J] were varied as [5,2], [4,2], [3,1] and [2,1]. In the Bacci di Capaci et al.11 compensator, a value of fd = 1 was used for all cases. As shown in the figure, the compensator could not eliminate the offset for some cases. For the proposed compensator, α = 10, TG = 100, ϵ = 0.5, Ap = 1 were used for all cases. It can remove oscillations and, at the same time, can track the set point properly for all cases. Accurate measurement of the stiction parameters for a real industrial plant is difficult. Therefore, the implementation of the Bacci di Capaci et al.11 compensator in a real plant will be difficult. The proposed compensator is simple and can be implemented in a real plant without knowing the value of stiction in the control valves. 3.5.4. Case of Nonhomogeneous Stiction. In real life, the amount of stiction in the upward direction of VT can differ from that of the downward direction of VT. Such a case is called nonhomogeneous stiction. It means that the values of the stickband plus the deadband for the upward (SU) and downward (SD) direction of VT are different. A modified version of stiction model that appeared in the work of Choudhury et al.2 was used for this simulation. For the upward direction of VT, the stiction amount for all simulations was SU = 3, J = 1 and for the downward direction of VT, the stiction

4. EXPERIMENTAL EVALUATION The performances of the Bacci di Capaci et al.11 compensator and the proposed compensator were evaluated in a tank level system of a computer-interfaced pilot plant located in the process control laboratory at the Chemical Engineering Department of Bangladesh University of Engineering and Technology (BUET) (see Figure 9). Stiction in the valve was introduced using the Choudhury model with S = 5, J = 3. Since stiction was introduced using a model, it was possible to specify fd correctly, which is a requirement for the Bacci di Capaci et al. compensator.11 Therefore, a value of fd = (S − J)/ 2 = (5 − 3)/2 = 1 was used for this compensator. 11333


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Figure 4. Comparison of disturbance rejection capability between the Bacci di Capaci et al.11 compensator and the proposed compensator.

Figure 5. Performance of the Bacci di Capaci et al.11 compensator in the presence of errors in the stiction amount.

Initially, the level was oscillatory, because of the presence of stiction in the control loop. Compensator was switched on at 2000 s for both compensators. Figure 10 shows the performance of the Bacci di Capaci et al.11 compensator. It could remove oscillations but there is an offset between SP and PV. At 5000 s, a step change of size 10 was introduced. Oscillations returned, as was also observed in the simulation case. The compensator could eliminate oscillation, but could not remove the offset. Therefore, the set-point tracking performance was not satisfactory.

On the other hand, the performance of the proposed compensator is shown in Figure 11. Although it took a slightly longer time, it could eliminate oscillation completely without any offset. A set-point change was introduced at 6300 s. Unlike the Bacci di Capaci et al.11 compensator, oscillation did not return. The compensator could track the set point satisfactorily without any offset. As is evident from the bottom panels of Figures 10 and 11, the VT is also less for the proposed compensator, in comparison to the Bacci di Capaci et al.11 compensator. 11334


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Figure 6. Comparison of performance between the Bacci di Capaci et al.11 compensator and the proposed compensator in the presence of varying amounts of stiction.

Figure 7. Performance of the Bacci di Capaci et al.11 compensator for nonhomogeneous stiction parameters.

5. CONCLUSIONS

(2008), (c) the constant reinforcement method by Xiang Ivan and Lakshminarayanan8 (2009), (d) the improved knocker method by Arumugam et al.9 (2014), (e) the model-free stiction compensation method by Arifin et al.10 (2014), (f) the four-move method by Bacci di Capaci et al.11 (2016), and (g) the proposed stiction compensation method that has been described in Part I of this study13 have been critically analyzed and compared using simulation and

Stiction in control valves produces oscillation in process variables and reduces the quality of control. It is a challenging task to compensate valve stiction and thus reduce process variable oscillation in process industries. In this study, the performances of seven stiction compensation methods namely, (a) the knocker method by Hägglund6 (2002), (b) the two-move method by Srinivasan and Rengaswamy7 11335


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Figure 8. Performance of the proposed compensator for nonhomogeneous stiction parameters.

Figure 9. Photograph of the tank level system located in the Chemical Engineering Department of BUET. Conference on Electrical and Computer Engineering, Dhaka, Bangladesh, 2018; pp 161−164. (2) Choudhury, M. A. A. S.; Thornhill, N.; Shah, S. Modelling valve stiction. Control Eng. Practice 2005, 13, 641−658. (3) Ale Mohammad, M.; Huang, B. Compensation of control valve stiction through controller tuning. J. Process Control 2012, 22, 1800− 1819. (4) Choudhury, M. A. A. S.; Shah, S.; Thornhill, N. Diagnosis of Process Nonlinearities and Valve Stiction. Data Driven Approaches; Springer−Verlag: Berlin, Heidelberg, Germany, 2008. (5) Nahid, A.; Choudhury, M. A. A. S. Compensating the Effect of Control Valve Stiction. In Fifth International Conference on Chemical Engineering, ICChE 2017, Dhaka, Bangladesh, 2017; pp 503−512. (6) Hägglund, T. A friction compensator for pneumatic control valves. J. Process Control 2002, 12, 897−904. (7) Srinivasan, R.; Rengaswamy, R. Approaches for efficient stiction compensation in process control valves. Comput. Chem. Eng. 2008, 32, 218−229. (8) Xiang Ivan, L. Z.; Lakshminarayanan, S. A New Unified Approach to Valve Stiction Quantification and Compensation. Ind. Eng. Chem. Res. 2009, 48, 3474−3483. (9) Arumugam, S.; Panda, R. C.; Velappan, V. A Simple Method for Compensating Stiction Nonlinearity in Oscillating Control Loops. Int. J. Eng. Technol. 2014, 6, 1846−1855.

experimental studies. All compensators exhibit good capabilities to reduce PV oscillation. Most of them cause excessive valve movements, and many of them require a priori process knowledge. It is observed that the four-move method by Bacci di Capaci et al.11 and the proposed compensator are the best among the compensators that have appeared so far in the literature. The proposed compensator works better than any of the other six stiction compensators, including the Bacci di Capaci et al.11 compensator.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

M. A. A. S. Choudhury: 0000-0001-9188-2851 Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Nahid, A.; Iftakher, A.; Choudhury, M. A. A. S. An Efficient Approach to Compensate Control Valve Stiction. In 10th International 11336


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Figure 10. Experimental results of the Bacci Di Capaci et al.11 model for step change.

Figure 11. Experimental results of the proposed model for step change. (10) Arifin, B. M. S.; Munaro, C. J.; Choudhury, M. A. A. S.; Shah, S. L. A Model Free Approach for Online Stiction Compensation. 19th IFAC World Congress 2014, 47, 5957−5962. (11) Bacci di Capaci, R.; Scali, C.; Huang, B. A Revised Technique of Stiction Compensation for Control Valves. In 11th IFAC Symposium on Dynamics and Control of Process Systems, 2016; Vol. 49, pp 1038−1043 (). (12) Bacci di Capaci, R.; Scali, C. Review and Comparison of Techniques of Analysis of Valve Stiction: from Modeling to Smart Diagnosis. Chem. Eng. Res. Des. 2018, 130, 230−265. (13) Nahid, A.; Iftakher, A.; Choudhury, M. A. A. S. Control Valve Stiction Compensation - Part I: A New Method for Compensating Control Valve Stiction. Ind. Eng. Chem. Res. 2019. (14) Arifin, B.; Munaro, C.; Angarita, O.; Cypriano, M.; Shah, S. Actuator stiction compensation via variable amplitude pulses. ISA Trans. 2018, 73, 239−248. (15) Wang, T.; Xie, L.; Tan, F.; Su, H. A new implementation of open-loop two-move compensation method for oscillations caused by control valve stiction. In 9th IFAC ADCHEM, 2015; pp 433−438.

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