Control Valve Stiction Compensation - Part I: A New Method for

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 11316−11325

Control Valve Stiction Compensation - Part I: A New Method for Compensating Control Valve Stiction Ahaduzzaman Nahid, Ashfaq Iftakher, and M. A. A. Shoukat Choudhury*

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Department of Chemical Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh ABSTRACT: Valve stiction is a hidden menace in process control loops. The presence of stiction in control valves limits the control loop performance. Compensation of its effect is beneficial before the sticky valve can be sent for maintenance. This work is the first of a two part study on control valve stiction compensation. This part proposes a novel stiction compensation method, while the second part compares the performance of this proposed stiction compensation method with some of other compensation methods appeared in the literature. The proposed compensator is developed based on reduction of control action and addition of an extra pulse of finite energy as required. A method for estimating an appropriate parameter for reducing controller action has been developed. The proposed stiction compensator has been extensively evaluated using the MATLAB Simulink environment. The compensator has also been implemented in a pilot plant experimental setup. It has been found to be successful in removing valve stiction-induced oscillations from process variables both in simulation and pilot plant experimentation. The compensator developed in this study has the capability of reducing process variability with a minimum number of valve reversals. In the two move method,9 the first move is used to overcome the static friction between the valve stem and packing, and the second move is used to bring the valve stem to its steady state position. The knowledge of the steady state valve stem position is required in this method.10 Measurement of the steady state valve position is difficult. Improvements to this method were proposed by de Souza L. Cuadros et al.,11 but it causes many valve reversals and cannot minimize the number of valve reversals.12 The method proposed by Sivagamasundari and Sivakumar13 is similar to the knocker method, but the difference lies in the selection of amplitude and duration of the pulse. This method reduces process oscillations at the cost of increasing valve stem movement. As a result, the operating lives of the valves get shortened due to rapid wear and tear. Similar to the knocker method, Arumugam et al.14 proposed a stiction compensation method where a constant sinusoidal action is added to the controller action instead of a constant pulse. The frequency of the sinusoidal action depends on the oscillation amplitude and time period of process output. This method can minimize oscillation of process variables but increases valve stem movement as was the case for the knocker method. Arifin et al.15 designed the compensating signal as the product of the error signal and controller output signal. The

1. INTRODUCTION Automatic control systems are ubiquitous in modern industrial process plants. The quality of product, energy efficiency, and profitability of the plant largely depend on the performance of an automatic control system.1 The presence of stiction in control valves limits the loop performance.2 It increases oscillation in process variables and decreases control loop efficiency. For the valve stiction problem, repair and maintenance are considered to be definitive solutions. But this requires plant shutdowns in most cases.3 Since plant overhauling takes place generally every two to three years, stiction compensation can help to minimize the effects of stiction in control valves until the next shutdown.2 Over the past few years, compensation of stiction has become an active area of research. There are several methods for compensating the effect of control valve stiction.4 As mentioned by Thornhill and Horch,5 there are two types of compensation methods, namely, invasive and noninvasive. This paper deals with the noninvasive methods of stiction compensation. Knocker method6 is one of the earliest methods proposed for stiction compensation. This method applies a constant pulse to the controller output signal to overcome valve stiction. It decreases the variance of the output process variable but increases the valve stem movement.7 The constant reinforcement method8 is an improvement to the knocker method and tries to overcome the backlash effect. In this method, the compensating signal is a constant value with the sign of the rate of change of the controller signal. This method increases valve stem movement, which does not improve situations. Excessive valve stem movements reduce the longevity of the valves.3 © 2019 American Chemical Society

Special Issue: Sirish Shah Festschrift Received: Revised: Accepted: Published: 11316

January 18, 2019 May 13, 2019 May 14, 2019 May 14, 2019 DOI: 10.1021/acs.iecr.9b00334 Ind. Eng. Chem. Res. 2019, 58, 11316−11325

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Industrial & Engineering Chemistry Research

parameter, α. For details of α estimation, refer to Section 2.2.4. This step is performed to reduce the controller action. The first output of eq 1 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, to cause the valve to slip from its stuck position (refer to eq 1). After time TG, the compensator outputs the “reduced control action”. Note that unlike the method of Mohammad and Huang,1 in our case, the controller tuning is unchanged rather the controller output is reduced by dividing it by a detuning parameter, α. How the proposed stiction compensator works inside a control loop is illustrated in Figure 1. The output of the proposed compensator, OP, is calculated as follows:

performance of the method was not satisfactory since it cannot minimize process oscillations satisfactorily. A recent stiction compensation method proposed by Bacci di Capaci et al.12 gives good performance. The amount of valve stiction is to be known a priori in this method. Also, it requires an estimation of the steady-state position of the valve stem. Stiction quantification is difficult in real life. Incorrect estimation of the valve stem position and stiction quantification can give a worse performance. The latest stiction compensation method by Arifin et al.16 is known as the variable amplitude pulse method. The main idea behind this method is to perform a unidirectional search for the amplitude of the pulse that brings the error within the specified limit. This method requires many parameters to be specified for proper compensation of stiction. These parameters are different for different processes. So, it is difficult to implement it in industrial process plants. In this study, a new stiction compensation method has been developed, which has the properties of a fewer number of valve reversals, removal/reduction of process oscillations, good set point tracking, and satisfactory disturbance rejection. It does not require prior process knowledge. 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 in the compensator. The method also shows good promise for implementation in real process industries. Previously, preliminary results of this study appeared in Nahid et al.17 and Ahaduzzaman and Choudhury.2 The rest of the paper has been organized as follows. Section 2 describes the detailed description of the proposed compensator. Section 3 narrates the method of estimating the detuning parameter required to reduce control action. The performance of the proposed compensator has been evaluated through simulation studies in Section 4, while Section 5 evaluates it experimentally through implementation in a pilot plant setup. The conclusion of the paper is drawn in Section 6.

l uc(kTs) o o o − A psign(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

(1)

where uc is the controller output at time kTs, Ts is sampling time, k is any integer, Ap is pulse amplitude, T0 is the time when pulse addition is started, T1 is the time when pulse is withdrawn, and α is a detuning parameter to reduce control action. How to choose parameters of the pulse generator including Ap is described in Section 2.2. It is to be noted that in this study OP is compensator output, not controller output. The controller output is denoted as uc. The addition of the pulse is started at time T0 when the error crosses a predefined threshold, ϵ, and continued 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. To add the pulse with the reduced control action, the change of direction of the error signal is taken into consideration. Now the working procedure of the proposed compensator is described using an illustrative example. Suppose that a FOPTD process with time constant 100 s, gain 50 s, and time delay 10 s is simulated for 15,000 s. The PI controller parameters are Kc = 0.046 and τI = 100 s as found using the internal model control (IMC) technique. For this simulation, set point (SP) and process variable (PV) data are plotted in the top panel of Figure 2. The first 5000 samples represent nonsticky valve conditions, and PV was tracking SP perfectly. After 5000 s, valve stiction was introduced using the Choudhury et al.3 model with S = 5

2. DESCRIPTION OF THE NOVEL COMPENSATION METHOD Generally, for a sticky valve, the stem cannot move easily due to stiction. A compensator helps the stem to slip from its stuck position. As shown in Figure 1, the proposed compensator

Figure 1. Block diagram illustrating the proposed model used in a feedback loop.

receives two signals, namely, a control error signal and controller output signal. If the valve stem becomes stuck at a fixed position, the error signal keeps increasing. When the error signal crosses a predefined threshold limit, the pulse generator inside the compensator is activated, and it generates a predesigned pulse. The pulse should be small enough so that the valve does not travel too much, and at the same time, it should be large enough so that the valve can slip easily from its stuck position. The proposed stiction compensator calculates either of the two outputs shown in eq 1. The second output of eq 1 called “reduced control action” is obtained by dividing the controller output with an appropriately estimated detuning

Figure 2. Inside look of the control loop when the compensator is in action in a control loop. 11317

DOI: 10.1021/acs.iecr.9b00334 Ind. Eng. Chem. Res. 2019, 58, 11316−11325

Article

Industrial & Engineering Chemistry Research and J = 3. The process variables started oscillating due to valve stiction. The proposed compensator was applied at 10,000 s. The pulse generator (the second to the last panel of Figure 2) has started working at T0 = 10,001 s and continued to work for 100 s. The compensator output is shown in the lower panel of Figure 2. After TG = 100 s, i.e., at time T1 s, the pulse generator was turned off. At this time, the compensator produces its second output, which is equal to the reduced control action only. As is evident from this figure, the proposed compensator could eliminate the stiction induced oscillation from the control loop completely. In order to get a better picture of what is happening during compensation, a zoomed-in version of Figure 2 from time 9500 s to 11,500 s is shown in Figure 3. As it can be

Figure 4. Flowchart of the proposed compensation method.

OP(kTs) = Figure 3. Compensator in action showing zoomed in version of Figure 2.

The proposed compensator was programmed as a drag and drop type block in MATLAB Simulink software. The details of the block are shown in Figure 5. 2.2. Compensator Parameters and Practical Issues. It would be convenient if the compensators could be used without any requirement of specifying parameters by the users. Unfortunately, all compensators need some parameters to be specified. The proposed compensator requires the usage of a simple pulse generator and a detuning parameter, α. This study found that the pulse generator parameters and the specified time limit, TG, can be kept constant for most of the processes. Only the detuning parameter, α, needs to be specified each time depending on the controller and the process. 2.2.1. Parameters for Pulse Generator. A pulse is required to push the valve stem from its initial stuck position. As shown in Figure 6, a pulse sequence is characterized by three parameters: pulse period, hk, pulse amplitude, Ap, and the pulse width, τd. These parameters are to be chosen suitably. The pulses should be sufficiently large, so that the valve slips quickly. At the same time, they must be small enough so that they do not cause any extra slip. Usually stiction varies from 0% to 20% for most industrial cases. On a normalized scale, it is suitable to choose the value of pulse amplitude in the interval of 1% ≤ AP ≤ 2%. It is important not to feed too much energy into the positioner at the moment when the valve slips. Therefore, it is desirable to use a relatively short pulse width. From the experience of the authors, the pulse width (τd) can be chosen as 7 to 8 times of the sampling time, Ts. It is desirable to keep pulse period (hk) from Ts to 2 × Ts larger than the pulse width so that two successive pulses cannot occur in one sampling time. 2.2.2. Specified Time Limit, TG. TG is the specified time when pulse generator is kept switched on. During this time, the generated pulse is added to the reduced control action to push

uc(kTs) − A psign(error) (2) α The sign of the error signal is taken into consideration to add the pulse signal. For the negative value of the error signal, the pulse is added to the reduced control action and vice versa. If Tp is greater than the predefined time period, TG, the compensator output, OP, will be OP(kTs) =

uc(kTs) α

(4)

• Finally, the output signal from the compensator, OP, is fed to the control valve.

seen from this figure, the first output of the compensator, i.e., output with pulse, is active only for 100 s, and after this time, the compensator is working with its second output, the reduced control action. If the control error again crosses the predefined error limit, the pulse generator will trigger again. Such examples are included in the simulation study and experimental study sections. 2.1. Programming the Proposed Compensator. The flowchart describing the algorithm of the proposed compensator is shown in Figure 4. The steps of the algorithm are as follows: • First, the controller output and the error signal are fed as inputs to the compensator. • Check whether the error signal is greater than a predefined threshold, ϵ. • If the error signal is greater than ϵ, activate the pulse generator and start counting time period Tp from its activation time. If Tp is less than the predefined time period, TG, the compensator output will be calculated as

OP(kTs) =

uc(kTs) α

(3)

• Again, if the error signal is less than ϵ, initiate Tp = 0 and the compensator output, OP, will be 11318


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Figure 5. Simulink block diagram of the proposed compensator.

IAE =

1 Tb − Ta

∫T

Tb

a

SP − PV dt

(5)

where SP is the desired set point and PV is process variable. Ta and Tb are the time intervals over which the IAE is calculated. The importance of correct estimation of α is illustrated using an example. Assume a first order process as given in eq 6,

Figure 6. Pulse sequence characterization of the proposed compensator model.

Gp(s) =

the control valve from its stuck position. Pulse is withdrawn when the control valve starts moving from its stuck position. After this, the reduced control action is only used to move the valve stem to the desired steady state position. So adding an extra pulse after the valve slips is not necessary. A large value of TG means adding an extra pulse after the valve slips. It causes extra valve movements, which is not desired. From the authors’ experience, 50 s ≤ TG ≤ 100 s is suitable for most sticky valves having 0%−20% stiction. While for simplicity TG can be kept constant for all type of processes, it can also be adjusted depending on the magnitude of the process time constant and the desired time to eliminate oscillation. It is to be noted that if sampling time is too large for a process, the value of TG should be adjusted accordingly. 2.2.3. Permissible Error, ϵ. Permissible error is the error that could be acceptable to the plant operators. It has the unit of process variable or error signal. Generally, it is taken as twice the standard deviation of the process variable when the valve has negligible stiction and the controller performance is satisfactory. Note that process variables are generally monitored within twice their standard deviations. 2.2.4. Detuning Parameter, α. In the proposed compensator, a detuning parameter, α, is required to reduce aggressiveness of the controller. If the controller is aggressive, then the value of α should be high and vice versa. A reliable estimation of this parameter is an important prerequisite of this method. The detuning parameter, α, is different for different processes. Incorrect estimation of α cannot mitigate the effect of stiction satisfactorily. The detuning parameter, α, can be selected by evaluating the integral absolute error, IAE, using eq 5. For a given process, IAE depends on α. The value of α which gives minimum IAE for a process would be the right detuning parameter for that process. The IAE is defined as

50e−10s 100s + 1

(6)

The process model in eq 6 was simulated with stiction parameters S = 5 and J = 3. The controller parameters for this process based on the Internal Model Control (IMC) are KC = 0.046 and τI = 100. The controller parameters were kept the same for all cases considered in this section. It can be seen from Figure 7(a) that the oscillation magnitude of the process variable is increased after installing the compensator at 4000 s with a small detuning parameter α = 5, thus resulting in a large IAE value of 4.13. A large value of α = 30 can reduce the oscillation but takes a longer time (about 3500 s) to reach the steady state as shown in Figure 7(c). Figure 7(b) shows that the compensator with α = 10 can mitigate the oscillation for the

Figure 7. Process output response curve of a single first order process for three different cases of α. 11319


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method or Skogestad’s half rule method.18 The general model for a FOPTD process can be written as

process successfully and achieves a small IAE value of 0.08. Therefore, the values of α play a significant role and should be determined correctly. A procedure to properly estimate α has been developed and is described in Section 3. 2.3. Initialization of Compensator. It was mentioned earlier that the proposed compensator works by reducing control action and adding an extra pulse. At the switching time during the start of the compensator, the input signal to the valve may cause some process upsets. The process output response curve for a typical case is shown in Figure 8, where the compensator starts working at 4000 s. The output of the process goes to lower values than it was before as shown in the enclosed circle in Figure 8.

Gp(s) =

To overcome this problem, the compensator output needs proper initialization. The initialization can be done using the average steady state value of the controller output immediately before starting the compensator. Figure 9 shows the perform-

Figure 9. Process output response for the proposed model with initialization.

ance of the compensator after such initialization. The average steady state value of the controller output was set as the initial output of the compensator at 4000 s. Such initialization enables the compensator to mitigate the stiction effect without creating much upset during the switching as shown in Figure 9. 2.4. Dealing with Stochastic or Noisy Signals. In order to handle noisy or stochastic signals, a time domain filter, e.g., an exponentially weighted moving average (EWMA) filter, can be used to filter noisy signals. The filter is as follows: λz z − (1 − λ)

(8)

τs + 1

where KP is process gain, τ is time constant, and θ is time delay. The process gain (KP), time constant (τ), and time delay (θ) were varied in the range of [1:5:51], [1:10:201], and [0:3:21], respectively. These combinations produced 1848 different FOPTD processes. Valve stiction was introduced using the widely used stiction model3 with parameter settings of S = 5 and J = 3. A white noise with zero mean and standard deviation σ = 0.01 was added to the process output. Before starting the compensator, the process output was oscillatory because of introduction of stiction to the valve, but some combinations of process parameters were not able to generate limit cycle oscillations because they did not fulfill the conditions of limit cycle initiation.3 Out of 1848 different FOPTD processes, 1431 FOPTD processes could generate limit cycle oscillations. The proposed stiction compensator was applied to mitigate the stiction effect in these 1431 FOPTD processes. For all cases, the following compensator parameters were used: Ts = 1 s, TG = 100 s, and ϵ = 0.5. Every process model was simulated for 10,000 s, and the compensator was started at 4000 s in each case. The detuning parameter, α, was varied in the range of [1:0.5:200] for each process, and the corresponding integral absolute error (IAE) for each FOPTD process was calculated using the last 3000 data points. The IAE values were different for different detuning parameters for each FOPTD process. The optimum detuning parameter was selected for which the IAE was minimum. Therefore, 1431 optimum detuning parameters were found for 1431 FOPTD models where the compensator worked satisfactorily and process variables remained steady with minimum oscillation. It is to be noted that the minimum IAE values were found to be less than 0.10 for all cases, whereas the IAE values were greater than 4 if no compensators were used. Figure 10 shows the optimum IAE values for 1431 processes.

Figure 8. Process output response for the proposed model without initialization.

Gf (z) =

K pe−θs

Figure 10. Minimum IAE of different processes for selected detuning parameter, α.

(7)

The value of λ depends on the extent of the noise. A typical value of λ can be chosen as 0.25.

Data from simulation of 1431 process models were fitted using different empirical models using standard regression analysis. For these 1431 FOPTD processes, the process variables (KP, τ, θ) and the PI controller settings (Kc, τI) are known. The following empirical models were tried: 1. α = AK px + Bτ y + Cθ z + D

3. ESTIMATION OF THE DETUNING PARAMETER, α As stated earlier, the detuning parameter, α, should be specified properly for the successful implementation of the compensator. For this purpose, a relationship between controller parameters and the detuning parameter, α, has been developed. It is difficult to find such a relationship theoretically. In order to find an empirical relationship, a simulation technique in combination with trial and error has been used. Without losing the generality, the proposed compensator was applied to various first order plus time delay (FOPTD) processes. Generally, most of the higher order processes can be approximated by a FOPTD process using different established techniques such as Taylor’s

2. α = AK px + Be τ / y + Cθ z + D 3. α = AK px + B 4. α = 5. α = 11320

( θτ )

y

AKcx + BτIy + x K A τc + D I

+D D

( )


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Industrial & Engineering Chemistry Research 6. 7. 8. 9.

α α α α

= = = =

10. α = 11. α = 12. α = 13. α = 14. α =

Therefore, the estimated empirical relation for α is

Ae x(Kc / τI) + D A(Kcx /τIy) + D A log(Kcx /τIy) + D A log(Kcx × τIy) + D AK px

(τθ ) y AKcx

α̂ =

834 − 12 + τ 0.7 + θ 0.9

+D

(

Cθ + D

For standard regression analysis, the first empirical model can be written as Y = Xβ + ε, where Y, X, and unknown vector of coefficients, β, are defined as below: ÄÅ É ÅÅ 1 K p x τ1y θ1z ÑÑÑ ÄÅ α ÉÑ ÅÅ ÑÑ ÅÅ 1 ÑÑ 1 ÄÅ ÉÑ ÅÅ ÑÑ ÅÅ ÑÑ ÅÅ D ÑÑ ÅÅ ÑÑ ÅÅ α ÑÑ x y z ÅÅ ÑÑ ÅÅ 1 K p τ2 θ2 ÑÑ ÅÅ 2 ÑÑ ÅÅ Ñ ÅÅ ÑÑ ÅÅÅ A ÑÑÑ 2 Ñ Å Ñ Å Ñ Y = ÅÅÅ − ÑÑÑ X = ÅÅÅ− − − − ÑÑÑ β = ÅÅÅ ÑÑÑ ÅÅ Ñ ÅÅ − ÑÑ ÅÅÅ B ÑÑÑ ÅÅ− − − − ÑÑÑ ÅÅ ÑÑ ÅÅ ÑÑ ÅÅ ÑÑ ÅÅ αn ÑÑ ÅÅÇ C ÑÑÖ ÅÅ ÅÅ ÑÑ 4×1 x y zÑ Ñ ÅÅÅ 1 K pn τn θn ÑÑÑ ÅÇÅ ÑÖÑ1431 × 1 ÅÇ ÑÖ1431 × 4

α̂ =

834

{

3τI (τI + 3θ )Kc

0.3

}

+

− 12 τI0.7

+θ

0.9

(14)

4. PERFORMANCE EVALUATION OF THE PROPOSED COMPENSATOR BASED ON SIMULATIONS The performance of the proposed compensator was evaluated using criteria such as set point tracking, disturbance rejection, number of valve reversals, and sensitivity to noise. Consider a FOPTD process as follows:

(9)

The coefficient vector, β, was estimated in a least-squares sense using pseudoinverse as follows:

Gp(s) =

(10)

50e−10s 100s + 1

1 yz i zz C(s) = 0.046jjj1 + 100s k {

(15)

The PI controller based on IMC was

The values of all power indices (x, y, z) in the above combinations were varied in the range of [0:0.1:5]. These variations of power indices (x, y, z) produce 51 × 51 × 51 = 132,651 number of equations for the first model. For each empirical model, Ŷ can be found using Ŷ = Xβ. The sum of squared errors, SSE, can be found as SSE = εTε. Here, ε is the difference between Y and Ŷ , which implies SSE = (Y − Y ̂ )T (Y − Y ̂ )

)

where τc has been chosen as τ/3. Replacing the process parameters by controller settings in eq 12, the final relationship for the detuning parameter is found to be

z

β = (XT X )−1(XT Y )

(12)

It can also be expressed in terms of controller settings. From the IMC method, PI controller settings for a FOPTD process are τ Kc = ; τI = τ τ Kp 3 + θ (13)

+ D [if θ is zero then set to 0.01 ]

A +D K px + τ y + θ z A +D Kcx /τIy AK px + Be−τ / y +

K p0.3

(16)

Valve stiction was introduced using the Choudhury stiction model3 setting the parameters to S = 5 and J = 3. A white noise with zero mean and standard deviation of σ = 0.01 was added to the process output. For the compensators, the following parameters were used: Ts = 1 s, TG = 100 s, ϵ = 0.5, and α = 10. The output process variable, PV, along with set point, SP, (top panel), and valve stem movement, MV, along with valve input signal, OP, (bottom panel) are shown in Figure 12. Figure 12 shows that the process variable, PV, was oscillatory up to 4000 s due to valve stiction. At 4000 s, the compensator was started, and the compensator could eliminate the oscillations completely in about 1200 s time period. Therefore,

(11)

From the 132,651 different simulation cases, the equation corresponding to the minimum SSE was selected. A similar procedure was repeated for all other empirical models. The minimum SSE values obtained for the above empirical models are shown in Figure 11.

Figure 11. Minimum SSE for different number of empirical models.

Figure 11 shows that empirical model 12 gives the minimum of the minimum SSE (min(min (SSE))). So, it can be said that among the empirical models tried, model 12 is the best where the deviation between the predictive and actual detuning parameters was minimum. The parameters corresponding to model 12 are

Figure 12. Simulation results for the proposed compensator of a single FOPTD process.

x = 0.3, y = 0.7, z = 0.9, A = 834, D = − 12 11321


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Industrial & Engineering Chemistry Research it can be said that the proposed compensator could mitigate the stiction effect satisfactorily by reducing process oscillation as well as valve stem movements (see MV plot, bottom panel, Figure 12). Though the compensation method has been evaluated using a FOPTD model, it can be applied to higher order processes as they can be approximated as a FOPTD process using standard reduction techniques. In Part 2 of this paper, the performance of the proposed compensator will be compared with some of other important compensators presented in the literature. 4.1. Evaluation of the Compensator Performance for Different Scenarios. The proposed compensation scheme was applied for the following different scenarios of the same process: set point tracking, disturbance rejection, varying noise levels, and varying amounts of stiction. For all cases, the compensator was inactive until 4000 s, and then, it was activated to compensate valve stiction. 4.1.1. Set Point Tracking. The performance of the proposed compensator was evaluated for set point changes in both the upward and downward direction. The results are shown in Figure 13. The top panel in Figure 13 shows that oscillations

Figure 14. Results for proposed compensator when a unit step disturbance is added at 7000 s.

Table 1. Effect of Noise on Stiction Compensation Variance of noise (σ)

IAEbefore

IAEafter

%IAEreduction

0 0.01 0.02 0.03 0.04 0.05 0.10 0.20 0.50

4.60 4.60 4.61 4.61 4.61 4.61 4.61 4.62 5.41

0.0002 0.0809 0.1138 0.1396 0.1620 0.1807 0.2572 0.3628 0.5709

99.99 98.24 97.53 96.97 96.49 96.08 94.42 92.15 89.44

For all noise levels, the compensator could eliminate the oscillations completely. The time trend for the case of σ = 0.5 is shown in Figure 15. It clearly shows that the compensator

Figure 13. Stiction compensation for set point tracking.

have been eliminated, and process variables can track the different set point changes successfully. The bottom panel shows that there is no excessive valve movement, and the number of valve reversals is also minimum. 4.1.2. Disturbance Rejection. Any type of disturbance tends to deviate the process output from its set point. A unit step type input disturbance was added to the process output at 7000 s. The proposed compensator could eliminate the disturbance effectively within a short period of time. The bottom panel of Figure 14 shows that there was no excessive valve movement. Therefore, it can be said that the disturbances can be eliminated effectively by the proposed compensator. 4.1.3. Varying Noise Levels. The performance of the proposed compensator was evaluated for different noise levels. The white noise sequences with different noise variances, σ, were added to the process output. The integral absolute error (IAE) was computed for each case. Table 1 summarizes the results. For each case, the model was run for 10,000 s. The integral absolute error, IAE, for every case was calculated for 1000 to 4000 s before starting the compensator. After starting the compensator, the IAE was also calculated for the last 3000 s.

Figure 15. Output response of a process when high level of noise was added.

works satisfactorily even in the presence of a high level of noise. For the last case of high noise variance, it could reduce IAE by 89.44%. 4.1.4. Varying Amounts of Stiction. The compensator developed in this study does not require exact knowledge of stiction parameters. The measurement of stiction parameters is cumbersome. The stickband plus deadband for upward and downward directions of valve travel can be different. A modified version of the stiction model presented in Choudhury et al.3 was used to simulate asymmetric stiction. The modified version was capable of specifying different amounts of stickband plus deadband in the upward and downward directions of valve travel. The deadband plus stickband parameter, S, is denoted as “SU” for upward and “SD” for downward directions. The other parameter slip jump is denoted by J. Various stiction cases were simulated for different stiction parameters listed in the first 11322


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Industrial & Engineering Chemistry Research Table 2. Impact of Stiction Parameters on Stiction Compensation

column of Table 2. The performances of the proposed compensator for these different cases were evaluated by calculating IAEbefore from 1000 to 4000 s and IAEafter from 7000 to 10,000 s. The compensator performed well in all cases, as shown in Table 2.

5. EXPERIMENTAL EVALUATION OF THE PROPOSED COMPENSATOR Experimental evaluation of the proposed stiction compensation method was performed in a tank level system of a computer interfaced pilot plant located in the process control laboratory of the Chemical Engineering Department, Bangladesh University of Engineering and Technology (Figure 16). A piping

Figure 17. P&ID diagram of tank level system located in the Chemical Engineering Department, Bangladesh University of Engineering and Technology.

Figure 16. Photograph of tank level system located in the Chemical Engineering Department, Bangladesh University of Engineering and Technology.

Figure 18. Open loop response curve of the level control loop.

Gp(s) =

and instrumentation diagram (P&ID) of the level control loop is shown in Figure 17. It has a pneumatic control valve to regulate the flow rate of water in order to control the tank level. 5.1. Model Identification. A step test was performed to identify the model of the tank level system. After the level reached a steady state at 15%, a step of size 0.5 mA corresponding to 3.13% of the valve opening in a scale of 4− 20 mA was made at 630 s. The step response curve is shown in Figure 18. The level started to increase at 640 s and eventually reached a new steady state value of 57%. The sampling time was 1 s. From Figure 18, the model parameters can be calculated as 57%−15% % follows: Process gain, KP = 14 mA−13.5 mA = 84 mA . Time delay, θ = 640 s − 630 s = 10 s. The time to reach 63.2% of the ultimate response is 820 s. Time constant, τ = 820 s − θ − 630 s = 820 s − 10 s − 630 s = 180 s. Therefore, the identified model of the process is

84e−10s 180s + 1

(17)

5.2. PI Controller Design. Initial controller parameters were obtained using internal model control (IMC) rules. Then, they were fine-tuned by the trial−error method. The final controller settings obtained were as follows: i 1 yz zz C(s) = 0.05jjj1 + 50s { k

(18)

The process response curve for different set point changes when this controller was in use is shown in Figure 19. The controller could track the set point successfully without much overshoot. Therefore, it can be said that the final controller settings appearing in eq 18 are quite reasonable. From Figure 19, it can also be inferred that the performance of the control valve is satisfactory showing negligible sign of stiction. 5.3. Performance Evaluation of the Compensator. As discussed in a previous section, the performance of the control 11323


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Figure 19. Process output response for the final controller settings (SP and PV are level in %).

valve used for this study was satisfactory, indicating a healthy valve with a negligible amount of stiction. To introduce stiction in the control valve, a soft stiction block of the two parameter stiction model19 was inserted in the control loop in the MATLAB Simulink interface of the plant. Stiction parameters were set to S = 5 and J = 3. The PI controller was the same as in eq 18. The parameters of the compensator were set to Ts = 1 s, TG = 100 s, Ap = 1%, and ϵ = 3%. The process variable, the tank level, was noisy. The standard deviation of the level was calculated as 1.42%. Considering this, the threshold limit was set to ϵ = 2 × 1.42% = 2.84% ≈ 3.0%. Using the process and controller parameters θ = 10, Kc = 0.05, and τI = 50, in eq 14, the detuning parameter, α̂ , was calculated as 19.62. A rounded up value of α̂ = 20 was used in this experiment. 5.3.1. Performance in the Presence of Set Point Changes. The lower panel of Figure 20 shows that the controller output

Figure 21. Experimental results of the proposed compensator for set point tracking for both upward and downward steps (SP and PV are level in %. OP is valve demand in %. MV is valve opening in %).

water pipe was introduced at 5000 s. As shown in Figure 22, the compensator could reject the disturbance successfully. Another

Figure 22. Experimental results of the proposed compensator for step disturbance rejection (SP and PV are level in %. OP is valve demand in %. MV is valve opening in %).

step of a smaller magnitude was introduced at 8400 s. Again the step disturbance effect was fully rejected by the compensator without causing any oscillation. 5.4. Quantification of Performance of the Compensator. Three cases were considered: control valve with negligible stiction, sticky control valve without compensator, sticky control valve with compensator. The time trends and the variance of the process variables for these three cases are shown in Table 3. For the control valve with negligible stiction, the process variable was noisy and does not show any oscillation. This results in a variance of 2.01% as shown in the top row of Table 3. For the case of the sticky control valve without compensator, the process variable was

Figure 20. Experimental results of the proposed compensator for set point tracking for upward steps (SP and PV are level in %. OP is valve demand in %. MV is valve opening in %).

oscillates from about 60% to 68% due to valve stiction. The upper panel shows that the level of water in the tank oscillates from 20% to 40%. At 1000 s, the proposed compensation scheme was applied. After starting the compensator, the oscillation of the tank level was eliminated completely within a short period of time. So, the compensator could remove the stiction-induced oscillation of the process variable satisfactorily. The set point was changed from 30% to 40% at 3000 s, 40% to 50% at 6000 s, and 50% to 60% at 8500 s. The compensation quality was not deteriorated due to set point changes. Figure 21 shows that the compensator works both for upward and downward directions steps. Therefore, the proposed compensator can work in the presence of both upward and downward set point changes and can remove process oscillations satisfactorily. 5.3.2. Disturbance Rejection. The proposed compensator was tested for disturbance rejection. A temporary water line using a flexible plastic hose pipe was used to introduce the disturbance. One end of the pipe was connected to an ordinary water tap, and the other end was into the tank. Therefore, it was not possible to measure the flow rate or step size quantitatively. A large step type disturbance in input flow using this temporary

Table 3. Process Variable Variance for Different Conditions

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(7) Brasio, A. S. R.; Romanenko, A.; Fernandes, N. C. P. Modeling, Detection and Quantification, and Compensation of Stiction in Control Loops: The State of the Art. Ind. Eng. Chem. Res. 2014, 53, 15020−15040. (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) Srinivasan, R.; Rengaswamy, R. Approaches for efficient stiction compensation in process control valves. Comput. Chem. Eng. 2008, 32, 218−229. (10) Silva, B. C.; Garcia, C. Comparison of Stiction Compensation Methods Applied to Control Valves. Ind. Eng. Chem. Res. 2014, 53, 3974−3984. (11) de Souza L. Cuadros, M. A.; Munaro, C. J.; Munareto, S. Improved stiction compensation in pneumatic control valves. Comput. Chem. Eng. 2012, 38, 106−114. (12) Bacci di Capaci, R.; Scali, C.; Huang, B. A Revised Technique of Stiction Compensation for Control Valves. 11th IFAC Symposium on Dynamics and Control of Process Systems 2016, 49, 1038−1043. (13) Sivagamasundari, S.; Sivakumar, D. A New Methodology to Compensate Stiction in Pneumatic Control Valves. Int. J. Soft Comput. Eng. (IJSCE) 2013, 2, 2231−2307. (14) 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. (15) Arifin, B. S.; Munaro, C.; Choudhury, M. A. A. S.; Shah, S. A Model Free Approach for Online Stiction Compensation. 19th IFAC World Congress 2014, 47, 5957−5962. (16) Arifin, B.; Munaro, C.; Angarita, O.; Cypriano, M.; Shah, S. Actuator stiction compensation via variable amplitude pulses. ISA Trans. 2018, 73, 239−248. (17) Nahid, A.; Iftakher, A.; Choudhury, M. A. A. S. An Efficient Approach to Compensate Control Valve Stiction. 10th International Conference on Electrical and Computer Engineering, Dhaka, Bangladesh 2018, 161−164. (18) Seborg, D. E.; Edgar, T. F.; Mellichamp, D. A. Process Dynamics and Control; John Wiley & Sons, Inc., 2012. (19) Choudhury, M. A. A. S.; Shah, S.; Thornhill, N. Diagnosis of Process Nonlinearities and Valve Stiction. Data Driven Approaches; Springer-Verlag: Berlin Heidelberg, 2008.

oscillatory due to stiction before starting the compensator. Consequently, the variance of the process variable was very high. It was 58.72%, as shown in the middle row of Table 3. After the compensator was switched on, it eliminated the oscillation completely, and the process variable almost returned to the previous state of good control valve with negligible stiction.Therefore, it can be said that the proposed compensator was able to mitigate the stiction effect quite effectively.

6. CONCLUSIONS Stiction in control valves produces oscillation in process variables and reduces the product quality. A novel method for compensating the effect of stiction in control valves has been developed. The main contributions of this work are as follows: • A new stiction compensator has been developed to mitigate the adverse impact of valve stiction. It can be applied online without stopping the process plant. • Methods for estimating the parameters of the proposed stiction compensator have also been developed. Default values of these parameters are suggested. • The performance of the proposed compensator has been extensively evaluated for different First Order Plus Time Delay (FOPTD) processes through simulation study. • Finally, the proposed compensator was applied to a level control loop in a pilot plant experimental setup and was found to be successful in removing the oscillations originated from valve stiction. The developed compensator has the capability of minimizing process variability with a minimum number of valve reversals. It has good set point tracking and disturbance rejection properties. The compensation scheme is simple yet powerful. It requires minimum process knowledge. As it was applied to a pilot plant, it is expected that it would not be difficult to implement the compensator in real process plants.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

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

The authors declare no competing financial interest.

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REFERENCES

(1) Mohammad, M. A.; Huang, B. Compensation of control valve stiction through controller tuning. Journal of Process Control 2012, 22, 1800−1819. (2) Nahid, A.; Choudhury, M. A. A. S. Compensating the Effect of Control Valve Stiction. In Proceeding of the Fifth International Conference on Chemical Engineering, ICChE 2017, Dhaka, Bangladesh, 2017; pp 503−512. (3) Choudhury, M. A. A. S.; Thornhill, N.; Shah, S. Modelling valve stiction. Control Engineering Practice 2005, 13, 641−658. (4) 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. (5) Thornhill, N.; Horch, A. Advances and new directions in plantwide controller performance assessment. 6th IFAC Symposium on Advanced Control of Chemical Processes 2006, 39, 29−36. (6) Hägglund, T. A friction compensator for pneumatic control valves. J. Process Control 2002, 12, 897−904. 11325


Control Valve Stiction Compensation - Part I: A New Method for

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