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Stiction Compensation in Process Control Loops: A Framework for Integrating Stiction Measure and Compensation Ranganathan Srinivasan and Raghunathan Rengaswamy* Department of Chemical Engineering, Clarkson University, Potsdam, New York 13699
In this paper, a framework that utilizes a stiction measure for effective stiction compensation in process control valves is proposed for the first time. The performance of a friction compensator termed the “knocker” proposed in the literature is studied. It is observed that the choice of knocker parameters has a significant influence on the performance of the compensator. It is shown that the choice of the knocker parameters can be automated based on the stiction severity exhibited by the loop. We propose the use of a combination of two approaches for estimating stiction severity. Experimental and simulation case studies are used to demonstrate the efficacy of the proposed approach. Results indicate that a reduction of 6-7 times can be obtained for the output variability. 1. Introduction Industrial surveys1-3 over the past decade indicate that only about one-third of industrial controllers provide acceptable performance and that about 20-30% of all control loops oscillate due to valve problems caused by stiction (static friction) or hysteresis. The presence of stiction increases the variability of the loop. Several researchers have addressed the problem of stiction diagnosis from two perspectives: a data-driven noninvasive heuristic approach4-9 that uses archived routine operating data and model-based approaches that characterize stiction. Since the maintenance costs of each valve are in the range of $400-$2000 and with around 3 million regulatory valves in the process industry, reliable diagnosis of valve stiction, by itself, will have a large economic impact. However, the sticky valves, after detection, most often continue to operate suboptimally until the next production stop, which is typically from every six months to every three years. The loss of energy and product quality during this intermediate period could be quite high. Stiction compensation algorithms can mitigate this problem to a large extent. Since 90% of control valves are operated pneumatically, this study is focused on stiction compensation in pneumatic control valves. Several approaches have been reported for stiction compensation of servo-systems.14 However, as process control valves exhibit slower dynamics than servosystems, compensation techniques reported by Armstrong-He`louvry et al.14 cannot be directly applied to process control loops. Kayihan and Doyle15 and Ha¨gglund16 have addressed stiction compensation algorithms for pneumatic control valves. The approach of Kayihan and Doyle15 requires a valve model with valve parameters (e.g., stem mass, stem length, etc.) and also the process model to be known a priori. Obtaining such detailed valve and model information for several hundred valves is a practical limitation. Ha¨gglund16 proposed a novel model-free approach called “knocker”, * To whom all correspondence should be addressed. Mailing address: P.O. Box 5705, Dept of Chemical Eng, Clarkson University, Potsdam, NY 13699. E-mail:
[email protected]. Telephone: (315) 268-4423. Fax: (315) 268-6654.
Figure 1. Knocker pulse.
where a dither signal (see Figure 1) characterized by an amplitude (a), a pulse width (τ), and a time between each pulse (hk) is added to the controller output (OP) to compensate stiction. Ha¨gglund16 in his work mentions that there is probably no reason to have an adjustable “a” but that a can be fixed once and for all. In our work, we found that choosing a correct a is extremely important for the knocker technique to work. In fact, we observe a local optimum value for a based on the integral square error (ISE) plot. We will demonstrate that this observation is valid with remarkable consistency through a number of simulation case studies and also an experimental setup. This finding leads to an approach for choosing an optimum value for the knocker amplitude a without any model information. The amplitude a is chosen based on a stiction severity estimated from the operating data. Many of the initial stiction detection algorithms did not quantify stiction; however, there has been recent work on quantifying stiction.7,8,12 We will use two stiction detection and quantification methods (for severity) that have been proposed in our previous work. Since stiction is a time varying phenomenon, robustness of the proposed framework to asymmetric and time-varying stiction is also considered. Ha¨gglund16 also suggests that there might not be significant wear on the valve due to the knocker technique. Our implementation of the knocker algorithm on a pneumatic valve shows significant valve movement with a possibility of wear. Optimization approaches to mitigate this problem will also be discussed. The proposed approach is demonstrated on a number of simulation examples and also on an experi-
10.1021/ie050748w CCC: $30.25 © 2005 American Chemical Society Published on Web 10/29/2005
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x(t) )
Figure 2. (a) Basic control loop. (b) Loop structure in the presence of stiction.
mental liquid level system. This paper is organized as follows: section 2 brings out the crucial role of the knocker parameters in reducing the variability of the loop output. A heuristic relationship for the knocker parameters based on a stiction measure is then derived. Section 3 presents our proposed framework that integrates the stiction detection and compensation procedures. In section 4, the proposed framework is demonstrated on a level loop. In section 5, practical issues involved in implementing the knocker method are discussed and recommendations for future work are made. 2. Influence of Knocker Parameters in Stiction Compensation In the Ha¨gglund16 technique, short pulses are added to the control signal in the direction of the rate of change of the control signal. With an integrator, the energy of the pulses becomes high enough to overcome stiction. However, there is a need to tune three parameters that characterize the short pulses (see Figure 1): amplitude (a), pulse width (τ), and time between each pulse (hk). Ha¨gglund16 recommends the following setting for the knocker parameters: the pulse amplitude (a) may be chosen in the range 1-5% (default 2%), pulse width (τ) can be fixed to one or a few sampling times (default τ ) h), and the time between each pulse (hk) is chosen between 2 and 5 sampling times (default hk ) 2h), where h denotes the sampling time of the system. Ha¨gglund16 reported the improvement obtained from the knocker using ratios of (IAEknocker/IAEPI) and (ISEknocker/ISEPI), where IAE is integrated absolute error and ISE is integrated squared error. ISE and IAE calculations obtained with the knocker “ON” are denoted with the subscript knocker, and calculations obtained otherwise are denoted with the subscript PI. To demonstrate and understand the impact of the knocker parameters on the compensator performance, we set up both a simulation framework and also an experimental system. The simulation and experimental setups and the key findings of this study will be discussed in this section. 2.1. Simulation Setup. 2.1.1. Stiction Model. Figure 2a shows a basic regulatory control loop, and Figure 2b shows the loop structure in the presence of stiction. Since valve dynamics are observed only after the start of stem movement, a stiction phenomenon, if present, precedes the valve dynamics. This is represented in Figure 2b. Though several forms of stiction models exist, a simple stiction model parametrized by one parameter “d” given in eq 1 is considered in this work.
{
x(t - 1) if |u(t) - x(t - 1)| e d u(t) otherwise
(1)
In process industries, stiction measurement is done when the loop is in manual mode. A slowly increasing ramp type control signal is given as the valve input. The valve input is increased until a noticeable change in the process variable is observed. Stiction is reported as a percent of the valve travel or span of the control signal. The stiction model given by eq 1 coincides with the procedure used for measuring stiction and is reported as the span of the control signal. The readers are referred to ref 12 for a detailed discussion on the applicability of this simple model for modeling stiction. 2.1.2. Simulation Case Study: Continuous Stirred Tank Reactors (CSTRs). The jacketed exothermic CSTR discussed by Luyben18 is considered here. This process involves a liquid-phase reaction A(l) f B(l). A proportional and integral (PI) controller manipulates the flow rate of cooling water to the jacket for controlling the reactor temperature. A proportional level controller manipulates the amount of liquid leaving the tank as a linear function of the volume in the tank. Constant holdup and perfect mixing are assumed in the cooling jacket. Appendix A gives the ordinary differential equations (ODEs) describing the system, and Table 4 gives the values of the parameters and steady-state conditions. To study the influence of the knocker parameters on knocker performance, a stiction of 4% (using eq 1, d ) 4%) was introduced in the coolant flow line. Since coolant flow affects the reactor temperature (and hence the product concentration), the variations in reactor temperature are observed. The sampling time of the system h was fixed to 0.01 h. Figure 3 shows the variations in reactor temperature and outlet concentration in the presence of stiction without a knocker implementation. Since the energy of each pulse in the knocker is aτ, it is expected that as the amplitude of the pulse increases, the achievable reduction in the variability of the output will vary. Four different knocker amplitudes were implemented, and the results are tabulated in Table 1. The ISE reduction ratio for the reactor temperature is calculated as (ISEPI/ ISEknocker). A value of this ratio greater than 1 indicates an improvement in performance (the variability reduced in the output after knocker implementation), and a value less than 1 indicates deterioration in performance (the variability increased in the output after knocker implementation). It is seen from Table 1 that when the pulse amplitude was 0.8%, the ISE reduction ratio was 1.7; however, when the same amplitude with a longer pulse width (τ ) 0.06) was used, the knocker reduced the output variability by 2-fold at an extra cost of higher energy (aτ) consumption. When the pulse amplitude was increased to 1.6% and the pulse width was reduced to 0.02h, knocker performance improved 3-fold. Further increasing the pulse amplitude to 4% leads to a reduction in knocker performance; i.e., the ISE reduction ratio came down by about 30%. From Table 1, it can be seen that, with a choice of knocker parameters (a ) 1.6%, hk ) 0.03 h, and τ ) 0.02 h), a tight product specification for outlet concentration can be achieved. Figure 4 shows the reactor temperature over time with knocker implementation. However, it may be observed that a different set of knocker parameters can lead to better compensation.
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Figure 3. Reactor temperature and coolant flow measurements in the presence of stiction (4%). Table 1. Sensitivity Analysis of Knocker Parameters: CSTR Case Study knocker parameters a (%)
hk (h)
τ (h)
ISE reduction ratio
0.8 0.8 1.6 4.0
0.03 0.07 0.03 0.03
0.02 0.06 0.02 0.02
1.7 3.3 5.0 3.4
To understand the influence of knocker parameters on the performance of the knocker, a set of 288 simulations were performed by varying the amplitude in the range a ) 0.8-4%, the pulse width in the range τ ) 0.01-0.09 h, and hk in the range 0.02-0.1 h. The results of these simulations are summarized in Figure 5. The three-dimensional plot shows the surface plot of the ISE reduction ratio obtained for various values of a and for the chosen range of hk. It is surprising to see that the highest ISE reduction ratio achievable was 8.4 when the knocker parameters are set to a ) 3.6%, hk ) 0.07 h, and τ ) 0.03 h. It is clearly seen from Figure 5 that the performance improvement can be anywhere from 1 to 9 and is sensitive to the selection of the knocker parameters, emphasizing the need for careful choice of the knocker parameters. Although a high reduction in output variability can be achieved with a large pulse amplitude, this may lead to an uncontrolled evacuation from the low-pressure side of the actuator. Therefore, it is reliable to keep a smaller pulse amplitude and still try to attain maximum reduction in the output variability. From Figure 5, there is a local maximum around 2% which is nearly half of the stiction measure (4%) for hk around 0.03 h and τ ) 0.02 h. To check the validity of these findings over a wider range of processes, two more case studies were evaluated. A first-order process (G(s) ) 0.4/(0.1s + 1), Kc ) 0.1, Ti ) 0.01) and a higher order (slow) process (G(s) ) 6/(2s + 1)(4s + 1)(6s + 1), Kc ) 0.751, Ti ) 10.5) were simulated. The ISE plot for each case study is shown
in Figures 6 and 7, respectively. It is evident from these plots that there is a local maximum around a ) d/2 for the knocker parameters. The examples considered so far used the simple stiction model (eq 1). Since the simple stiction model is only an approximation of a real control valve, to further confirm our findings on knocker parameters, a control valve characterized using a detailed model was considered. A first-order process with a time delay (G(s) ) 1.54e-1.07s/(5.93s + 1), Kc ) 1.1, Ti ) 2.95) was simulated using a pneumatic operated diaphragm sliding stem control valve modeled using Newton’s second law. The frictional forces inside the valve were modeled using a classical friction model.
x˘ 1 ) x2 mx˘ 2 ) Sau - kx1 - F - vFv v ) x2
(2)
where x1 is the position of the stem, v is the stem velocity, and F is the friction force given below.
{
F(v) if v * 0 if v ) 0 and |Fe| < Fs F ) Fe Fs sign(Fe) if v ) 0 and |Fe| g Fs where δ
F(v) ) Fc sign(v) + (Fs - Fc)e(v/vs) sign(v)
(3)
Equations 2 and 3 describe the valve model with friction forces. Here, m is the mass of the stem, k is a spring constant, Sa is the diaphragm area, Fv is the viscous friction coefficient, Fs is the static friction, Fc is the Coulomb friction, vs is Stribeck’s constant, and Fe (equal to Sau) is the applied external force. The model parameters used in the simulation are the following: m ) 0.1
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Figure 4. Stiction compensation for the CSTR case study: control with PI only until t ) 8 h, and the knocker is turned ON at t ) 8 h.
Figure 5. CSTR case study: surface plot of variations in the ISE reduction ratio obtained verses the knocker parameters.
Figure 6. Linear system 1 [G(s) ) 0.4/(0.1s + 1)]: knocker sensitivity analysis for stiction band d ) 0.6.
kg, Sa ) 2 m2, k ) 2 N m-1, Fv ) 0.1 N s m-1, Fs ) 0.25 N, Fc ) 0.15 N, and vs ) 0.01. It is observed again from the ISE plot (see Figure 8) that there is a local maximum around a ) d/2 (0.11) for the knocker parameters, where d (0.22) was calculated as the peakto-peak amplitude (or span) of the oscillating controller output before the knocker was implemented. The simulation studies indicate that, if the stiction severity can be quantified using a stiction measure from routine operating data, then the knocker parameters can be fixed in an automated fashion. However, simulation studies and industrial settings vary considerably. To confirm this heuristic relationship between knocker amplitude and the stiction measure, similar stiction experiments were conducted on a liquid level pilot plant system. A description of the liquid level system and the results obtained from various stiction experiments on this setup are discussed in the next section. 2.2. Pilot Plant Case Study: Liquid Level System. 2.2.1. Experimental Setup. Figure 9 depicts the
liquid level system. It is a water-flow system with a linear needle plug valve assembly. The control valve is an Anderson Hi-Flow Lin-E-Aire 1/2′′ valve (VA200032-220). The actuator is configured “air to close” with a fail safe setting to open fully. The installed control valve did not have a positioner. The level measurement (process variable (PV)) is acquired in the computer using a data acquisition card (PMD-1208LS). The level control was accomplished with a PI controller implemented in a Matlab (Simulink) environment with a sampling time of 0.5 s. Simple step tests for the control signal indicated a first-order linear process with a gain Kp ) -4.5 and an approximate time constant τp ) 80 s. The parameters of the PI controller were (Kc ) 0.88 and Ti ) 0.0138 s-1) obtained using the IMC rule for λ ) 4. The control valve exhibited negligible static friction (
