Stiction Compensation in Process Control Loops: A Framework forIntegrating 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 compensationin process control valves is proposed for the first time. The performance of a friction compensatortermed the “knocker” proposed in the literature is studied. It is observed that the choice of knockerparameters has a significant influence on the performance of the compensator. It is shown thatthe choice of the knocker parameters can be automated based on the stiction severity exhibitedby the loop. We propose the use of a combination of two approaches for estimating stictionseverity. Experimental and simulation case studies are used to demonstrate the efficacy of theproposed approach. Results indicate that a reduction of 6-7 times can be obtained for the outputvariability.

1. Introduction

Industrial surveys1-3 over the past decade indicatethat only about one-third of industrial controllersprovide acceptable performance and that about 20-30%of all control loops oscillate due to valve problems causedby stiction (static friction) or hysteresis. The presenceof stiction increases the variability of the loop. Severalresearchers have addressed the problem of stictiondiagnosis from two perspectives: a data-driven nonin-vasive heuristic approach4-9 that uses archived routineoperating data and model-based approaches that char-acterize stiction. Since the maintenance costs of eachvalve are in the range of $400-$2000 and with around3 million regulatory valves in the process industry,reliable diagnosis of valve stiction, by itself, will have alarge economic impact. However, the sticky valves, afterdetection, most often continue to operate suboptimallyuntil the next production stop, which is typically fromevery six months to every three years. The loss of energyand product quality during this intermediate periodcould be quite high. Stiction compensation algorithmscan mitigate this problem to a large extent. Since 90%of control valves are operated pneumatically, this studyis focused on stiction compensation in pneumatic controlvalves.

Several approaches have been reported for stictioncompensation of servo-systems.14 However, as processcontrol valves exhibit slower dynamics than servo-systems, compensation techniques reported by Arm-strong-Helouvry et al.14 cannot be directly applied toprocess control loops. Kayihan and Doyle15 and Hag-glund16 have addressed stiction compensation algo-rithms for pneumatic control valves. The approach ofKayihan and Doyle15 requires a valve model with valveparameters (e.g., stem mass, stem length, etc.) and alsothe process model to be known a priori. Obtaining suchdetailed valve and model information for several hun-dred valves is a practical limitation. Hagglund16 pro-posed a novel model-free approach called “knocker”,

where a dither signal (see Figure 1) characterized byan amplitude (a), a pulse width (τ), and a time betweeneach pulse (hk) is added to the controller output (OP) tocompensate stiction.

Hagglund16 in his work mentions that there is prob-ably no reason to have an adjustable “a” but that a canbe fixed once and for all. In our work, we found thatchoosing a correct a is extremely important for theknocker technique to work. In fact, we observe a localoptimum value for a based on the integral square error(ISE) plot. We will demonstrate that this observationis valid with remarkable consistency through a numberof simulation case studies and also an experimentalsetup. This finding leads to an approach for choosingan optimum value for the knocker amplitude a withoutany model information. The amplitude a is chosen basedon a stiction severity estimated from the operating data.Many of the initial stiction detection algorithms did notquantify stiction; however, there has been recent workon quantifying stiction.7,8,12 We will use two stictiondetection and quantification methods (for severity) thathave been proposed in our previous work. Since stictionis a time varying phenomenon, robustness of theproposed framework to asymmetric and time-varyingstiction is also considered.

Hagglund16 also suggests that there might not besignificant wear on the valve due to the knockertechnique. Our implementation of the knocker algo-rithm on a pneumatic valve shows significant valvemovement with a possibility of wear. Optimizationapproaches to mitigate this problem will also be dis-cussed. The proposed approach is demonstrated on anumber of simulation examples and also on an experi-

* To whom all correspondence should be addressed. Mailingaddress: P.O. Box 5705, Dept of Chemical Eng, ClarksonUniversity, Potsdam, NY 13699. E-mail: raghu@clarkson.edu.Telephone: (315) 268-4423. Fax: (315) 268-6654.

Figure 1. Knocker pulse.

9164 Ind. Eng. Chem. Res. 2005, 44, 9164-9174

10.1021/ie050748w CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 10/29/2005

mental liquid level system. This paper is organized asfollows: section 2 brings out the crucial role of theknocker parameters in reducing the variability of theloop output. A heuristic relationship for the knockerparameters based on a stiction measure is then derived.Section 3 presents our proposed framework that inte-grates the stiction detection and compensation proce-dures. In section 4, the proposed framework is demon-strated on a level loop. In section 5, practical issues in-volved in implementing the knocker method are dis-cussed and recommendations for future work are made.

2. Influence of Knocker Parameters in StictionCompensation

In the Hagglund16 technique, short pulses are addedto the control signal in the direction of the rate of changeof the control signal. With an integrator, the energy ofthe pulses becomes high enough to overcome stiction.However, there is a need to tune three parameters thatcharacterize the short pulses (see Figure 1): amplitude(a), pulse width (τ), and time between each pulse (hk).Hagglund16 recommends the following setting for theknocker parameters: the pulse amplitude (a) may bechosen in the range 1-5% (default 2%), pulse width(τ) can be fixed to one or a few sampling times (de-fault τ ) h), and the time between each pulse (hk) ischosen between 2 and 5 sampling times (default hk )2h), where h denotes the sampling time of the sys-tem. Hagglund16 reported the improvement obtainedfrom the knocker using ratios of (IAEknocker/IAEPI) and(ISEknocker/ISEPI), where IAE is integrated absolute errorand ISE is integrated squared error. ISE and IAEcalculations obtained with the knocker “ON” are de-noted with the subscript knocker, and calculationsobtained otherwise are denoted with the subscript PI.

To demonstrate and understand the impact of theknocker parameters on the compensator performance,we set up both a simulation framework and also anexperimental system. The simulation and experimentalsetups and the key findings of this study will bediscussed in this section.

2.1. Simulation Setup. 2.1.1. Stiction Model. Fig-ure 2a shows a basic regulatory control loop, and Figure2b shows the loop structure in the presence of stiction.Since valve dynamics are observed only after the startof stem movement, a stiction phenomenon, if present,precedes the valve dynamics. This is represented inFigure 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.

In process industries, stiction measurement is donewhen the loop is in manual mode. A slowly increasingramp type control signal is given as the valve input. Thevalve input is increased until a noticeable change inthe process variable is observed. Stiction is reported asa percent of the valve travel or span of the control sig-nal. The stiction model given by eq 1 coincides withthe procedure used for measuring stiction and is re-ported as the span of the control signal. The readersare referred to ref 12 for a detailed discussion onthe applicability of this simple model for modelingstiction.

2.1.2. Simulation Case Study: Continuous StirredTank Reactors (CSTRs). The jacketed exothermicCSTR discussed by Luyben18 is considered here. Thisprocess involves a liquid-phase reaction A(l) f B(l). Aproportional and integral (PI) controller manipulates theflow rate of cooling water to the jacket for controllingthe reactor temperature. A proportional level controllermanipulates the amount of liquid leaving the tank as alinear function of the volume in the tank. Constantholdup and perfect mixing are assumed in the coolingjacket. Appendix A gives the ordinary differential equa-tions (ODEs) describing the system, and Table 4 givesthe values of the parameters and steady-state condi-tions. To study the influence of the knocker parameterson knocker performance, a stiction of 4% (using eq 1, d) 4%) was introduced in the coolant flow line. Sincecoolant flow affects the reactor temperature (and hencethe product concentration), the variations in reactortemperature are observed. The sampling time of thesystem h was fixed to 0.01 h.

Figure 3 shows the variations in reactor temperatureand outlet concentration in the presence of stictionwithout a knocker implementation. Since the energy ofeach pulse in the knocker is aτ, it is expected that asthe amplitude of the pulse increases, the achievablereduction in the variability of the output will vary. Fourdifferent knocker amplitudes were implemented, andthe results are tabulated in Table 1. The ISE reductionratio for the reactor temperature is calculated as (ISEPI/ISEknocker). A value of this ratio greater than 1 indicatesan improvement in performance (the variability reducedin the output after knocker implementation), and avalue less than 1 indicates deterioration in performance(the variability increased in the output after knockerimplementation).

It is seen from Table 1 that when the pulse amplitudewas 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 varia-bility by 2-fold at an extra cost of higher energy (aτ)consumption. When the pulse amplitude was increasedto 1.6% and the pulse width was reduced to 0.02h,knocker performance improved 3-fold. Further increas-ing the pulse amplitude to 4% leads to a reduction inknocker performance; i.e., the ISE reduction ratio camedown 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 foroutlet concentration can be achieved. Figure 4 showsthe reactor temperature over time with knocker imple-mentation. However, it may be observed that a differentset of knocker parameters can lead to better compensa-tion.

Figure 2. (a) Basic control loop. (b) Loop structure in the presenceof stiction.

x(t) ) {x(t - 1) if |u(t) - x(t - 1)| e du(t) otherwise

(1)

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To understand the influence of knocker parameterson the performance of the knocker, a set of 288 simula-tions were performed by varying the amplitude in therange 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 resultsof these simulations are summarized in Figure 5. Thethree-dimensional plot shows the surface plot of the ISEreduction ratio obtained for various values of a and forthe chosen range of hk. It is surprising to see that thehighest ISE reduction ratio achievable was 8.4 when theknocker parameters are set to a ) 3.6%, hk ) 0.07 h,and τ ) 0.03 h. It is clearly seen from Figure 5 that theperformance improvement can be anywhere from 1 to9 and is sensitive to the selection of the knockerparameters, emphasizing the need for careful choice ofthe knocker parameters. Although a high reduction inoutput variability can be achieved with a large pulseamplitude, this may lead to an uncontrolled evacuationfrom the low-pressure side of the actuator. Therefore,it is reliable to keep a smaller pulse amplitude and stilltry to attain maximum reduction in the output vari-ability. From Figure 5, there is a local maximum around2% which is nearly half of the stiction measure (4%) forhk around 0.03 h and τ ) 0.02 h.

To check the validity of these findings over a widerrange of processes, two more case studies were evalu-ated. 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) weresimulated. The ISE plot for each case study is shown

in Figures 6 and 7, respectively. It is evident from theseplots that there is a local maximum around a ) d/2 forthe knocker parameters.

The examples considered so far used the simplestiction model (eq 1). Since the simple stiction model isonly an approximation of a real control valve, to furtherconfirm our findings on knocker parameters, a controlvalve characterized using a detailed model was consid-ered. A first-order process with a time delay (G(s) )1.54e-1.07s/(5.93s + 1), Kc ) 1.1, Ti ) 2.95) was simulatedusing a pneumatic operated diaphragm sliding stemcontrol valve modeled using Newton’s second law. Thefrictional forces inside the valve were modeled using aclassical friction model.

where x1 is the position of the stem, v is the stemvelocity, and F is the friction force given below.

where

Equations 2 and 3 describe the valve model with frictionforces. Here, m is the mass of the stem, k is a springconstant, Sa is the diaphragm area, Fv is the viscousfriction coefficient, Fs is the static friction, Fc is theCoulomb friction, vs is Stribeck’s constant, and Fe (equalto Sau) is the applied external force. The model param-eters used in the simulation are the following: m ) 0.1

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 0.03 0.02 1.70.8 0.07 0.06 3.31.6 0.03 0.02 5.04.0 0.03 0.02 3.4

x1 ) x2

mx2 ) Sau - kx1 - F - vFv

v ) x2 (2)

F ) {F(v) if v * 0Fe if v ) 0 and |Fe| < Fs

Fs sign(Fe) if v ) 0 and |Fe| g Fs

F(v) ) Fc sign(v) + (Fs - Fc)e(v/vs)δ

sign(v) (3)

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kg, Sa ) 2 m2, k ) 2 N m-1, Fv ) 0.1 N s m-1, Fs ) 0.25N, Fc ) 0.15 N, and vs ) 0.01. It is observed again fromthe ISE plot (see Figure 8) that there is a localmaximum around a ) d/2 (0.11) for the knockerparameters, where d (0.22) was calculated as the peak-to-peak amplitude (or span) of the oscillating controlleroutput before the knocker was implemented.

The simulation studies indicate that, if the stictionseverity can be quantified using a stiction measure fromroutine operating data, then the knocker parameterscan be fixed in an automated fashion. However, simula-tion studies and industrial settings vary considerably.To confirm this heuristic relationship between knockeramplitude and the stiction measure, similar stictionexperiments were conducted on a liquid level pilot plantsystem. A description of the liquid level system and theresults obtained from various stiction experiments onthis setup are discussed in the next section.

2.2. Pilot Plant Case Study: Liquid Level Sys-tem. 2.2.1. Experimental Setup. Figure 9 depicts the

liquid level system. It is a water-flow system with alinear needle plug valve assembly. The control valve isan Anderson Hi-Flow Lin-E-Aire 1/2′′ valve (VA2000-32-220). The actuator is configured “air to close” with afail safe setting to open fully. The installed control valvedid not have a positioner. The level measurement(process variable (PV)) is acquired in the computer usinga data acquisition card (PMD-1208LS). The level controlwas accomplished with a PI controller implemented ina Matlab (Simulink) environment with a sampling timeof 0.5 s. Simple step tests for the control signal indicateda first-order linear process with a gain Kp ) -4.5 andan approximate time constant τp ) 80 s. The parametersof the PI controller were (Kc ) 0.88 and Ti ) 0.0138 s-1)obtained using the IMC rule for λ ) 4. The control valveexhibited negligible static friction (<0.1%). The stictionmodel given by eq 1 was implemented at the controlleroutput before the control signal was sent to the valve.In these experiments, though the stiction phenomenonis introduced through a model, we want to emphasize

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 ISEreduction ratio obtained verses the knocker parameters.

Figure 6. Linear system 1 [G(s) ) 0.4/(0.1s + 1)]: knockersensitivity analysis for stiction band d ) 0.6.

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that the valve dynamics are real and, hence, thecompensation results that we report here are achievablein real systems. The proposed approach allows us tostudy variations in stiction level across the stem thatcan happen in a real valve and so on. We also show arepresentative result for the case where static frictionof about 5.5% of the controller span (0-100%) wasintroduced in the valve by tightening the stem packing.

2.2.2. Experimental Study. Figure 10 shows thelevel measurement and controller output data for astiction band of 4%. Closed loop data for four differentknocker settings was recorded, and the results aretabulated in Table 2. Higher ISE reduction ratios wereobtained when compared to the CSTR simulation casestudy.

The knocker performance was again influenced by thechoice of knocker parameters. The knocker showedsimilar characteristics as seen in the CSTR case study.A set of 12 experiments were conducted to investigate

the existence of a relationship between the knockeramplitude and the stiction severity measure.

Figure 11 compiles the results as a surface plot of ISEreduction ratios obtained for various values of a (1, 2,3, and 4%), τ (1, 2, and 3 s), and hk (2, 3, and 10 s). It isclear from Figure 11 that there exists an acceptableperformance (ISE reduction ratio ) 7) for a relativelysmall amplitude and short pulse width in the regionaround 2% which is nearly half of the stiction measure(4%). This further validates the results from the simula-tion studies. Figure 12 shows the knocker results(turned ON at t ) 500 s for a ) 2.0%, hk ) 2.5 s, and τ) 1 s). The reduction achieved in output variability wasquite significant and indicated that simulation resultsare extendable to physical systems.

The sensitivity analysis of the knocker parameters forcompensating stiction in the CSTR and the liquid levelsystem revealed that the knocker provided an economi-cally beneficial performance (i.e., smaller pulse ampli-

Figure 7. Linear system 2 [G(s) ) 6/(2s + 1)(4s + 1)(6s + 1)]:knocker sensitivity analysis for stiction band d ) 0.2.

Figure 8. Linear system 3 [G(s) ) 1.54e-1.07s/(5.93s + 1)]: knockersensitivity analysis using a classical stiction model.

Figure 9. Liquid level system.

Figure 10. Measurement data of liquid level for a stiction bandof 4%.

Figure 11. Level loop: surface plot of variations in the ISEreduction ratio obtained verses the knocker parameters.

Table 2. Sensitivity Analysis of Knocker Parameters:Level Loop

knocker parameters

a (%) hk (s) τ (s) ISE reduction ratio

1.0 2.5 1 2.512.5 2.5 1 10.63.25 2.5 1 5.23.5 2.5 1 2.56

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tude and lower pulse energy) when the (1) pulse ampli-tude was nearly half the stiction measure (d), (2) pulsewidth (τ) was about twice the sampling time, and (3)the time between pulses (hk) was about 4-6 times thesampling time of the system (see Figures 5-8 and 11).

Hagglund16 had also suggested similar settings for τand hk and indicated that keeping shorter pulses willnot feed much energy into the valve. On the basis ofthis observation from several case studies, the knockerparameters for τ, hk, and a can be set to 2h, 5h, andd/2, respectively, where h is the sampling time and d isthe stiction measure. It is reasonable to assume thatthe sampling time of the system will be chosen basedon the system time constant.

Hence, for compensation to be effective and beneficial,a systematic way of finding the severity measure d iscrucial and has to be estimated in an automated fashion.We propose to achieve this in a framework that usestwo different techniques for estimating the stictionmeasure d from archived routine operating data. Thisis discussed in the following section.

3. Proposed Stiction Compensation Framework

The proposed framework integrates the tasks ofstiction detection estimation and compensation. This isgiven in Figure 13. The basic idea is as follows: Twodifferent techniques ascertain the presence of stictionusing the archived data. When stiction is detected, astiction measure (d) is obtained using the definition ofstiction given by eq 1. Then, the knocker parametersare set using the heuristic relationship discussed before.A logical switch regulates the input to the valve byflipping between positions 1 (PI output, no stictiondetected) and 2 (knocker output, stiction detected).

3.1. Stiction Detection and Estimation. Severalresearchers have addressed the problem of stictiondiagnosis from a data-driven noninvasive approachusing archived routine operating data.4-9 Althoughstiction detection is an important task by itself, the taskof estimating the severity of stiction is addressed by onlya few authors.7,10-12 In this paper, we apply our earlierwork8,12 for diagnosing and estimating stiction.

3.1.1. Shape-Based Technique. Stiction in controlvalves leaves distinct qualitative shapes in the con-troller output (OP) and controlled process variable

(PV) data. These shapes can be generally categorizedas being square, triangular, and sinusoidal. Table 3,summarized from ref 8, categorizes the observed stictionpatterns of OP and PV for slow and fast dynamicprocesses. When oscillations are not caused due tostiction, the shapes of OP and PV data are sinusoidalin nature due to the continuous presence of feedback.In this method, a pattern matching approach classifiesthe shapes in OP and PV data and diagnoses stiction ifthe shapes match the template given by Table 3. Asuccinct discussion of this method is given here; fordetails refer to ref 8.

In this approach, only oscillating signals are consid-ered and the signal is tested for the presence ofoscillation. An oscillation characterization algorithmthen identifies the zero-crossings in the measurements,the amplitude, and time period of oscillation for eachcycle of oscillation. At least 10 cycles (where available)are considered for shape classification. Then, a referencetemplate pattern (square, triangular, etc.) for both OPand PV is generated for each of the 10 cycles. On thebasis of this reference set, classification of the testpattern (as being square, triangular, sinusoidal, etc.) isdone using dynamic time warping (DTW).20

If the identified shapes of OP and PV match the shapelibrary given in Table 3, stiction is reported. A measure,which is a ratio of the number of cycles identified assticky against the total number of cycles that are takenfor analysis, is reported as a confidence measure forstiction. If stiction is detected, based on the definitionof stiction given in eq 1, the maximum peak-to-peakamplitude of the analyzed OP cycles considered for DTWanalysis is reported as the stiction measure.

3.1.2. Model-Based Technique. The model-basedapproach is based on the identification of a Hammer-stein model of the system comprised of the sticky valveand the process. A Hammerstein system consists of anonlinear element followed by linear dynamics. The taskof stiction diagnosis, as seen from Figure 2b, can beaccomplished by identifying the Hammerstein systemcontaining the stiction nonlinearity and linear plantdynamics from routine operating data. A brief explana-tion of estimating the stiction band is given below. Fora detailed discussion, see ref 8.

A one-dimensional grid is generated for the stictionband d. A value is taken from the grid, and the simple

Figure 12. Stiction compensation results for the liquid levelsystem (a ) 2.0%, hk ) 2.5 s, and τ ) 1 s).

Figure 13. Framework for integrated stiction detection andcompensation.

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model (as given in eq 2 of ref 8) is applied on thecontroller output (OP) to get the stem movements. Sincethe process output (PV) is measured, input-outputrelationships between the calculated stem movement forthe chosen d and process output (PV) can be obtainedusing the ARMAX structure that gives the least Akaikeinformation criterion (AIC) index. This identified rela-tionship models the linear component of the Hammer-stein system.

If the chosen stiction band d is close to a real physicalstiction phenomenon, then the identified process modeloutput prediction will closely match with the measuredprocess output (PV). The closeness measure is calculatedas the mean square error (MSE) between the predictedprocess output (using the known or identified model)and the measured output. The stiction band d ischanged incrementally, and the model identificationprocedure is repeated iteratively until the grid isexhausted. The value of d that gives the minimumobjective function across the grid is the stiction measure.

A nonzero stiction band d indicates the presence ofstiction, and estimation of d quantifies the severity ofstiction. Two different approaches for estimating stictionmeasure are used to improve the robustness of ouroverall approach, as discussed below.

1. Although the shape-based method is intuitive toapply, the stiction shape patterns can change in OP andPV when multiple faults (e.g., external disturbance)affect the loop at the same time. In such cases, theshape-based approach may fail. However, the model-based method, which accounts for external disturbancesas a part of the process model, can give a better stictionmeasure. Hence, both techniques can complement eachother and report a robust stiction measure.

2. It is important to note that the knocker parametersensitivity analysis results showed that the pulseamplitude (a) has to be fixed based on the severity ofthe stiction measure. Both techniques quantify stictionseverity using the stiction model given by eq 1. Also,both methods have been tested on industrial loops.It should be emphasized that stiction diagnosis usingother reported techniques can also be considered as longas an equivalent stiction measure can be obtained.

3.1.3. Knocker Parameter Settings and Imple-mentation. The knocker parameters can be fixed in anautomated fashion based on the reported stiction mea-sure. The stiction measure (d) directly fixes the ampli-tude of the pulse. Typical d values will be in the range0.5-8% and are reported as a percentage of the OP span(0-100%). In practice, some negligible stiction (<0.2%)always exists and d ) 0.5% can be the cutoff range fortriggering stiction compensation. The following are therecommended settings for the knocker: pulse ampli-tude a ) d/2, pulse width τ ) 2h, and pulse frequencyhk ) 5h, where h is the sampling time of the system.This knocker pulse is added to the control signal atevery execution step. The sign of the knocker pulsedepends on the direction of the rate of change of thecontrol signal and is calculated from the slope of thecontrol signal. Since noisy process measurements cangive noisy control signals, slope estimation becomes

difficult. An efficient algorithm that approximates amoving horizon fixed window of the control signal isimplemented for derivative estimation. It can be pointedout that the suggested knocker parameters offer twobenefits: a high ISE reduction ratio and relatively lesspulse energy. The proposed framework is validated onthe level loop.

3.2. Validation of the Proposed Framework:Liquid Level System. Figure 14 shows the measure-ment data (OP, PV, and set point (SP)) during a 15 minoperation of the liquid level pilot plant generated witha stiction band (d ) 6%). The model-based techniquewas applied on the data. The MSE plot for variousstiction bands d showed that the stiction estimate of (d) 6%) explains the closed loop data adequately. Theshape-based technique when applied (in the presenceof stiction, the expected OP and PV shape is triangular;see Table 3) reported a stiction measure (d ) 5.84%)with a confidence measure of 100 obtained from analyz-ing seven full cycles in the data range (t ) 12-876 s).

An average of these two stiction measures, i.e., 5.92%,was used to fix the knocker parameters. Since thesampling time of the system was 0.5 s, the knockerparameters were fixed as pulse amplitude a ) 2.96%,pulse width τ ) 1 s, and pulse frequency hk ) 2.5 s andthe knocker was turned on at t ) 900 s. Figure 15 showsthe results with stiction compensation. The ISE reduc-tion ratio achieved was 6.4, demonstrating the benefitin integrating stiction estimation and compensation.

3.2.1. Validation on a Real Sticky Valve. Asmentioned before, static friction of about 5.5% of thecontroller span (0-100%) was introduced in the valveby tightening the stem packing. A linear variabledifferential transformer (LVDT) (1000 DC-SE Schaevitzsensors) was installed to measure the stem position. Thestem measurement was acquired in the computer usinga data acquisition card (PMD-1208LS). Figure 16 givesthe stiction compensation result obtained for this realsticky valve. The ISE reduction achieved at the process

Table 3. Stiction Pattern Shapes for Flow, Pressure, Temperature, and Integrating Processes

fast process (flow)measurement dominant (I) action dominant (P) action

slow process(press. and temp)

integrating process(level)

level withPI control

OP triangular (sharp) rectangular triangular (smooth) triangular (sharp) triangular (sharp)PV square rectangular sinusoidal triangular (sharp) parabolic

Figure 14. Level loop data with PI controller generated withstiction band d ) 6%.

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output was observed to be better than that obtainedusing software-based stiction compensation results,demonstrating the effectiveness of this proposed frame-work.

3.2.2. On-Line Implementation. An important as-pect that is missing in this framework is that thistechnique is not completely an on-line method, as boththe stiction estimation techniques applied are off-lineprocedures. However, this framework can be imple-mented in a truly “on-line” way by implementing theon-line oscillation detection algorithm proposed byand using that to trigger the model-based and shape-based stiction estimation methods. On the basis ofthe stiction estimated, the knocker settings can be setin an automated fashion and the knocker can beswitched on.

3.2.3. Varying Stiction. Since wear can be nonuni-form along the valve body, frictional forces can bedifferent at different stem positions, making frictionphenomenon vary with time and operating regimes. To

study the knocker performance for varying asymmetricstiction characteristics, an experiment was conductedon the liquid level system. The experiment used thefollowing model for implementing asymmetric stiction:

where d1 and d2 are the static friction during upwardand downward stem movement. The values of d1 andd2 were 4 and 3.6%, respectively. The knocker settingswere (a ) 2%, hk ) 2.5 s, and τ ) 1 s). Figure 17 showsthe corresponding data. Stiction compensation resultsindicate that the knocker is robust to asymmetricstiction behavior.

3.3. Discussion. It was seen that the proposedframework facilitated good compensation results byintegrating stiction estimation and compensation tech-niques. However, there remains an important practicalissue with the underlying knocker technique. Since thestiction model given by eq 1 was used in this work,based on it the stem measurement can be calculated.Figures 16c, 18, and 19 show the resulting stem move-ments when stiction compensation was implemented for

Figure 15. Stiction compensation of the level loop. The resultswere obtained using the proposed framework. The knocker isswitched ON at t ) 900 s.

Figure 16. Stiction compensation results for the level loop witha really sticky valve. The estimated static friction is 5.5%. Stictioncompensation started at time t ) 4000 s. The knocker settingsare as follows: a ) 2.5%, hk ) 2.5 s, and τ ) 1 s. The ISE reductionobtained after knocker implementation in the PV was 12.7. (a)Level and set point; (b) compensated controller output; and (c) stemposition measurement.

Figure 17. Asymmetric stiction behavior: liquid level system.An inlet disturbance at about t ) 850 s was also rejected.

Figure 18. Stem movement predicted for the level case studyunder stiction compensation (for the results shown in Figure 12).

xt ) {xt-1 if (ut - xt-1) e d1 or (xt-1 - ut) e d2ut otherwise

(4)

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the CSTR and the liquid level system, respectively(corresponding OP and PV data are shown in Figures4, 12, and 16a and b, respectively). It can be observedthat the stem switches aggressively between two posi-tions to compensate stiction. To compensate stiction, thestem switches so rapidly that there will be negligibletime for the flow to effect any change in level.

Although the basic idea helps in compensating stictionand improving end-product quality with low variability,such aggressive stem movement will wear out the stemfast. This is an important issue that has to be addressedfor stiction compensation to be widely accepted in theindustry. Changing the value of hk resulted in reducingthe switching frequency of stem movement. However,as observed by Hagglund,16 it resulted in poor compen-sation.

In all of the discussion above, we have assumed thatgood reduction in the ISE ratio is the main objective.This would be the case for loops where the variabilityin the process variable can be tied directly to businessobjectives. These are cases where profit enhancementas a result of variability reduction through stictioncompensation will far outweigh the valve maintenancecosts. There will also be a significant number of valveswhere stiction compensation needs to be balancedagainst valve maintenance/replacement costs. In thesesituations, the objective function needs to be a weightedcombination of the ISE reduction and the variabilitytransferred to the valve. One could explicitly optimizethe knocker to handle such cases. Figure 20 shows anexample where different knocker parameters than whatare suggested here are used to perform this jointoptimization. It is seen that the stem movement hasbeen reduced significantly for a corresponding loss ofperformance in ISE reduction.

In our simulation results, we also noticed cases wherethe stem movement is tremendously minimized withouta loss in ISE reduction performance. Figure 21 showsone such example. This result is achieved by serendipity,where the knocker was turned on for a long durationat the right time such that the valve position movedcloser to its steady-state value than would have beenachieved in the absence of stiction. Due to this, the errorcomes down to a small value and is not further inte-grated enough to cause oscillations.

If this simulation is continued for a longer horizon

and a step disturbance is introduced (see Figure 22),the process moves away from its set point and the limitcycle reappears, indicating a need for new knockersettings.

To summarize, a meaningful set of requirements thatare to be met for a successful stiction compensation canbe listed as follows: (i) less aggressive stem movement(or valve movement); (ii) reduced output variability; (iii)less energy in the signal that is added to the controlsignal. While these seem contradictory objectives, acareful observation of surface plots (see Figures 5-8 and11) combined with the discussion in the previousparagraph suggests that with a little tradeoff in knockerperformance the above stated requirements can besatisfied reasonably. An explicit optimization approachmight be needed to achieve this. The main idea that wepropose here, which is the need for a framework thatintegrates stiction severity with compensation, must bethe building block for any of these approaches forstiction compensation. Further, from the viewpoint of

Figure 19. Stem movement predicted for the CSTR case studyunder stiction compensation (for the results shown in Figure 4). Figure 20. Loss of performance for less stem movement using

knocker settings (a ) 0.088%, hk ) 0.7 s, τ ) 0.3 s) for the process[G(s) ) 1.54e-1.07s/(5.93s + 1)].

Figure 21. Less stem movement using knocker settings (a )0.066%, hk ) 0.8 s, τ ) 0.7 s) for the process [G(s) ) 1.54e-1.07s/(5.93s + 1)].

9172 Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005

industrial implementation, this brings in the questionof maintaining process models for thousands of controlvalves. In contrast, the heuristic knocker approach iseasy to implement and has no model requirements.Hence, we believe that the method of choice willultimately depend on various issues such as cost ofmaintaining models, time length for which the compen-sator will be turned on, valve maintenance costs, andthe criticality of the loop. Also, it is important to studythe implication of energy costs due to aggressive stemmovement versus the quality improvement achieved atthe process output when stiction compensation is ON.For the experimental study considered in this work, theenergy associated with moving the actuator comes fromair-supply pressure (0-18 psi) and current (4-20 mA)for the current to pressure transducer. This cost isinconsequential and cannot be ascertained. More de-tailed study on this aspect is required for stictioncompensation in industrial valves.

4. Conclusion

In this paper, the performance of the friction com-pensator called the knocker proposed by Hagglund16 wasstudied. A new framework that integrates stictionestimation procedures for effective compensation wasproposed. It was demonstrated through experimentaland simulation case studies that the choice of knockerparameters influences the knocker performance. Thesensitivity analysis of the knocker parameters in com-pensating for stiction in the CSTR and the liquid levelsystems uncovered that the knocker provided economi-cally beneficial performance (i.e., small pulse amplitudeand low pulse energy) around the region when the pulseamplitude was nearly half of the stiction measure, thepulse width (τ) was about twice the sampling time, andthe time between pulses (hk) was about 4-6 times thesampling time of the system.

The proposed framework, when implemented on alevel loop, resulted in a reduction in measurement vari-ability of 6-7 times. Future work will include the studyof an optimization approach that finds a trade-offbetween ISE reduction and aggressive stem movement.

Acknowledgment

The authors are grateful to Mark Cooke, Sr. Techni-cian, for interfacing the liquid level system with thecomputer. The authors also thank Clarkson Universityfor funding this work.

Appendix

A. Exothermic CSTR Case Study. The case studyfor the implementation of stiction compensation is anonisothermal jacketed nonlinear CSTR. The processinvolves a liquid-phase reaction A(l) f B(l) which is firstorder in A (see Figure 23). This reaction is highlyexothermic, and the temperature controller controls thetemperature of the reactor by manipulating the flowrate of the coolant (Fj) flowing through the jacket. Thelevel in the reactor is controlled by the level controllerby manipulating the outlet flow rate (F) from thereactor. Both the reactor and the jacket are modeledwith perfectly mixed tank dynamics.

The reactor holdup V and concentration CA at anytime are given by

where Cao, Fo, and To are the concentration, flow rate,and temperature of A at the inlet, respectively, and ko,E, and ∆H are the rate constant, activation energy, andheat of the reaction, respectively. Assuming constantspecific heat capacities Cp and densities F and an overallheat transfer coefficient U and an effective heat transferarea A, an overall heat balance on the reactor gives thereactant temperature T as

Tj, the coolant temperature, is given by a heat balanceon the jacket,

where Fj, Tjo, and Vj are the flow rate, the inlettemperature of the coolant, and the coolant holdup,respectively, and Cj and Fj are the specific heat capacityand the density of the coolant, respectively. The nominalsteady-state operating conditions along with the pa-

Figure 22. Less stem movement using the knocker and thesubsequent effect of disturbance for the process [G(s) ) 1.54e-1.07s/(5.93s + 1)].

Figure 23. CSTR case study.

dVdt

) Fo - F

rA ) Cako exp(-ERT) (5)

dCA

dt)

Fo

V(Cao - Ca) - rA

dTdt

)Fo

V(To - T) +

rA(-∆H)FCp

-UA(T - Tj)

VFCp(6)

dTj

dt)

Fj

Vj(Tjo - Tj) +

UA(T - Tj)VjFjCj

(7)

Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005 9173

rameters used in the model and controller settings arepresented in Table 4, where the subscripts “s” and “n”are used to denote the steady-state and nominal valuesof the quantities and variables described in the aboveequations. The steady state is a highly unstable steadystate, and even a slight deviation from the steady state(due to finite precision arithmetic of computing devicesused for simulation or noise in the system) is sufficientto cause the system to move to a different steady state.The system can be stabilized by using a simple propor-tional controller. A proportional level controller ma-nipulates the liquid leaving the tank, F, as a linearfunction of the volume of the tank.

A second controller (PI) manipulates the flow rate ofthe cooling water to the jacket, Fj, in proportion to thetemperature in the reactor.

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Received for review June 22, 2005Revised manuscript received August 19, 2005

Accepted August 29, 2005

IE050748W

Table 4. Parameters and Nominal Operating Conditionsfor the CSTR

variable value variable value

Vs 48 ft3 Ti 1Vj 3.85 ft3 E 30000 Btu mol-1

CAs 0.245 mol ft-3 ko 7.08 × 1010 h-1

CAon 0.5 mol ft-3 -∆H 30000 Btu mol-1

Ton 530 °R R 1.99 Btu mol-1 °R-1

Ts 600.0 °R U 150 Btu h-1 ft-2 °R-1

Tjon 530 °R A 250 ft2

Tjs 594.6 °R Cp 0.75 Btu lbm-1 °R-1

Fon 40 ft3 h-1 Cj 1.0 Btu lbm-1 °R-1

Fjs 49.9 ft3 h-1 Fj 62.3 lbm ft-3

Kv 10 r 50 lbm ft-3

Kc 4

F ) Fh - Kv(Vh - V) (8)

Fj ) Fh j - Kc((Th - T) + 1Ti∫0

t(Th - T)) dt (9)

9174 Ind. Eng. Chem. Res., Vol. 44, No. 24, 2005