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Automatic on-line estimation of backlash in control loops

Tore Hagglund *

Department of Automatic Control, Lund University, Box 118, SE-22100 Lund, Sweden

Received 16 October 2006; received in revised form 11 January 2007; accepted 13 January 2007

Abstract

This paper describes a new method for detection and estimation of backlash in control loops. The detection procedure is based onnormal operating data. It is not assumed that the output from the backlash is measured. The procedure is automatic in the sense thano information has to be provided from the user to run the procedure. Since an estimate of the dead band caused by the backlash isprovided by the procedure, the procedure gives all information needed to compensate for the backlash. 2007 Elsevier Ltd. All rights reserved.

Keywords: Backlash; Hysteresis; Dead band; Supervision; Detection; Monitoring; Diagnosis; Estimation; Compensation

1. Introduction

Control valves are subject to wear. After some time in

operation, this wear results in friction and backlash thatdeteriorates the control performance. Therefore, valveshave been identified as the major source of problems atthe loop level in process control [1,2].

Valves with a high level of static friction (stiction) resultsin stick-slip motion that causes the control loops to oscil-late. As the amount of friction increases, so does the back-lash in the linkage mechanism in the positioner andactuator of the valve. The backlash adds a time delay tothe control loop which deteriorates the control. In [3], itis reported that a backlash of 10% increases the peak errorat load disturbances with 50% and the integrated absolute

error (IAE) with 100%. These figures are dependent on themagnitude of the load disturbances, but simulation studiespresented later in this paper verify them. Since controlloops in process control applications often are coupled tosurrounding control loops, there is also a risk that the dis-turbances caused by backlash in one loop will propagate toother loops.

When the stiction or backlash becomes large, the valveshould, of course, be repaired or replaced. However, thiscan normally not be done without interrupting the process

For this reason, and other economical reasons, it is ointerest to try to keep the valve running for as long timeas possible. Stiction can be compensated for using themethod presented in[4]. Backlash is easier to compensatefor, since it is an invertible nonlinearity. This will be dis-cussed further in Section3 in this paper.

Even though the problems caused by stiction and back-lash are severe, they are often not discovered by operatorsin process control plants. The main reason is that thereduction of personnel has resulted in a situation whereeach operator simply has too many loops to superviseFor this reason, the research on procedures for automatic

performance monitoring has been very active in the lastdecade. The industrial use of these procedures has alsoincreased rapidly in recent years. Good surveys of perfor-mance monitoring procedures are given in [58]. Thereare several methods suggested for detecting control loopswith stiction, e.g. [912]. However, no efficient procedureto detect backlash has been presented so far, but this paperprovides such a procedure.

In the next section, a description and an analysis obacklash is presented. Section 3 gives some methods tocompensate for backlash. The main section of this paper

0959-1524/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jprocont.2007.01.002

* Tel.: +46 46 2228798; fax: +46 46 138118.E-mail address:[email protected]

www.elsevier.com/locate/jprocon

Journal of Process Control 17 (2007) 489499
mailto:[email protected]:[email protected]



is Section4, where the new backlash estimator is presented.Section5 shows some simulation examples of the backlashestimation procedure. The procedure has also been testedin a paper mill. Results of these industrial tests are pre-sented in Section6.

2. Backlash

Fig. 1 shows a block diagram of a control loop withbacklash. The controller C has setpoint ysp and processoutputyas inputs, and control signal uas output. The con-troller output u is not the input to process P, but it goesthrough a backlash that gives the true process input ub.

Fig. 2describes the function of the backlash, where thedead band caused by the backlash is denoted d. When thecontrol signal u is reversed, the process input ub remainsconstant until u has passed the dead band d.

The describing function YNof a backlash is

ReYNa1

p

p

2arcsin 1

d

a

1

d

a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid

a 2

d

a

s !;

ImYNad

pa 2

d

a

;

1

where ais the input amplitude and dis the backlash giveninFig. 2[13].

The negative inverse of the describing function of thebacklash is shown in Fig. 3. The figure shows also theNyquist plots of two loop transfer functions obtained whenan integrating and a stable process, respectively, are con-trolled by PID controllers. From this figure it can be con-cluded that backlash generates limit cycles whenintegrating processes are controlled by controllers withintegral action. The figure also shows that backlash will

normally not generate limit cycles when the process is sta-ble, provided that the controller is well tuned.

Sincedis divided bya at every position where it appearsin(1), the shape of the describing function is independentof d. This has an interesting consequence. It means thatthe magnitudedof the backlash will influence the oscilla-tion amplitude, but since the intersection with the Nyquistplot occurs at the same position, the oscillation period willremain the same independent of the magnitude of thebacklash.

Throughout this paper it is assumed that the controllerC is a PID controller. This is mostly the case in practice.

However, the results presented in this paper can quite eas-ily be modified to other controllers having integral action.The PID controller used in the following examples has thestructure:

ut K yft 1

Ti

Z yspt yftdt Td

dyft

dt

;

2

whereu is the controller output,yspis the setpoint, yfis thefiltered process output, and the controller parameters aregain K, integral time Ti, and derivative time Td. The con-troller has setpoint weights equal to zero in both the pro-

portional term and the derivative term. This is common

yspu ub y

C PBacklash

Fig. 1. Block diagram of a control loop with backlash. The controller Chas inputs setpointyspand process outputy. The controller outputu goesthrough the backlash and is modified to ub before it enters the input ofprocess P.

u

ub

d

Fig. 2. The output ubfrom a backlash with input u. The dead band of the

backlash is d.

3 2.5 2 1.5 1 0.5 0 0.5 13

2.5

2

1.5

1

0.5

0

0.5

1

Fig. 3. The negative inverse of the describing function of a backlash (solidline) and the Nyquist plots of the loop transfer functions obtained whenthe processes P1=e

0.2s/(s(1 + 0.8s)) (dashed line) and P2= 1/(1 + s)4

(dashed-dotted line) are controlled with PID controllers.

490 T. Hagglund / Journal of Process Control 17 (2007) 489499



in industrial controllers[14]. The process output is filteredthrough a second-order low-pass filter

Yfs 1

1 sTf2Ys; 3

where Yand Yfare the Laplace transforms of the process

output and the filtered process output, respectively. A sec-ond-order filter is used to guarantee high-frequency roll offin the controller, and the filter-time constant is Tf=Td/5.If a PI controller is used, it is suggested to use the filter-timeconstantTf=Ti/10[14].

The following two examples illustrate the problemscaused by backlash in the feedback loop.

Example 1 (Control of an integrating process with back-lash). An integrating process with transfer function

P1s 1

s1 0:8se0:2s 4

is controlled by a PID controller of the form (2) withparameters

K 1:9; Ti 2:4; Td 0:67:

The controller parameters are derived using the MIGO de-sign method[14]. A backlash of 5% (d= 0.05) is introducedin the control loop.

Fig. 3 shows the Nyquist plot of the loop transferfunction and the negative inverse describing function of thebacklash. The curves intersect, which indicates that a limitcycle will occur. The describing function analysis predicts alimit cycle with an amplitude in the process output of 4.4%and an oscillation period of 7.7 s.

Fig. 4 shows the results of the simulations, where asetpoint change is made at t = 0 and a load disturbance isapplied at the process input at t= 100. The figure showsthat the control loop oscillates. The amplitude of theprocess output is 3.2% and the oscillation period is 5.7 s.

This is fairly close to what was predicted by the describingfunction analysis.

Example 2 (Control of a stable process with backlash). Aprocess with transfer function

P2s

1

1 s4 5

is controlled by a PID controller of the form (2) withparameters

K 1:2; Ti 2:2; Td 1:2:

The controller parameters are derived using the MIGO design method[14]. A backlash of 5% (d= 0.05) is introducedin the control loop.

Fig. 3 shows the Nyquist plot of the loop transferfunction and the negative inverse describing function of thebacklash. The curves do not intersect, which indicates thatno limit cycle will occur.

Fig. 5 shows the results of the simulations, where asetpoint change is made at t = 0 and a load disturbance isapplied at the process input at t = 100. Furthermore, noisewith a standard deviation of 1% is added to the processoutput. The figure shows that even though there is no limitcycle, as in the previous example, there is a severedeterioration of the control caused by the backlashBecause of the noise, the control error will never settleThe control signal has to pass the dead band every time theprocess input is to be reversed. This means that there willbe low-frequency disturbances of the process output.

The describing function analysis and the examples illus-trate the control problems that arise when backlash isintroduced in the control loop. Control loops where inte-grating processes are controlled with controllers havingintegral action will go into a limit-cycle oscillation. Theseoscillations will be detected by oscillation detection proce-dures[9].

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100 120 140 160 180 2000.4

0.2

0

0.2

0.4

time (s)

y

u

Fig. 4. Control of the integrating processP1with 5% backlash.

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

time (s)

y

u

Fig. 5. Control of the stable process P2with 5% backlash.

T. Hagglund / Journal of Process Control 17 (2007) 489499 491



Except for extremely lag-dominant processes, the con-trol loops where the process is stable will normally notgo into limit-cycle oscillations. However, the control per-formance is deteriorated even in these cases. This is illus-

trated inFig. 6. The figure shows how the IAE value andthe peak error emax at load disturbances increase whenbacklash appears in the control loop presented inExample2. Both the IAE value and emax increase as the backlash dincreases, even though emax is very noise sensitive. Theincrease is dependent on the magnitude of the load distur-bances. The results agree well with those given in[3], whereit is claimed that 10% backlash results in 100% increase inthe IAE value and 50% increase in the peak error.

The backlash introduces a dead time in the control loop.The length of this dead time is dependent on several statesand parameters. The dead time appears only when the con-

trol signal action is reversed. The dead time is the time ittakes for the control signal to pass the dead band. A lowintegral gain K/Ti gives a long dead time. The dead timebecomes short if the control error is large. It means thatthe dead time is shorter for large load disturbances thanfor shorter. This explains the results shown inFig. 6.

Stable loops with backlash are normally not detected byoscillation detection procedures, since the oscillationamplitude is quite small. A new detection procedure forthese processes is presented in Section4.

3. Backlash compensation

When it is discovered that a control valve has got somuch backlash that the control is deteriorated, the bestaction to take is, of course, to replace or repair the valve.The fact that the amount of backlash normally increaseswith time makes this even more important.

However, to replace or repair a valve means normallythat the production has to be stopped. For this reason,and for the economical reason that it is of interest to usea valve for as long time as possible, it is of interest to com-pensate for the backlash.

A control valve will normally not move on its own orwhen the control signal is constant unless the actuator is

undersized or the positioner is unstable [15]. Therefore,

the position of the control signal with respect to the back-lash is given by the control signal and its history. Thismeans that the backlash is an invertible nonlinearity.

An obvious way to compensate for the backlash is to

make the control signal jump through the backlash everytime the control action is reversed. The compensation canbe seen as a feedforward compensation

u uFB uFF; 6

where u is the controller output, uFBis the feedback term,e.g. the output from the PID controller (2), and uFFis theterm compensating for the backlash.

An ideal backlash compensation would be

uFFd

2sign

du

dt

: 7

This compensation is not realizable in a noisy environment.A possible modification is to filter the control signal beforetaking the derivative. It gives the compensation

uFFd

2sign

dufdt

; 8

whereufis the filtered control signal. Note that the gain ofthe compensator is changed from the true backlash dto avalue dwhere d 6 d. The filtering of the control signal willintroduce a delay in the detection of the sign changes of thecontrol signal rate. This means that the control signal hasalready started its way through the backlash when the rate

change is detected. Therefore, the compensation must besmaller than in the ideal case.

There are other possibilities to perform the backlash com-pensation. In (8), the control signal u has been passed trougha low-pass filter to reduce the noise introduced in the con-troller by the process output y. Inside the controller, themeasurement signal is fed through a high-pass filter becauseof the derivative term. So, the noise level is first amplifiedand then reduced by the low-pass filter. A more direct wayis to base the feedforward on the measurement signaldirectly. One approach that will be used in this paper is

uFF

d

2 signe; 9

0 2 4 6 8 100

50

100

150

0 2 4 6 8 100

10

20

30

40

50IAE emax

dd

Fig. 6. The percentage increase of the IAE value (left) and the peak erroremax(right) at load disturbances caused by backlash inExample 2for values ofthe backlash up to d= 10%. The solid line corresponds to a load change of 10%, and the dashed line to a load change of 20%.




where the control error is e= ysp yfand yfis the filteredprocess output given by (3). When the control error echanges sign, so does the rate of the integral term in thecontroller. Therefore, the feedforward (9) can be seen asan approach where only the noise-insensitive integral partof the controller is considered, and the noise-sensitive pro-

portional and derivative parts are excluded from thecompensation.The backlash compensation will now be illustrated for

the two examples in the previous section.

Example 3 (Backlash compensation for an integrating pro-cess). Consider the control problem in Example 1. Abacklash compensator of the form (8) is added to thecontroller. The filtered control signal is generated as

Ufs 1

1 sTd=52Us: 10

This is a filter with relatively high bandwidth. On the

other hand, the process output is noise free in this exam-ple. Because of this, the gain of the compensator was cho-sen equal to the backlash, i.e. d= d= 0.05, so thecompensator coincides with the ideal compensator (7).The results of the simulations are given in Fig. 7. Com-paringFigs. 4 and 7 it is obvious that the backlash com-pensator gives an almost ideal compensation in this noise-free case.

Example 4 (Backlash compensation for a stable pro-cess). Consider the control problem inExample 2. A back-lash compensator of the form(9)is added to the controller.In this example, the compensation is more complicatedthan in the previous example since the process output iscorrupted with noise.

Fig. 8 shows the result when a compensator withd= d = 0.05 is used. It is obvious that the gain of thecompensator is too high, and that the compensator causes

the loop to oscillate. Reducing the compensator gain tod= 0.4 gives the results shown in Fig. 9. This compensatorgives a process output that is almost unaffected by thebacklash. The control signal has some high-frequencyshifts at certain periods. This could have been avoided byadjusting the filtering of the process output. On the otherhand, these variations do not cause any valve movementsbecause of the backlash.

Fig. 6 shows that a backlash of 5% gives an increasedIAE value of about 45% when the load changes 20%. Withthe compensator, this increase is reduced to about 15%.

4. Backlash estimation

Because of the reduction of personnel in process controlplants, the times between the manual inspections of the

control loops is often long. Therefore, it is of interest to

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100 120 140 160 180 2000.4

0.2

0

0.2

0.4

time (s)

y

u

Fig. 7. Control of the integrating processP1with 5% backlash (d= 0.05)

and a backlash compensator with d =d= 0.05.

0 20 40 60 80 100 120 140 160 180 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

time (s)

y

u

Fig. 8. Control of the process P2 with 5% backlash (d= 0.05) and abacklash compensator with d =d= 0.05.

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

time (s)

y

u

Fig. 9. Control of the process P2 with 5% backlash (d= 0.05) and abacklash compensator with d = 0.04.




detect and estimate the amount of backlash automaticallybased normal operating data. Automatically means thatno parameters or other guidance should have to be pro-vided by the personnel. This feature is a prerequisite forthe acceptance of the procedure in process control applica-tions. Such a procedure is presented below. The procedure

treats only stable process. As mentioned before, integratingprocesses with backlash will result in an oscillating controlloop. These loops are detected by the procedure presentedin[9].

Fig. 10shows a part of the simulation given in Fig. 5.The process output y has been filtered through the filter(3). It means that the process output presented in Fig. 10is the signal that enters the PID algorithm. The signalsshow the typical pattern obtained when a stable processis controlled by a controller having integral action andwhen there is backlash in the control loop. The process out-put remains a distance Dyfrom the setpoint while the con-trol signal drifts through the dead band caused by thebacklash. When the control signal has changed an amountDu, the process output is moved towards the setpoint. Thetime instances when the process output crosses the setpointare marked in the figure. The time between these zerocrossings is Dt= ti+1 ti.

The change Duof the control signal is mainly caused bythe integral part of the controller. It means that

Du K

Ti

Z ti1ti

jejdtK

TiDyDt; 11

where

DyZ t

i1

ti

jejdt=Dt; 12

seeFig. 10.

If the signals change slowly, the process dynamics can beneglected and the relation between the process output andthe control signal is mainly determined by the static processgain Kp. The relation is

Dy KpDutrue; 13

where Dutrueis the part ofDuwhere the backlash is closedand the valve moves. It means that

Du Dutrue d: 14

From Eqs.(11)(14)the following equation for estimatingthe backlash is obtained:

d Du DutrueK

TiDyDt

Dy

Kp

K

TiDt

1

Kp

Dy: 15

The backlash estimator (15) assumes that the signalschange slowly. A convenient way to check this is to see ifDt is long compared to the closed-loop time constant. Inthe examples presented later, estimation is only performedwhen DtP 5Ti.

The information required to determine the backlash on-line is the controller parameters K and Ti, and the staticprocess gain Kp. Further, it is necessary to measure Dyfrom(12), i.e. to integrate the control error between zerocrossings, and the time Dt between zero crossings. Notethat it is not necessary to have access to the control signalu.

It is a drawback that the process gain Kp is used in thealgorithm, since this gain often is unknown. On the otherhand, the estimate dis quite insensitive to errors in the esti-

mate ofKp. To see this, rewrite (15)to

d K Dt

Ti

1

KKp

Dy: 16

35 40 45 50 55 60 650.38

0.39

0.4

35 40 45 50 55 60 650.35

0.4

time (t)

t

y

u

ti ti+1

yf

u

Fig. 10. Part of the simulation given in Fig. 5.




The first term inside the brackets is always greater than 5,since estimation is only performed when DtP 5Ti. Forwell-tuned controllers applied to processes that are not de-lay-dominated, the productKKpis normally larger than 0.5[14]. Assuming these extreme values, i.e.

^d K 5

2

Kp

Dy; 17

a default value Kp= 1.5 will give estimation errors lessthan 20% as long as the true process gain is in the range1 < Kp< 3.4. This is the case in most process controlplants, since industrial controllers normally work with nor-malized signals.

It is important that the noise does not cause zero-cross-ings. Therefore, the process outputy is not only filtered bythe second-order filter(3), but an additional second-orderfilter is applied before the signal is treated in the estimationprocedure. In the examples presented in this paper, the timeconstant of this filter is Ti/2.

On-line procedures like this must always have a securitynet[16,17]. The final derivation of this security net must bedeveloped during industrial field tests. One element of thisnet has already been implemented. Load disturbances mayobviously deteriorate the backlash estimation. To checkthat the process output has a form similar to the one inFig. 10, estimation is only performed when emax< 2Dy,whereemaxis the absolute value of the largest control errorin the interval [ti, ti+1]. A skeleton code describing the back-lash estimator is given inFig. 11.

The estimation procedure can be used in several ways.

First of all, it can be used as a detection procedure in away similar to the oscillation detection procedure in [9].In [9], the magnitudes of the IAE values between zero

crossings of the control error are studied, and it is con-cluded that an oscillation is present if the rate of largeIAE values becomes high. In this paper, the control perfor-mance between zero crossings is also studied. Analogouslyto [9], it can be concluded that backlash is present in theloop if the rate of backlash detections gets high.

If backlash is detected, and if the estimated backlashvalues are close, then one can also draw a conclusion aboutthe amount of backlash. This is necessary if the goal is notonly to detect backlash, but also to compensate for it.

If there is stiction present in the control loop, the back-lash estimated by the estimation procedure is the sum ofthe backlash and the dead band caused by stiction. Thisis probably a good feature, since the backlash compensatorwill then not only compensate for the backlash, but also forthe stiction.

The derivation of the backlash estimator is made assum-ing that a PID controller is used. However, it is straightfor-ward to modify the method to other controllers havingintegral action.

5. Simulation example

The detection and estimation procedure derived in theprevious section will now be illustrated through simula-tions of the control loop presented inExample 2. ProcessP2 given by (5) is controlled with a PID controller tunedby the MIGO tuning rules. Measurement noise with a stan-dard deviation of about 1% is added to the process outputThe setpoint is changed at time t= 0 and a load distur-

bances at the process input is applied at time t= 100.Figs. 1215 show the results obtained for differen

amounts of backlash, varying from d= 1% to d= 10%

Fig. 11. Skeleton code for the backlash estimator.




The times of detection are marked in the graphs, as well asthe values of the backlash estimates d.

The figures show that the deterioration of the controlincreases as the amount of backlash increases. During thesimulation time of 200 s, between five and seven detectionsare made in each case. The accuracy of the backlash esti-mates increases as the backlash increases. The estimatedbacklash d is in most cases smaller than the true backlashd. This is a good property, since it is important that thebacklash compensator does not use a gain that is too high.

The simulation experiments show that the estimationprocedure works well. Even for a backlash as small asd= 1%, where the effects in the process output are hardlynoticeable because of the noise level, the procedure man-ages to detect the backlash and to provide fairly accurate

estimates.

6. Industrial tests

The backlash estimation procedure has been tested ona flow control loop in a paper mill. The process sectionis a pipe where pulp is transported from a recycling-pulptower to a tank. See the P&I diagram in Fig. 16. A PIDcontroller (FIC) controls the pulp flow through a valve.The process output y is the pulp flow, measured in therange 0900 m3/h, and the controller output u is in therange 0100%.

The setpoint is external, and is given by a controller(LIC) that controls the tank level downstream. This meansthat the flow controller is a slave controller in a cascadeconfiguration. The pulp flow is driven by a pump which

is controlled by a pressure controller (PIC). The flow and

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

2.8 2.6 2.6 2.5 2.6 2.6 2.5

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

time (s)

y

u

d = 3%

d =

Fig. 13. Backlash estimation applied to the control loop in Example 2with the backlash d= 3%. The times of detection and the values of dareindicated in the upper graph.

0 20 40 60 80 100 120 140 160 180 200

0

0.2

0.4

0.6

0.8

1

4.9 4 .6 4.5 4.9 4.7 4.6 4.6

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

time (s)

y

u

d = 5%

d =


0 20 40 60 80 100 120 140 160 180 200

0

0.2

0.4

0.6

0.8

1

0.6 0.5 0.4 0.5 0.4

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

time (s)

y

u

d = 1%

d =


0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

1

11.2 10 9.6 10.1 9.7

0 20 40 60 80 100 120 140 160 180 2000

0.2

0.4

0.6

0.8

time (s)

y

u

d = 10%

d =

Fig. 15. Backlash estimation applied to the control loop in Example 2with the backlashd= 10%. The times of detection and the values of dareindicated in the upper graph.




the pressure controllers interact. To reduce this interaction,the bandwidth of the flow loop, which normally is quitefast, has been reduced by introducing a low-pass filter witha time constant of 20 s in the loop.

A manual test was performed to check the amount ofbacklash in the valve. The result is shown in Fig. 17. Theflow controller output is first increased to ensure that the

gap is closed. Since the flow increases, the gap is closedwhen the control signal is at the final value u= 39%. Thecontroller output is then reversed and decreased in stepsof 1%. The first steps do not result in any flow decrease,indicating that the control signal is inside the dead band.However, the step made from the value u= 36% gives aflow decrease, showing that the gap is closed near this valueof the control signal. The test shows that the backlash isaround d= 3%.

The flow controller is a PI controller with parametersK= 0.6 and Ti= 28 s. The signals used in the controllerare normalized to the range [0,1]. The static process gainwas estimated to Kp= 1.3. Fig. 18 shows the result of a

recording made for about 4000 s. The loop is oscillating

because of the oscillating setpoint. The setpoint oscillationsare probably generated by the flow variations caused by thebacklash.

Fig. 18shows that backlash was detected five times dur-ing the test, with backlash estimates ranging from 2.5% to3.1%. These estimates are close to those obtained from themanual tests inFig. 17.

Setpoint variations may disturb the backlash estimatorIf the test emax< 2Dy were not present, fifteen detectionswould have been obtained during the test, and especiallythe last two major setpoint changes would have given back-lash estimates that are far too large.

To get rid of the disturbances caused by the external set-point, experiments with a fixed internal setpoint were alsoperformed.Fig. 19shows the results of such a test.

ComparingFigs. 18 and 19, it is obvious that the oscil-lations caused by the external setpoint have disappearedFig. 19 shows that there are some low-frequency distur-

bances present. They are probably caused by interactionfrom the pressure control loop. These disturbances aremore difficult to handle than the high-frequency noise inthe simulation experiments in the previous sections.

Three backlash detections were made during the experi-ments, with the estimates 1.6%, 2.4%, and 2.4%, respec-tively. These values are slightly lower than those obtainedin Fig. 18. This is expected, since the setpoint variationsin the previous example amplifies the effect of the backlashFurthermore, already the derivation of the method and thesimulation examples have shown that the backlash esti-mates are expected to be conservative.

To summarise, the industrial tests show that the back-lash estimation procedure works also in an industrial envi-ronment with difficult low-frequency disturbances. Toobtain a robust procedure that is automatic in the sensethat no user interaction is needed, more industrial fieldtests have to be performed, and it is likely that the supervi-sory net must be extended.

7. Conclusions

Stiction and backlash in control valves are the majorproblem at the loop level in process control plants. There

are two aspects of the problem. First of all, the nonlinear-

Pulp tower TankPIC

PT

LIC

FIC

FT

LT

Fig. 16. Process and instrumentation diagram of the pulp flow section.

0 50 100 150 200 250410

420

430

440

450

0 50 100 150 200 25032

34

36

38

40

Flow [0-900m3/ h]

Control signal [0-100%]

time (s)

Fig. 17. Manual test to check the amount of backlash in the valve. Thebacklash is estimated to d= 3%.



http:///reader/full/automatic-on-line-estimation-of-backlash-in-control-loops-t

0 500 1000 1500 2000 2500 3000 3500 40000.38

0.4

0.42

0.44

0.46

0.48

0.5

0 500 1000 1500 2000 2500 3000 3500 4000

0.24

0.26

0.28

0.3

0.32

d = 2.5 2.7 3.1 2.9 2.9

Normalized flow

Normalized control signal

time (s)

Fig. 18. Backlash estimation applied to the pulp flow control loop. The upper graph shows the external setpoint (noisy signal) and the process output(flow). The lower graph shows the control signal. The estimated values of dare indicated in the upper graph.

0 500 1000 1500 2000 2500 30000.39

0.4

0.41

0.42

0.43

0 500 1000 1500 2000 2500 3000

0.25

0.26

0.27

0.28

d = 1.6 2.4 2.4

Normalized flow

Normalized control signal

time (s)

Fig. 19. Backlash estimation applied to the pulp flow control loop. The upper graph shows the constant internal setpoint and the process output (flow).

The lower graph shows the control signal. The estimated values of dare indicated in the upper graph.



http:///reader/full/automatic-on-line-estimation-of-backlash-in-control-loops-t

ities deteriorate the control performance. Furthermore, theloops facing these problems often remain undiscovered bythe personnel in process control plants.

Procedures for stiction detection and for stiction com-pensation have been available for over a decade, and theyare used in many industrial plants today. Compensation

for backlash is simple, but these procedures are seldomused in process control plants. The major reason for thisis that no backlash detection and backlash on-line estima-tion procedure have been presented.

This paper presents an on-line procedure for detectionand estimation of backlash in control loops. It is givenby Eq. (15) and some further details are summarized inFig. 11. The method is automatic in the sense that no infor-mation has to be provided from the user. The only infor-mation needed except for the signals are the controllerparameters. The effectiveness of the method has been dem-onstrated through simulations and industrial field tests.The method is patent pending.

References

[1] D.B. Ender, Process control performance: not as good as you think,Control Engineering 40 (10) (1993) 180190.

[2] W.L. Bialkowski, Dream vs. reality a view from both sides of thegap, Pulp and Paper Canada 11 (1994) 1927.

[3] G. McMillan, Valve response control, improvement, Encyclopedia ofChemical Processing and Design 61 (1997) 99113.

[4] T. Hagglund, A friction compensator for pneumatic control valves,Journal of Process Control 12 (2002) 897904.

[5] S. Qin, Control performance monitoring a review and assessmentComputers and Chemical Engineering 23 (1998) 173186.

[6] T.J. Harris, C.T. Seppala, L.D. Desborough, A review of performance monitoring and assessment techniques for univariate andmultivariate control systems, Journal of Process Control 9 (1) (1999117.

[7] M.A. Paulonis, J.W. Cox, A practical approach for large-scalecontroller performance assessment, diagnosis, and improvementJournal of Process Control 13 (2003) 155168.

[8] M. Jelali, An overview of control performance assessment technologyand industrial applications, Control Engineering Practice 14 (5(2006) 441466.

[9] T. Hagglund, A control-loop performance monitor, Control Engineering Practice 3 (1995) 15431551.

[10] A. Horch, A simple method for detection of stiction in control valvesControl Engineering Practice 7 (10) (1999) 12211231.

[11] N.F. Thornhill, T. Hagglund, Detection and diagnosis of oscillationin control loops, Control Engineering Practice 5 (1997) 13431354.

[12] A. Singhal, T. Salsbury, A simple method for detecting valve stictionin oscillating control loops, Journal of Process Control 15 (4) (2005)371382.

[13] M. Vidyasagar, Nonlinear systems analysis, second ed., Prentice Hall1993.[14] K.J. Astrom, T. Hagglund, Advanced PID Control. ISA Th

Instrumentation, Systems, and Automation Society, Research Trian-gle Park, NC 27709, 2005.

[15] T.L. Blevins, G.K. McMillan, W.K. Wojsznis, M.W. BrownAdvanced Control Unleashed. ISA, Research Triangle Park, NC2003.

[16] T. Hagglund, Industrial implementation of on-line performancemonitoring tools, Control Engineering Practice 13 (2005) 13831390

[17] T. Hagglund, K.J. Astrom, Supervision of adaptive control algorithms, Automatica 36 (2000) 11711180.


automatic on-line estimation of backlash in control loops tore hugland.pdf

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