Autotuning of PID Controllers [electronic resource]: A Relay Feedback Approach

267 Pages·2006·8.09 MB·english

by  Yu

Autotuning of PID Controllers
Cheng-Ching Yu
Autotuning of
PID Controllers
A Relay Feedback Approach
2nd Edition
With140Figures
123
Cheng-ChingYu,PhD
DepartmentofChemicalEngineering
NationalTaiwanUniversity
1RooseveltRoad
Section4
Taipei106-17
Taiwan
BritishLibraryCataloguinginPublicationData
Yu,Cheng-Ching,1956-
AutotuningofPIDcontrollers.-2nded.
1.PIDcontrollers
I.Title
629.8
ISBN-10:1846280362
LibraryofCongressControlNumber:2005931920
ISBN-10: 1-84628-036-2 2ndedition e-ISBN 1-84628-037-0 Printedonacid-freepaper
ISBN-13: 978-1-84628-036-8 2ndedition
ISBN: 3-540-76250-7 1stedition
©Springer-VerlagLondonLimited2006
Firstpublished1999
Secondedition2006
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Preface
This edition is a major revision to the first edition. The revision is motivated by
thenewprogressinrelayfeedbackautotuning,asproposed byBillLuyben,where
the shape of therelay response can be utilized to identify likely model structure.
Several new chapters have been added, notably the use of the shape-factor for
autotuning and controller monitoring, incorporating autotuning in a multiple-
model setup, dealing with an imperfect actuator. Atthe turn of thecentury, com-
petitiveness in the global economy remains the same and the need for rapid and
flexiblemanufacturinghasbecomestandardpractice. Thishas given process con-
trolengineersanexpandedroleinprocessoperation.
Ithaslongbeenrecognizedthatindustrialcontrolisoneofthekeytechnologies
to make existing processes economically competitive. In theory, sophisticated
control strategies–supervisory, adaptive, model predictive control–should be the
norm of industrial practice in modern plants. Unfortunately, a recent survey, by
Desborough and Miller has shown otherwise. This indicates that 97% of regula-
tory controllers are of the proportional–integral–derivative (PID) type and only
32%oftheloops show“excellent”or “good” performance.Six yearshavepassed
sincethefirstedition was published,andthepracticeofindustrialprocess control
isverymuchthesame:PIDcontrollersarewidelyusedbutpoorlytuned.
This book is aimed at engineers and researchers who are looking for ways to
improve controller performance. It provides a simpleand yet effective method of
tuning PID controllers automatically. Practical tools needed to handle various
processconditions,e.g.loaddisturbance,nonlinearityandnoise,arealsogiven.
The mathematics of the subject is kept to a minimum level and emphasis is
placed on experimental designs that give relevant process information for the in-
tended tuning rules. Numerous worked examples and case studies are used to il-
lustratetheautotuningprocedureandclosed-loopperformance.
This book is an independent learning tool that has been designed to educate
peoplein technologies associated with controller tuning. Most aspects ofautotun-
ingarecovered,andyouareencouragedtotrythemoutonindustrialcontrolprac-
tice.
The book is divided into 12 chapters. In Chapter 1, perspectives on process
control and the need for automatic tuning of PID controllers are given. The PID
vii
viii Preface
controller is introduced in Chapter 2. Corresponding P, I, and D actions are ex-
plained and typical tuningrules aretabulated. Chapter 3 shows how and whythe
relayfeedback tests can beused asameans ofautotuning,andan autotuningpro-
cedure is also given. A simple and an improved algorithm are explored and ana-
lytical expressions forrelayfeedback responses arealsoderived. Theshapeofre-
layfeedback is discussed in Chapter 4. This gives useful information on possible
model structure and ranges of model parameters. Once model structure is avail-
able, anappropriatetuningrulecan beapplied for improved controlperformance.
InChapter5,aramptypeofrelayisproposedtoprovidebetteraccuracyinidenti-
fying process parameters. The improved experimental design is shown to work
well for both single-input–single-output (SISO)andmultivariablesystems. Chap-
ter 6 is devoted to a morecommon situation: multivariablesystems. Experiments
are devised and procedures aregiven for theautomatic tuning of multiloop SISO
controllers.Chapter7isdevotedtoapracticalproblem:autotuningunderloaddis-
turbance. A procedure is presented to find controller parameters under load
changes. Themultiple-modelapproach isknown tobeeffectivein handlingproc-
esses thatarenonlinear, andChapter 8extendstherelayfeedback autotuningin a
multiple-modelframework.InChapter 9, thecontrollermonitoringproblemisad-
dressed. Again, the shape of relayfeedback response gives a useful indication on
theappropriatenessofthetuningconstant.Moreover,monitoringandretuningare
completed in a single-relay feedback test. The issue of an imperfect actuator is
dealtwithinChapter10.Forcontrolvalvewithhyteresis,anautotuningprocedure
isproposedtoovercomethefrequentlyencounteredprobleminpractice. InChap-
ter 11, the importance of control structure design is illustrated using a plantwide
control example. Procedures for thedesign ofthecontrol structureandthetuning
oftheentireplantaregivenandtheresultsclearlyindicatethatthecombinationof
better process understanding and improved tuning makes the recycle plant much
easiertooperate.Chapter12summarizestheguidelinesforautotuningprocedures
anddescribeswhenandwhattypeofrelayfeedbacktestshouldbeemployed.
Thebook is based on workmystudentsand Ihavebeen engagedin for almost
20 years to improve PID controller performance. I wrote the book because I be-
lievestronglyin thebenefitsofimproved control, andawell-tunedPIDcontroller
isafundamentalstepforimprovedprocessoperation.
Acknowledgements
Thanks are due to K. J. Åström, T. Hägglund, W. L. Luyben, Q. G. Wang, I. B.
Lee, andmycolleagueH. P. Huang,whohavecontributed tothedevelopmentof
relay feedback autotuning. Undergraduate and graduate students and postdoc fel-
lowsofNTUandNTUSThavecontributedtothisbookbytheirquestionsandin-
terestin thesubject. Inparticular,thecontinuous feedback fromWaltersShen,K.
L. Wu,D.M.Chang, Y.C.Cheng, Y.H. Chen,T.Thyagarajan,and R.C.Panda
needs to be acknowledged. The superb editing work of Brenda Tsai and Vincent
Changmadethisbookpossible.Finally,withouttheunderstandingandsupportof
myfamily,thisbookwouldnothavebeenundertaken,orcompleted.
Contents
1 Introduction...................................................................................................1
1.1 ScopeofProcessControl.........................................................................1
1.2 Proportional–Integral–DerivativeControlPerformance............................2
1.3 RelayFeedbackIdentification.................................................................5
1.4 Conclusion..............................................................................................6
1.5 References..............................................................................................7
2 FeaturesofProportional(cid:2)Integral(cid:2)DerivativeControl................................9
2.1 Proportional–Integral–DerivativeController............................................9
2.1.1 ProportionalControl........................................................................9
2.1.2 Proportional–IntegralControl.........................................................10
2.1.3 Proportional–Integral–DerivativeControl.......................................12
2.2 Proportional–Integral–DerivativeImplementation..................................13
2.2.1 ResetWindup................................................................................13
2.2.2 ArrangementofDerivativeAction..................................................15
2.3 Proportional–Integral–DerivativeTuningRules.....................................17
2.3.1 Ziegler–NicholsTypesofTuningRules..........................................17
2.3.2 Model-basedTuning......................................................................19
2.4 Conclusion............................................................................................20
2.5 References............................................................................................20
3 RelayFeedback...........................................................................................23
3.1 ExperimentalDesign.............................................................................24
3.2 ApproximateTransferFunctions:Frequency-domainModeling.............26
3.2.1 SimpleApproach...........................................................................27
3.2.2 ImprovedAlgorithm......................................................................30
3.2.3 ParameterEstimation.....................................................................32
3.2.4 Examples.......................................................................................32
3.3 ApproximateTransferFunctions:Time-domainModeling.....................36
3.3.1 DerivationforaSecond-orderOverdampedSystem........................39
3.3.2 Results...........................................................................................41
ix
x Contents
3.3.3 Validation......................................................................................44
3.4 Conclusion............................................................................................44
3.5 References............................................................................................46
4 ShapeofRelay.............................................................................................47
4.1 ShapesofRelayResponse.....................................................................47
4.1.1 Shapes...........................................................................................48
4.1.2 ModelStructures............................................................................50
4.1.2.1First-orderPlusDeadTime.......................................................50
4.1.2.2Second-orderPlusSmallDeadTime.........................................51
4.1.2.3HighOrder...............................................................................52
4.2 Identification.........................................................................................52
4.2.1 IdentificationofCategory1:First-orderPlusDeadTime................52
4.2.1.1Category1a:TrueFirst-orderPlusDeadTime...........................52
4.2.1.2Category1b:ApproximatedFirst-orderPlusDeadTime............55
4.2.2 IdentificationofCategory2:Second-orderPlusSmallDeadTime..56
4.2.3 IdentificationofCategory3:Highorder..........................................58
4.2.4 Validation......................................................................................59
4.3 ImplicationsforControl........................................................................62
4.3.1 Proportional–Integral–DerivativeControl.......................................62
4.3.1.1Category1:First-orderPlusDeadTime....................................62
4.3.1.2Category2:Second-orderPlusSmallDeadTime......................64
4.3.1.3Category3:HighOrder.............................................................64
4.3.2 Results...........................................................................................64
4.3.3 Extension.......................................................................................70
4.3.3.1Dead-time-DominantProcess....................................................70
4.3.3.2HigherOrderProcess................................................................71
4.4 Conclusion............................................................................................72
4.5 References............................................................................................73
5 ImprovedRelayFeedback...........................................................................75
5.1 Analysis................................................................................................76
5.1.1 Ideal(On–Off)RelayFeedback......................................................76
5.1.2 SaturationRelayFeedback.............................................................78
5.1.3 PotentialProblem...........................................................................83
5.2 ImprovedExperimentalDesign.............................................................84
5.2.1 SelectionoftheSlopeofSaturationRelay......................................84
5.2.2 Procedure.......................................................................................89
5.3 Applications..........................................................................................89
5.4 Conclusion............................................................................................95
5.5 References............................................................................................96
6 MultivariableSystems.................................................................................97
6.1 Concept................................................................................................97
6.1.1 Single-input–Single-outputAutotuning...........................................97
6.1.2 Multiple-input–Multiple-outputAutotuning....................................99
6.2 Theory................................................................................................101
Contents xi
6.2.1 SequentialDesign........................................................................101
6.2.2 ProcessCharacteristics.................................................................104
6.2.3 SequentialIdentification...............................................................108
6.3 ControllerTuning................................................................................111
6.3.1 PotentialProbleminZiegler–NicholsTuning...............................111
6.3.2 ModifiedZiegler–NicholsMethod................................................111
6.3.3 PerformanceEvaluation:LinearModel.........................................115
6.4 Properties............................................................................................117
6.4.1 Convergence................................................................................117
6.4.2 TuningSequence..........................................................................119
6.4.3 ProblemofVariablePairing.........................................................120
6.4.4 SummaryofProcedure.................................................................122
6.5 Applications........................................................................................123
6.5.1 Moderate-purityColumn..............................................................123
6.5.2 High-purityColumn.....................................................................124
6.5.3 T4Column...................................................................................128
6.6 Conclusion..........................................................................................130
6.7 References..........................................................................................130
Appendix....................................................................................................132
7 LoadDisturbance......................................................................................135
7.1 Problems.............................................................................................135
7.1.1 StepChangeversusContinuousCycling.......................................135
7.1.2 EffectofLoadChangeonRelayFeedbackTest............................138
7.2 Analyses.............................................................................................139
7.2.1 CausesofErrors...........................................................................139
7.2.2 Output-biasedRelayFeedbackSystem.........................................142
7.2.3 DerivationofBiasValue(cid:2) ........................................................144
o
7.2.3.1EffectofLoadDisturbance.....................................................144
7.2.3.2OppositeEffectfromOutput-biasedRelay..............................146
7.3 SummaryofProcedure........................................................................148
7.4 Applications........................................................................................149
7.4.1 LinearSystem..............................................................................150
7.4.2 BinaryDistillationColumn..........................................................152
7.5 Conclusion..........................................................................................153
7.6 References..........................................................................................154
8 MultipleModelsforProcessNonlinearity................................................155
8.1 AutotuningandLocalModel...............................................................156
8.2 ModelScheduling...............................................................................157
8.2.1 Takagi–SugenoFuzzyModel.......................................................157
8.2.1.1SingleInputSystems..............................................................158
8.2.1.2MultipleInputsSystems..........................................................160
8.2.2 SelectionofScheduledVariable...................................................162
8.3 NonlinearControlApplications...........................................................163
8.3.1 TransferFunctionSystem.............................................................163
8.3.2 TennesseeEastmanProcess..........................................................167
xii Contents
8.4 Conclusion..........................................................................................173
8.5 References..........................................................................................173
9 ControlPerformanceMonitoring.............................................................175
9.1 ShapeFactorforMonitoring................................................................176
9.1.1 ShapesoftheRelayFeedback......................................................176
9.2 PerformanceMonitoringandAssessment............................................179
9.2.1 OptimalPerformance...................................................................179
9.2.2 ProposedMonitoringandAssessmentProcedure..........................180
9.2.2.1Case1:(cid:4) /(cid:4)=1 ....................................................................180
I
9.2.2.2Case2:(cid:4) /(cid:4)>1 ....................................................................180
I
9.2.2.3Case3:(cid:4) /(cid:4)<1 ....................................................................181
I
9.2.3 IllustrativeExamples....................................................................184
9.3 Applications........................................................................................188
9.3.1 Second-orderPlusDeadTimeProcesses.......................................188
9.3.2 High-orderProcesses...................................................................193
9.4 Conclusion...........................................................................................196
9.5 References...........................................................................................196
10 ImperfectActuators................................................................................197
10.1 PotentialProblems............................................................................197
10.2 IdentificationProcedure....................................................................202
10.2.1 Two-stepProcedure...................................................................202
10.2.2 SimultaneousIdentification........................................................205
10.3 Applications......................................................................................206
10.3.1 LinearSystems...........................................................................206
10.3.1.1Noise-freeSystem.................................................................206
10.3.1.2SystemswithMeasurementNoise.........................................207
10.3.1.3LoadDisturbance..................................................................210
10.3.2 NonlinearProcess......................................................................212
10.3.2.1Two-stepProcedure..............................................................212
10.3.2.2SimultaneousProcedure........................................................212
10.4 Conclusion........................................................................................216
10.5 References........................................................................................217
11 AutotuningforPlantwideControlSystems............................................219
11.1 RecyclePlant....................................................................................219
11.2 ControlStructureDesign...................................................................222
11.2.1 UnbalancedSchemes..................................................................222
11.2.1.1ColumnOverwork................................................................222
11.2.1.2ReactorOverwork.................................................................226
11.2.2 BalancedScheme.......................................................................227
11.2.3 Controllability............................................................................228
11.2.4 Operability.................................................................................231
11.3 ControllerTuningforEntirePlant.....................................................232
11.3.1 TuningSteps..............................................................................233