Table Of ContentMichaelA.Johnson
MohammadH.Moradi
PIDControl
NewIdentificationandDesignMethods
Michael A.Johnson and Mohammad H.Moradi (Editors)
With
J.Crowe,K.K.Tan,T.H.Lee,R.Ferdous,M.R.Katebi,H.-P.Huang,
J.-C. Jeng,K.S.Tang,G.R.Chen,K.F.Man,S.Kwong,A.Sánchez,
Q.-G. Wang,Yong Zhang,Yu Zhang,P.Martin,M.J.Grimble and
D.R. Greenwood
PID Control
New Identification and Design Methods
With285Figures
1 3
MichaelA.Johnson,PhD MohammadH.Moradi,PhD
IndustrialControlCentre ElectricalEngineeringGroup
UniversityofStrathclyde FacultyofEngineering
GrahamHillsBuilding Bu-AliSinaUniversity
50GeorgeStreet Hamadan
Glasgow Iran
G11QE
UK
BritishLibraryCataloguinginPublicationData
PIDcontrol:newidentificationanddesignmethods
1.PIDcontrollers
I.Johnson,MichaelA.,1948- II.Moradi,MohammadH.
(MohammadHassan),1967-
629.8
ISBN1852337028
LibraryofCongressCataloginginPublicationData
PIDcontrol:newidentificationanddesignmethods/MichaelA.Johnson
(editor),MohammedH.Moradi(editor);withJ.Crowe...[etal.]
p. cm.
Includesbibliographicalreferencesandindex.
ISBN1-85233-702-8
1.PIDcontrollers–Designandconstruction.I.Johnson,MichaelA.,1948-II.Moradi,
MohammadH.(MohammadHassan),1967-III.Crowe,J.
TJ223.P55P532005
629.8--dc22 2004057797
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For the gift ofloving parents and family and for my grandchildren,Ethan and
Teigan
MichaelA.Johnson
To my wife,Mehri,and my sons,Arefand Ali,for their understanding and
consideration;To my parents for their love over many years and to my family
for their support.
MohammadH.Moradi
Preface
Theindustrialevidenceisthatformanycontrolproblems,particularlythoseoftheprocessindustries,
theProportional,IntegralandDerivative(PID)controlleristhemaincontroltoolbeingused.Forthese
industrial problems,the PID control module is a building block which provides the regulation and
disturbance rejection for single loop, cascade, multi-loop and multi-input multi-output control
schemes. Over the decades, PID control technology has undergone many changes and today the
controllermaybeastandardutilityroutinewithinthesupervisorysystemsoftware,adedicatedhard-
ware process controller unit or an input–output module within a programmable electronic system
whichcanbeusedforcontrolsystemconstruction.
With such a well-developed industrial technology available it is not surprising that an academic
colleagueonlearningthatweplannedabookonPIDcontrolexclaimed,“Surelynot!Isthereanything
lefttobesaid?”.Ofcourse,theshortansweristhattechnologydoesnotstandstill:newsolutioncapabil-
itiesarealwaysemergingandPIDcontrolwillevolvetoo.Indeed,theZiegler–Nicholsruleshavebeen
famousforoversixtyyearsandtheÅströmandHägglundrelayexperimenthasbeenaroundfortwenty
years,soitwouldbedisappointingifsomenewapproachestoPIDcontrolhadnotemergedinthemean-
time.However,thatisnottoclaimthatallthemethodsdiscussedinthisbookwillreplaceexistingtech-
nologies;noristhisbookadefinitivesurveyof allthathastakenplaceinthedevelopmentsof PID
controlsince,say,1985.Thebookwasoriginallyconceivedasasetofchaptersaboutnewideasthatare
beinginvestigatedinPIDcontrol;itmightbemoreaccuratelysubtitled“Somenewidentificationand
designmethods”.
Thefirstproposalsforthisbookwereconstructedusingaclassificationschemebasedontheextentto
whichamethodusedamodel,thenwhattypeofmodelandthenwhetherthemethodusedoptimisation
principlesornot;averyacademicapproach.Suchaschemedoeswork,but,asonereviewerremarked,it
isperhapsunnecessarilyrigid.However,anotherobjectiveoftheEditorswastoincorporateintothetext
asetofcontributionsfrominternationalauthors,andthisismoredifficulttoachievewithaverystrict
classificationframework.Consequently,thefinishedbookhasamorerelaxedstructurebutretainsan
inherentmethodologicalagenda.
ThebookopenswithtwobasicchaptersaboutPIDcontrollers.Industrialtechnologyisexamined
using discussions,examples and pictures in Chapter 1.Two interesting industrial product reviews
significantlyaddtothevalueofthischapter.Chapter2isconstructedaroundasetofusefulconcepts
whichsaymoreaboutthePIDnotationandconventionsthananythingelse.Thematerialinthesetwo
openingchaptersisdescriptiveandinformative;someofitistheory,butitisselective.Itisdesignedto
bepartlyarepositoryofexistingtechnologyandexpertiseandpartlyanintroductiontosomeofthe
terminologyandconceptsthatwillbeusedinsubsequentchapters.Thesectionsinthesetwochapters
viii Preface
arewrittenwithsomerepetitionofmaterialtoenableindividualsectionstobereadinisolationwhen
usingthetextinreferencemode.
Thisisfollowedby11chaptersthatmakedifferentcontributionstoideasforidentificationforPID
control,andtothetuningofPIDcontrollers.Almostallofthecontributionsarisefromproblemsand
researchissueswhichhaveintriguedthevariousauthors,andthechaptersdescribesomeanswersto
theseproblems.Thisisnotjusttheleaveningofasetofthevariousauthors’publishedpapersbutafully
explainedpresentationoftheinvestigativedirectionsbeingfollowedbythecontributors.TheEditors
hopethatthereaderwillfindthepresentationsquitereadableandbeabletofollowuptheresearch
literaturedirectly.
Theunderlyingcontinuityinthebookisthat,asthechaptersfolloweachother,thequalityofmodel
informationusedbytheproblemformulationandsolutionincreases.ThisagendastartsatChapter3,
wherethemethodsassumenomodelinformationatall.Thenextgroupofchapters,numbers4to7,use
nonparametric models. Because the reaction curve method is historically associated with
nonparametricmethods,Chapter8onextensionstothereactioncurvemethodisplacednext.Inthegap
betweennonparametricandparametricmodel-basedmethods,Chapters9and10reportonthegenetic
algorithmsandfuzzymodelapproachandonaso-calledsubspaceidentificationmethod,respectively.
Finally,methodsbasedonparametricmodelstakethestageinthefinalthreechaptersofthebook.The
lastofthesechapterslooksattheideaofpredictivePIDcontrol.
The emphasis within each chapter varies depending on what is important to the method being
described.Forexample,achaptermightdescribehowtoobtaintheappropriatemodelinformationfora
PIDcontroldesignmethod,orhowtousetheappropriatemodelinformationinPIDcontroldesign
algorithm;sometimesbothaspectsofidentificationanddesignaretreated.Atnopointcanitbeclaimed
thatexistingPIDtuningmethodsaretreatedsystematically;rather,thebookhassomechaptersthat
explainsomenewideas,whilstinotherchaptersexistingtechniquesaregivenandthenextended,rein-
terpretedandrenovated.ThebookismostcertainlynotacookbookforPIDcontroltuningrecipes,and
toreturntoourcolleague’ssurprised,“Isthereanythinglefttobesaid?”,thebooknowwrittenshows
clearlythatthePIDcontrolstillhasmanyavenuestobeexplored.
Thisisalsotheplacetogivethankstovariouspeoplewhohavebeensohelpfulinthecompilation,
constructionandproductionofthebook.Allthecontributorsareverygratefullythankedforagreeing
toparticipateandfortheirpatienceduringtheeditorialperiod.Itwasanextraordinarypleasureto
meetsomeofthemattheirhomeinstitutionsinSingaporeandTaipei,Taiwan,in2000,andothersat
variousrecentinternationalcontrolconferences.
ProfessorM.J.GrimbleisgratefullythankedforallowingEmeritusProfessorM.A.Johnsontheuseof
facilitiesattheIndustrialControlCentre,UniversityofStrathclydeinGlasgow,duringthewritingof
thisbook.
Finally,theEditorswouldliketothankthepublishingstaffatSpringer-VerlagLondon,OliverJackson
andAnthonyDoyle,andatSpringerVerlag’sNewYorkoffices,JennyWolkowicki,fortheirkindencour-
agement,andpatienceduringthegestationperiodofthebook.Alsothecopyeditorandtypesetter,Ian
Kingston,isthankedforhisthoroughnesswiththemanuscriptandfortheexcellentmoderntypograph-
icalinterpretationofthetext.
MichaelA.JohnsonandMohammadH.Moradi
December2004
How to Use This Book
Inmanycasestheproductionofacontributedbookleadstoanopuswhichlookslikesetofcollected
papersfromtheauthors.Inthecaseof thisbook,carehasbeentakentohavesufficientexplanation
introducedsothatthebookmightalsobeusedconstructively.Withthisagenda,thetypicalstructure
forachapteris:
(cid:1) Learningobjectives
(cid:1) Introductorymaterial
(cid:1) Mainalgorithmsdescribed
(cid:1) Workedexamplesandcasestudies
(cid:1) Conclusionsanddiscussion
(cid:1) Referencesandbibliography
Thusitishopedthatthisbookcanbeusedfor:
(cid:1) Supportmaterialforpossibleadvancedcoursestudy
(cid:1) Selfstudybyindustrialandacademiccontrolengineers
(cid:1) Asourceforfutureresearchideasandprojects
(cid:1) Areferenceresourceandasourceofreferences
(cid:1) ContactingresearchersworkingonparticularPIDcontroltopics
Toassistthereaderinnavigatingthevariousapproachesandmethodsitisusefultohaveamapofthe
book.Firstly,thedesignapproachesaregivenbroaddefinitions,andatreediagramofthebookstruc-
turefollows.Thebroadclassificationschemethathasbeenusedtoorganisethisbookisbasedonthe
qualityandtypeoftheprocessmodelinformationusedandthenwhetherornotoptimisationconcepts
havebeenusedtogeneratethePIDcontrollertunings.Abriefdescriptionofthemaincategoriesfollows
next.
(cid:1) Model-freemethods:themethoddoesnotusetheexplicitidentificationofsignificantmodelpointsor
aparametricmodelperse.
(cid:1) Nonparametric model methods: the method uses the explicit identification of significant model
pointsoranonparametricmodel,butdoesnotuseaparametricmodelperse.
x HowtoUseThisBook
(cid:1) Data-intensive methods: these methods are halfway between the nonparametric and parametric
model-basedmethods.Theyarecharacterisedbytheuseofprocessdata,asinthesubspacemethod,
orgreyknowledge,asinthecaseoffuzzy-logicmethods.
(cid:1) Parametricmodelmethods:themethodstraightforwardlydependsontheuseofaparametricmodel;
usuallyatransferfunctionmodel.
Thesecondcategorisationdependsonwhetherthetuningmethodusesoptimisationconcepts.Asan
example,manyoptimisation-basedmethodsusetheappropriateclassiclinearquadraticcostfunction
overadeterministicorstochasticproblemformulation.Figure1showsthetreediagrammapof the
bookchapters.
PIDtuningmethods Basicmaterial:Chapters1and2
Model-free Non-parametric Data-intensive Parametric
methods methods methods methods
Optimal Non-optimal Non- Optimal Non- Optimal
methods methods optimal methods optimal methods
methods methods
Chapter3 Chapters4,5,6,7 Chapter Chapters
Chapter9 10 Chapters 12,13
4,8,11,
Figure1 Bookchapters:treediagrammap.
Contents
EditorialResponsibilities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · xix
Notation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · xxv
1 PIDControlTechnology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1
LearningObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 BasicIndustrialControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 ProcessLoopIssues–aSummaryChecklist . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Three-TermControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 ParallelPIDControllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 ConversiontoTimeconstantPIDForms . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 SeriesPIDControllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.4 SimplePIDTuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 PIDControllerImplementationIssues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.1 Bandwidth-LimitedDerivativeControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.2 ProportionalKick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3.3 DerivativeKick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3.4 IntegralAnti-WindupCircuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3.5 Reverse-ActingControllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4 IndustrialPIDControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4.1 TraditionalIndustrialPIDTerms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.2 IndustrialPIDStructuresandNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.4.3 TheProcessControllerUnit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.4.4 SupervisoryControlandtheSCADAPIDController . . . . . . . . . . . . . . . . . . . . 35
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2 SomePIDControlFundamentals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 47
LearningObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1 ProcessSystemModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.1.1 StateSpaceModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.1.2 ConvolutionIntegralProcessModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.1.3 LaplaceTransferFunctionModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
xii Contents
2.1.4 CommonLaplaceTransformProcessModels . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.2 ControllerDegreesofFreedomStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.1 OneDegreeofFreedomControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.2 TwoDegreeofFreedomControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.3 ThreeDegreeofFreedomStructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.3 PIDControlPerformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.3.1 ControllerPerformanceAssessment–GeneralConsiderations . . . . . . . . . . . . . . 60
2.3.2 ControllerAssessment–theEffectivenessofPIDControl . . . . . . . . . . . . . . . . . 66
2.3.3 ClassicalStabilityRobustnessMeasures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.3.4 ParametricStabilityMarginsforSimpleProcesses . . . . . . . . . . . . . . . . . . . . . 79
2.4 StateSpaceSystemsandPIDControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.4.1 LinearReferenceErrorFeedbackControl . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.4.2 TwoDegreeofFreedomFeedbackControlSystem . . . . . . . . . . . . . . . . . . . . . . 90
2.4.3 StateFeedbackWithIntegralErrorFeedbackAction . . . . . . . . . . . . . . . . . . . . 91
2.4.4 StateSpaceAnalysisforClassicalPIControlStructure . . . . . . . . . . . . . . . . . . . 95
2.5 MultivariablePIDControlSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2.5.1 MultivariableControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2.5.2 CascadeControlSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3 On-lineModel-FreeMethods · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 109
LearningObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.1.1 AModel-FreeControlDesignParadigm . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.2 IterativeFeedbackTuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.2.1 GeneratingtheCostFunctionGradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.2.2 CaseStudy–aWastewaterProcessExample . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.2.3 SomeRemarksonIterativeFeedbackTuning . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3 TheControllerParameterCyclingTuningMethod . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.3.1 GeneratingtheGradientandHessian–SomeTheory . . . . . . . . . . . . . . . . . . . . 125
3.3.2 IssuesforaControllerParameterCyclingAlgorithm . . . . . . . . . . . . . . . . . . . . 131
3.3.3 TheControllerParameterCyclingAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . 135
3.3.4 CaseStudy–MultivariableDecentralisedControl . . . . . . . . . . . . . . . . . . . . . . 136
3.4 SummaryandFutureDirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Appendix3.A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4 AutomaticPIDControllerTuning–theNonparametricApproach · · · · · · · · 147
LearningObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
4.2 OverviewofNonparametricIdentificationMethods . . . . . . . . . . . . . . . . . . . . . . . . 149
4.2.1 TransientResponseMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.2.2 RelayFeedbackMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.2.3 FourierMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.2.4 Phase-LockedLoopMethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
