Basicoverview
PIDcontroller(ProportionIntegrationDifferentiation.ProportionIntegrationDifferentiation.Proportion-Integral-DerivativeController),consistingofproportionalunitP,integralunitIandderivativeunitDcomposition.ThroughthesettingofKp,KiandKdthreeparameters.PIDcontrollersaremainlysuitableforsystemswhosebasiclinearityanddynamiccharacteristicsdonotchangewithtime.
PIDcontrollerisacommonfeedbackloopcomponentinindustrialcontrolapplications.Thiscontrollercomparesthecollecteddatawithareferencevalue,andthenusesthisdifferencetocalculateanewinputvalue.Thepurposeofthisnewinputvalueistoallowthesystemdatatoreachormaintainthereferencevalue.Differentfromothersimplecontrolcalculations,PIDcontrollercanadjusttheinputvalueaccordingtohistoricaldataandtheoccurrencerateofdifference,whichcanmakethesystemmoreaccurateandmorestable.ItcanbeprovedbymathematicalmethodsthataPIDfeedbackloopcankeepthesystemstablewhenothercontrolmethodsleadtosystemstabilityerrorsorprocessrepetitions.
Feedbackloop
Acontrolloopconsistsofthreeparts:
Themeasurementresultsobtainedbythesystem’ssensors,thecontrollermakesthedecisionandreactsthroughanoutputdevicetocontrolThedeviceobtainsthemeasurementresultfromthesensor,andthensubtractsthemeasurementresultfromthedemandresulttogettheerror.Thenusetheerrortocalculateacorrectionvaluetothesystemastheinputresult,sothatthesystemcaneliminatetheerrorfromitsoutputresult.
InaPIDloop,therearethreealgorithmsforthiscorrectionvalue,eliminatingerrors,averagingpasterrors,andpredictingfutureerrorsthroughchangesinerrors.
Forexample,ifawatertankisprovidingwaterforaplant,thewaterinthistankneedstobekeptatacertainheight.Asensorwillbeusedtochecktheheightofthewaterinthetank,sothatthemeasurementresultisobtained.Thecontrollerwillhaveafixeduserinputvaluetoindicatetherequiredwatersurfaceheightofthewatertank,assumingthisvalueistomaintain65%ofthewatervolume.Theoutputdeviceofthecontrollerwillbeconnectedtoamotor-controlledwatervalve.Openingthevalvewillfillthewatertank,andclosingthevalvewillreducetheamountofwaterinthewatertank.Thecontrolsignalofthisvalveisthevariablewecontrol,anditisalsotheinputofthissystemtokeepthewatertankfixed.
PIDcontrollercanbeusedtocontrolanyvariablethatcanbemeasuredandcontrolled.Forexample,itcanbeusedtocontroltemperature,pressure,flow,chemicalcomposition,speedandsoon.Thecruisecontrolfunctiononacarisanexample.
SomecontrolsystemsconnectseveralPIDcontrollersinseries,orchainthemintoanetwork.Inthiscase,amaincontrollermayoutputresultsforothercontrols.Acommonexampleisthecontrolofmotors.Wewilloftenneedthemotortohaveacontrolledspeedandstopatacertainposition.Inthisway,asub-controllermanagesthespeed,butthespeedofthissub-controllerismanagedbythemaincontrollerthatcontrolsthepositionofthemotor.
Combinationandseriescontrolareverycommoninchemicalprocesscontrolsystems.
Theory
PIDisnamedafteritsthreecorrectionalgorithms.Allthreealgorithmsuseadditiontoadjustthecontrolledvalue.Infact,mostoftheseadditionoperationsbecomesubtractionoperationsbecausetheaddendisalwaysnegative.Thesethreealgorithmsare:
Proportion-Tocontrolthecurrent,theerrorvalueismultipliedbyanegativeconstantP(proportion),andthenpre-determinedAddthevaluesof.Pisonlytruewhentheoutputofthecontrollerisproportionaltotheerrorofthesystem.Thechangeofthecontrolleroutputisproportionaltothedeviationoftheinputcontroller.Forexample,thescalerangeofanelectricheatercontrolleris10°C,anditspredeterminedvalueis20°C.Thenitwilloutput100%at10°C,50%at15°C,and10%at19°C.Notethatwhentheerroris0,theoutputofthecontrollerisalso0.
Integration-Tocontrolthepast,theerrorvalueisthesumoftheerrorsinthepastperiodoftime,andthenmultipliedbyanegativeconstantI,andthencomparedwiththepredeterminedvalueadd.IFindtheaverageerrorbetweentheoutputresultofthesystemandthepredeterminedvaluefromtheaverageerrorvalueinthepast.Asimpleproportionalsystemwilloscillateandchangebackandfortharoundapredeterminedvaluebecausethesystemcannoteliminateredundantcorrections.Byaddinganegativeaverageerrorratiovalue,theaveragesystematicerrorvaluewillalwaysdecrease.Therefore,intheend,thePIDloopsystemwillbesetatapredeterminedvalue.
Derivative-Tocontrolthefuture,calculatethefirstderivativeoftheerror,multiplyitwithanegativeconstantD,andfinallyaddittothepredeterminedvalue.Thecontrolofthisderivativewillreacttochangesinthesystem.Thelargertheresultofthederivative,thefasterthecontrolsystemwillreacttotheoutputresult.ThisDparameterisalsothereasonthatPIDiscalledapredictablecontroller.TheDparameterisveryhelpfultoreducetheshort-termchangesofthecontroller.SomeslowsystemsinpracticemaynotneedtheDparameter.Inmoreprofessionalterms,aPIDcontrollercanbecalledafilterinthefrequencydomainsystem.Thisisusefulwhencalculatingwhetheritwilleventuallyreachastableresult.Ifthevalueisnotselectedproperly,theinputvalueofthecontrolsystemwilloscillaterepeatedly,whichmaycausethesystemtoneverreachthepresetvalue.
Controllaw
Althoughdifferenttypesofcontrollershavedifferentstructuresandprinciples,thereareonlythreebasiccontrollaws:proportional(P)control,integral(I)controlAndderivative(D)control.Thesecontrollawscanbeusedalone,buttheyareusedincombinationinmoreoccasions.Suchasproportional(P)control,proportional-integral(PI)control,proportional-integral-derivative(PID)control,etc.
Proportional(P)control
Singleproportionalcontrolisalsocalled"differencecontrol",theoutputchangeisproportionaltothedeviationoftheinputcontroller,Thegreaterthedeviation,thegreatertheoutput.Inpracticalapplications,thedegreeofproportionalityshouldbedeterminedaccordingtothespecificsituation.Toolargeaproportionality,tooweakcontroleffect,isnotconducivetothesystemtoovercomedisturbances,themarginistoolarge,thecontrolqualityispoor,andthereisnocontroleffect;theproportionalityistoosmall,Thecontroleffectistoostrong,itiseasytocausethestabilityofthesystemtodeteriorateandcauseoscillation.
Forthecontrolledobjectwithsensitiveresponseandstrongamplificationability,inordertoimprovethestabilityofthesystem,theproportionalityshouldbeslightlylarger;forthecontrolledobjectwithslowresponseandweakamplificationability,theproportionalThedegreecanbeselectedtobesmallertoimprovethesensitivityoftheentiresystemandtoreducetheresidualsaccordingly.
Pureproportionalcontrolissuitableforoccasionswherethedisturbanceissmall,thehysteresisissmall,theloadchangeissmall,therequirementsarenothigh,andacertainmarginisallowed.Theuseofproportionalcontrollawinindustrialproductionismorecommon.
Proportionalintegral(PI)control
Proportionalcontrollawisthemostbasicandmostcommonlyusedoneofthebasiccontrollaws.ItsgreatestadvantageisControlistimelyandrapid.Aslongasthereisadeviation,thecontrollerimmediatelytakescontrol.However,thedisadvantageofnotbeingabletofinallyeliminatetheresiduallimitsitsusealone.Thewaytoovercometheresidualistoaddintegralcontrolonthebasisofproportionalcontrol.
Theoutputoftheintegralcontrollerisproportionaltotheintegraloftheinputdeviationovertime.The"points"heremeans"accumulation".Theoutputoftheintegralcontrollerisnotonlyrelatedtothemagnitudeoftheinputdeviation,butalsorelatedtothetimethedeviationexists.Aslongasthedeviationexists,theoutputwillcontinuetoaccumulate(theoutputvalueisgettinglargerorsmaller),andtheaccumulationwillstopuntilthedeviationiszero.Therefore,integralcontrolcaneliminateresiduals.Theintegralcontrollawisalsocalledthenon-differencecontrollaw.
Thesizeoftheintegraltimecharacterizesthestrengthofintegralcontrol.Thesmallertheintegraltime,thestrongerthecontroleffect;onthecontrary,theweakerthecontroleffect.
Althoughintegralcontrolcaneliminatetheresidualerror,ithasthedisadvantageofnottimelycontrol.Becausetheaccumulationofintegraloutputisgradual,thecontroleffectitproducesalwayslagsbehindthechangeofthedeviation,andtheinfluenceofinterferencecannotbeovercomeintimeandeffectively,anditisdifficulttostabilizethecontrolsystem.Therefore,inpractice,integralcontrolisgenerallynotusedalone,butcombinedwithproportionalcontroltoformproportionalintegralcontrol.Inthisway,theadvantagesofthetwoareusedtomakeupforeachother,whichnotonlyhastherapidandtimelyeffectofproportionalcontrol,butalsohastheabilityofintegralcontroltoeliminatetheresidualerror.Therefore,proportionalintegralcontrolcanachieveamoreidealprocesscontrol.
Proportionalintegralcontrolleristhemostwidelyusedcontroller,whichismostlyusedinthecontrolsystemofliquidlevel,pressure,flow,etc.inindustrialproduction.Sincetheintroductionofintegralactioncaneliminatetheresidualerror,makeupfortheshortcomingsofpureproportionalcontrol,andobtainbettercontrolquality.Buttheintroductionofintegralactionwillmakethestabilityofthesystemworse.Forcontrolsystemswithlargeinertialag,trytoavoidusingthem.
Proportionalderivative(PD)control
Proportionalintegralcontrolisnotidealforthecontrolledobjectwithtimelag.Theso-called"timelag"refersto:whenthecontrolledobjectisdisturbed,thecontrolledvariabledoesnotchangeimmediately,butthereisatimedelay,suchasacapacitylag,whentheproportionalintegralcontrolappearssluggishanduntimely.Forthisreason,peopleimagined:Canthecorrespondingcontrolactionbemadeaccordingtothechangingtrendofthedeviation?Justlikeexperiencedoperators,theycanchangethevalveopeningaccordingtothemagnitudeofthedeviation(proportionaleffect),andcanpredictthesituationthatwilloccuraccordingtothespeedofthedeviationchange,andcarryoutexcessivecontrolinadvanceto"preventproblemsbeforetheyoccur.".Thisisthedifferentialcontrollawwith"advanced"controlfunction.Theoutputofthederivativecontrollerdependsonthespeedatwhichtheinputdeviationchanges.
Thedifferentialoutputisonlyrelatedtothechangespeedofthedeviation,andhasnothingtodowiththesizeofthedeviationandwhetherthedeviationexistsornot.Ifthedeviationisafixedvalue,nomatterhowlarge,aslongasitdoesnotchange,theoutputchangemustbezero,andthecontrollerhasnocontroleffect.Thelongerthederivativetime,thelongerthederivativeoutputismaintained,sothestrongerthederivativeaction;otherwise,theweaker.Whenthederivativetimeis0,thereisnoderivativecontroleffect.Inthesameway,theselectionofthedifferentialtimealsoneedstobedeterminedaccordingtotheactualsituation.
Thecharacteristicsofthedifferentialcontrolfunctionare:rapidaction,withadvancedadjustmentfunction,whichcaneffectivelyimprovethecontrolqualityofthecontrolledobjectwithalargetimelag;butitcannoteliminatetheresidual,especiallyfortheconstantdeviationinputThereisnocontroleffectatall.Therefore,thedifferentialcontrollawcannotbeusedalone.
Thecombinationofproportionalanddifferentialactionisfasterthanpureproportionalaction.Especiallyforobjectswithlargecapacitylag,theamplitudeofdynamicdeviationcanbereduced,controltimecanbesaved,andcontrolqualitycanbesignificantlyimproved.
PIDcontrol
Themostidealcontrolistheproportional-integral-derivativecontrollaw.Itcombinestheadvantagesofthethree:boththeproportionalactionistimelyandrapid,theintegralactioncaneliminatetheresidualerror,andthedifferentialactionhastheadvancedcontrolfunction.
Whenthedeviationstepoccurs,thederivativewillactimmediatelytosuppressthisleapofdeviation;theratioalsoplaysaroleineliminatingthedeviation,sothatthedeviationrangeisreduced,becausetheproportionaleffectislastingandeffective.Themaineffectofthecontrollaw,sothatthesystemcanbemorestable;andtheintegraleffectgraduallyovercomestheresidualerror.Aslongasthecontrolparametersofthethreefunctionsareselectedproperly,theadvantagesofthethreecontrollawscanbefullyutilizedandamoreidealcontroleffectcanbeobtained.
Debuggingmethod
Adjustmentoftheproportionalcoefficient
TheadjustmentrangeoftheproportionalcoefficientPisgenerally0.1--100.
Ifthegainvalueis0.1,thePIDregulatoroutputchangestoone-tenthofthedeviationvalue.Ifthegainvalueis100,theoutputofthePIDregulatorchangestoonehundredtimesthedeviationvalue.
Itcanbeseenthatthelargerthevalue,thegreaterthegaineffectproducedbytheratio.Intheinitialadjustment,chooseasmallervalue,andthenslowlyincreaseituntilthesystemfluctuationissmallenough,andthenadjusttheintegralordifferentialcoefficient.AtoolargePvaluewillcausethesystemtobeunstableandcontinuetooscillate;atoosmallPvaluewillmakethesystemunresponsive.Theappropriatevalueshouldenablethesystemtohavesufficientsensitivitybutnottoosensitive.Thedelayforacertainperiodoftimeshouldbeadjustedbytheintegrationtime.
Adjustmentoftheintegralcoefficient
Thedefinitionoftheintegraltimeconstantisthetimethatthedeviationcausestheoutputtoincrease.Iftheintegrationtimeissetto1second,thetimerequiredfora100%outputchangeis1second.Intheinitialadjustment,settheintegrationtimelonger,andthenslowlyadjustituntilthesystemisstable.
Adjustmentofthedifferentialcoefficient
Thedifferentialvalueistherateofchangeofthedeviationvalue.Forexample,iftheinputdeviationvaluechangeslinearly,aconstantadjustmentamountissuperimposedontheoutputsideoftheregulator.Mostcontrolsystemsdonotneedtoadjustthederivativetime.Becauseonlysystemswithtimelagneedtoaddthisparameter.Ifsuperfluousandaddingthisparameter,thecontrolofthesystemwillbeaffected.Iftheidealcontrolrequirementisstillnotreceivedthroughtheadjustmentoftheproportionalandintegralparameters,thederivativetimecanbeadjusted.Intheinitialadjustment,setthiscoefficienttoasmallvalue,andthenslowlyincreaseituntilthesystemisstable.
Parametertuning
PIDcontrollerparametertuningisthecorecontentofcontrolsystemdesign.Itdeterminestheproportionalcoefficient,integraltimeandderivativetimeofthePIDcontrolleraccordingtothecharacteristicsofthecontrolledprocess.TherearemanymethodsforPIDcontrollerparametertuning,whichcanbesummarizedintotwocategories:Oneisthetheoreticalcalculationtuningmethod.Itismainlybasedonthemathematicalmodelofthesystemtodeterminethecontrollerparametersthroughtheoreticalcalculations.Thecalculateddataobtainedbythismethodmaynotbedirectlyusable,andmustbeadjustedandmodifiedthroughactualengineering.Thesecondistheengineeringtuningmethod,whichmainlyreliesonengineeringexperienceandiscarriedoutdirectlyinthetestofthecontrolsystem,andthemethodissimpleandeasytomaster,andiswidelyusedinengineeringpractice.TheengineeringtuningmethodsofPIDcontrollerparametersmainlyincludecriticalproportionmethod,responsecurvemethodandattenuationmethod.Thethreemethodshavetheirowncharacteristics.Thecommonpointisthattheypassthetest,andthenadjustthecontrollerparametersaccordingtotheengineeringexperienceformula.However,nomatterwhichmethodisused,thecontrollerparametersobtainedneedtobeadjustedandperfectedinactualoperation.Thecriticalratiomethodisgenerallyusednow.ThestepsfortuningPIDcontrollerparametersusingthismethodareasfollows:(1)First,pre-selectashortenoughsamplingperiodforthesystemtowork;(2)Onlyaddproportionalcontrollinksuntilthesystemhascriticaloscillationsinitsstepresponsetotheinput.Writedowntheproportionalamplificationfactorandcriticaloscillationperiodatthistime;(3)Underacertaindegreeofcontrol,theparametersofthePIDcontrollercanbecalculatedbyformulas.
Adaptivecontrol
Firstofall,figureoutwhatisadaptivecontrol
Intheproductionprocess,inordertoimproveproductquality,increaseoutput,saverawmaterials,productionmanagementandTheproductionprocessisalwaysinoptimalworkingcondition.Therefore,anoptimalcontrolmethodisproduced,whichiscalledadaptivecontrol.Inthiskindofcontrol,thesystemisrequiredtobeabletoautomaticallyadjustthesystemaccordingtothechangesinthemeasuredparameters,theenvironmentandthecostofrawmaterials,sothatthesystemisinthebeststateatanytime.Adaptivecontrolincludesthreelinks:performanceestimation(discrimination),decision-makingandmodification.Itisthedevelopmentdirectionofthemicrocomputercontrolsystem.However,becausethecontrollawisdifficulttograsp,therearestillsomedifficultproblemstopromote.
Addingadaptivepidcontrolbringssomeintelligentfeatures,whichcanadapttochangesinexternalconditionslikeacreature.
Thereisalsoaself-learningsystem,whichmakesitmoreintelligent.
Controllerperformance
ProblemsinPIDcontrol
Therearedocumentsthatpointoutthat60%ofcontrollersintheactualindustryhaveperformanceproblems.Intheindustrialprocess,thereasonsforthepoorperformanceofthecontrolloopcanbeattributedtooneormoreofthefollowingsituations:1)Thecontrollerispoorlytunedandlacksmaintenance.Thereasonsforthissituationinclude:thecontrollerhasneverbeentunedoristunedbasedonamismatchmodel,oranimpropertypeofcontrollerhasbeenused.Intheindustrialprocessautomaticcontrolsystem,morethan90%ofthecontrollersarePIDtypecontrollers,evenifothercontrollersmaybeusedinsomecases,betterperformancemaybeobtained.Infact,themostcommoncauseofpoorcontrolloopperformanceisthelackofmaintenanceofthecontroller.Afteryearsofoperation,thedynamiccharacteristicsoftheactuatorandthecontrolledobjectmaychangeduetowearandotherreasons.Onlyafewengineersmaintainthecontrolloop,andoperatorsandengineersoftenlackunderstandingofthereasonsforthepoorperformanceofthecontrolloop.
2)Equipmentfailureorunreasonablestructuredesign.Poorcontrolloopperformancemaybecausedbysensororactuatorfailure(suchasexcessivefriction).Ifthedesignoftheindustrialdeviceorthecomponentsofthedeviceisnotreasonable,theproblemmaybemoreserious.Theseproblemscannotbeeffectivelysolvedbyre-tuningthecontroller.
3)Lackorinsufficientfeedforwardcompensation.Ifhandledimproperly,externaldisturbanceswilldeterioratetheperformanceoftheloop.Therefore,whenthedisturbanceismeasurable,itisrecommendedtouseFeedforvvardControl(FFC)tocompensateforthedisturbance.
4)Thecontrolstructuredesignisunreasonable.Inappropriateinput/outputpairing,ignoringthemutualcouplingbetweensystemvariables,CompetingControllers,insufficientdegreesoffreedom,strongnonlinearity,andlackofcompensationforlargetimedelaysmayallleadtocontrolstructureproblems.
PIDcontrolperformanceevaluation
ExistingdocumentshavepointedoutthatitisfeasibletoestimatetheminimumvariancethatcanbeachievedbyPIDcontrolwithconventionaloperatingdatainaknownprocess;forPIDcontrol,itcanbeachievedbyusingPIDAstheevaluationbenchmark,theevaluationresultsaremorereasonable;thePIDcontrollerparametersestimatedafterfittingthemodelcansignificantlyreducetheprocessoutputvariance.
Controlperformancemonitoring/assessment(CPM/CPA)forcontrolsystemsisoneofthemostconcernedresearchdirectionsintheworldofprocesscontrol.ControllerperformancemonitoringandevaluationcanbetracedbacktotheworkofAstrom(1967),DeVrieWu(1978)andothersinthe1960sand1970s;by1970,Box,Jenkins(1976),Astrominimumvariancecontrol(minimumvariancecontrol),MVC);In1989,Harris(1989)usedtheminimumvariancecontroltoevaluatethevarianceperformanceoftheSISOsystem,whichmadethisfieldhavepioneeringresultsandnewgoalsinrandomperformancemonitoringandevaluation.Sincethen,CPM/CPAtechnologyhasattractedtheattentionandresearchofalargenumberofcontroltheoryscholarsandhasachievedrapiddevelopment.Throughtheeffortsofpredecessors,thistechnologyhasdevelopedintoacross-integratedtechnologyinvolvingcontroltheory,systemidentification,signalprocessing,probabilityandstatistics,etc.Itisusuallyreferredtoastheperformancemonitoringandevaluationofthecontrolloop,andtheperformancemonitoringandevaluationofthecontroller.Evaluation,performanceevaluation,etc.
InordertosolvetheproblemofPIDcontrollerloopperformancedegradationcausedbysystemtime-varyingintheindustrialsystem,LiuXiaoyanofZhejiangUniversityputforwardthePIDaccessibilityevaluationbenchmarkproposedbyEdgar.Amethodforperformanceevaluation,optimizationandmonitoringofPIDcontrollers,namely:PIDloopevaluationoptimizationalgorithm.Thealgorithmusestheclosed-loopinputandoutputdataofthesystemtoperformonlineslidingwindowidentification,usestheMVC(MinimumVarianceControl)-basedPIDminimumvarianceaccessibilitycriteriontoevaluatetheperformanceofthePIDcontroller,andcalculatestheoptimalPIDcontrollerparametersinthesenseoftheminimumvariance;Comparethetheoreticalminimumvariancewiththeoutputvarianceasthestart-stopthresholdforonlineoptimizationofthePIDsystem.Simulationhasproveditseffectiveness.