控制中英文对照翻译.docx

控制中英文对照翻译.docx

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控制中英文对照翻译

外文资料与翻译

PIDControl

Introduction

ThePIDcontrolleristhemostcommonformoffeedback.Itwasanessentialelementofearlygovernorsanditbecamethestandardtoolwhenprocesscontrolemergedinthe1940s.Inprocesscontroltoday,morethan95%ofthecontrolloopsareofPIDtype,mostloopsareactuallyPIcontrol.PIDcontrollersaretodayfoundinallareaswherecontrolisused.Thecontrollerscomeinmanydifferentforms.Therearestandalonesystemsinboxesforoneorafewloops,whicharemanufacturedbythehundredthousandsyearly.PIDcontrolisanimportantingredientofadistributedcontrolsystem.Thecontrollersarealsoembeddedinmanyspecialpurposecontrolsystems.PIDcontrolisoftencombinedwithlogic,sequentialfunctions,selectors,andsimplefunctionblockstobuildthecomplicatedautomationsystemsusedforenergyproduction,transportation,andmanufacturing.Manysophisticatedcontrolstrategies,suchasmodelpredictivecontrol,arealsoorganizedhierarchically.PIDcontrolisusedatthelowestlevel;themultivariablecontrollergivesthesetpointstothecontrollersatthelowerlevel.ThePIDcontrollercanthusbesaidtobethe“breadandbutterofcontrolengineering.Itisanimportantcomponentineverycontrolengineer’stoolbox.

PIDcontrollershavesurvivedmanychangesintechnology,frommechanicsandpneumaticstomicroprocessorsviaelectronictubes,transistors,integratedcircuits.ThemicroprocessorhashadadramaticinfluencethePIDcontroller.PracticallyallPIDcontrollersmadetodayarebasedonmicroprocessors.Thishasgivenopportunitiestoprovideadditionalfeatureslikeautomatictuning,gainscheduling,andcontinuousadaptation.

6.2TheAlgorithm

WewillstartbysummarizingthekeyfeaturesofthePIDcontroller.The“textbook”versionofthePIDalgorithmisdescribedby:

6.1

whereyisthemeasuredprocessvariable,rthereferencevariable,uisthecontrolsignalandeisthecontrolerror（e=

−y）.Thereferencevariableisoftencalledthesetpoint.Thecontrolsignalisthusasumofthreeterms:

theP-term（whichisproportionaltotheerror）,theI-term（whichisproportionaltotheintegraloftheerror）,andtheD-term（whichisproportionaltothederivativeoftheerror）.ThecontrollerparametersareproportionalgainK,integraltimeTi,andderivativetimeTd.Theintegral,proportionalandderivativepartcanbeinterpretedascontrolactionsbasedonthepast,thepresentandthefutureasisillustratedinFigure2.2.ThederivativepartcanalsobeinterpretedaspredictionbylinearextrapolationasisillustratedinFigure2.2.Theactionofthedifferenttermscanbeillustratedbythefollowingfigureswhichshowtheresponsetostepchangesinthereferencevalueinatypicalcase.

EffectsofProportional,IntegralandDerivativeAction

ProportionalcontrolisillustratedinFigure6.1.ThecontrollerisgivenbyD6.1EwithTi=

andTd=0.Thefigureshowsthatthereisalwaysasteadystateerrorinproportionalcontrol.Theerrorwilldecreasewithincreasinggain,butthetendencytowardsoscillationwillalsoincrease.

Figure6.2illustratestheeffectsofaddingintegral.ItfollowsfromD6.1EthatthestrengthofintegralactionincreaseswithdecreasingintegraltimeTi.Thefigureshowsthatthesteadystateerrordisappearswhenintegralactionisused.Comparewiththediscussionofthe“magicofintegralaction”inSection2.2.ThetendencyforoscillationalsoincreaseswithdecreasingTi.ThepropertiesofderivativeactionareillustratedinFigure6.3.

Figure6.3illustratestheeffectsofaddingderivativeaction.TheparametersKandTiarechosensothattheclosedloopsystemisoscillatory.Dampingincreaseswithincreasingderivativetime,butdecreasesagainwhenderivativetimebecomestoolarge.RecallthatderivativeactioncanbeinterpretedasprovidingpredictionbylinearextrapolationoverthetimeTd.UsingthisinterpretationitiseasytounderstandthatderivativeactiondoesnothelpifthepredictiontimeTdistoolarge.InFigure6.3theperiodofoscillationisabout6sforthesystemwithoutderivativeChapter6.PIDControl

Figure6.1

Figure6.2

DerivativeactionsceasetobeeffectivewhenTdislargerthana1s（onesixthoftheperiod）.Alsonoticethattheperiodofoscillationincreaseswhenderivativetimeisincreased.

APerspective

ThereismuchmoretoPIDthanisrevealedby（6.1）.Afaithfulimplementationoftheequationwillactuallynotresultinagoodcontroller.ToobtainagoodPIDcontrolleritisalsonecessarytoconsider。

Figure6.3

∙Noisefilteringandhighfrequencyrolloff

∙Setpointweightingand2DOF

∙Windup

∙Tuning

∙Computerimplementation

InthecaseofthePIDcontrollertheseissuesemergedorganicallyasthetechnologydevelopedbuttheyareactuallyimportantintheimplementationofallcontrollers.Manyofthesequestionsarecloselyrelatedtofundamentalpropertiesoffeedback,someofthemhavebeendiscussedearlierinthebook.

6.3FilteringandSetPointWeighting

Differentiationisalwayssensitivetonoise.ThisisclearlyseenfromthetransferfunctionG（s）=sofadifferentiatorwhichgoestoinfinityforlarges.Thefollowingexampleisalsoilluminating.

wherethenoiseissinusoidalnoisewithfrequencyw.Thederivativeofthesignalis

Thesignaltonoiseratiofortheoriginalsignalis1/anbutthesignaltonoiseratioofthedifferentiatedsignalisw/an.Thisratiocanbearbitrarilyhighifwislarge.

Inapracticalcontrollerwithderivativeactionitistherefornecessarytolimitthehighfrequencygainofthederivativeterm.Thiscanbedonebyimplementingthederivativetermas

6.2

insteadofD=sTdY.Theapproximationgivenby（6.2）canbeinterpretedastheidealderivativesTdfilteredbyafirst-ordersystemwiththetimeconstantTd/N.Theapproximationactsasaderivativeforlow-frequencysignalcomponents.Thegain,however,islimitedtoKN.Thismeansthathigh-frequencymeasurementnoiseisamplifiedatmostbyafactorKN.TypicalvaluesofNare8to20.

Furtherlimitationofthehigh-frequencygain

ThetransferfunctionfrommeasurementytocontrolleroutputuofaPIDcontrollerwiththeapproximatederivativeis

Thiscontrollerhasconstantgain

athighfrequencies.ItfollowsfromthediscussiononrobustnessagainstprocessvariationsinSection5.5thatitishighlydesirabletorolloffthecontrollergainathighfrequencies.Thiscanbeachievedbyadditional

lowpassfilteringofthecontrolsignalby

whereTfisthefiltertimeconstantandnistheorderofthefilter.ThechoiceofTfisacompromisebetweenfilteringcapacityandperformance.ThevalueofTfcanbecoupledtothecontrollertimeconstantsinthesamewayasforthederivativefilterabove.Ifthederivativetimeisused,Tf=Td/Nisasuitablechoice.IfthecontrollerisonlyPI,Tf=Ti/Nmaybesuitable.

Thecontrollercanalsobeimplementedas

6.3

ThisstructurehastheadvantagethatwecandevelopthedesignmethodsforanidealPIDcontrolleranduseaniterativedesignprocedure.ThecontrollerisfirstdesignedfortheprocessP（s）.ThedesigngivesthecontrollerparameterTd.AnidealcontrollerfortheprocessP（s）/（1+sTd/N）2isthendesignedgivinganewvalueofTdetc.Suchaprocedurewillalsogiveaclearpictureofthetradeoffbetweenperformanceandfiltering.

SetPointWeighting

Whenusingthecontrollawgivenby（6.1）itfollowsthatastepchangeinthereferencesignalwillresultinanimpulseinthecontrolsignal.Thisisoftenhighlyundesirablethereforderivativeactionisfrequentlynotappliedtothereferencesignal.Thisproblemcanbeavoidedbyfilteringthereferencevaluebeforefeedingittothecontroller.Anotherpossibilityistoletproportionalactionactonlyonpartofthereferencesignal.Thisiscalledsetpointweighting.APIDcontrollergivenby（6.1）thenbecomes

6.4

wherebandcareadditionalparameter.Theintegraltermmustbebasedonerrorfeedbacktoensurethedesiredsteadystate.ThecontrollergivenbyD6.4Ehasastructurewithtwodegreesoffreedombecausethesignalpathfromytouisdifferentfromthatfromrtou.Thetransferfunctionfromrtouis

6.5

Timet

Figure6.4Responsetoastepinthereferenceforsystemswithdifferentsetpointweightsb=0dashed,b=0.5fullandb=1.0dashdotted.TheprocesshasthetransferfunctionP（s）=1/（s+1）3andthecontrollerparametersarek=3,ki=1.5andkd=1.5.

andthetransferfunctionfromytouis

6.6

Setpointweightingisthusaspecialcaseofcontrollershavingtwodegreesoffreedom.

Thesystemobtainedwiththecontroller（6.4）respondtoloaddisturbancesandmeasurementnoiseinthesamewayasthecontroller（6.1）.Theresponsetoreferencevaluescanbemodifiedbytheparametersbandc.ThisisillustratedinFigure6.4,whichshowstheresponseofaPIDcontrollertoset-pointchanges,loaddisturbances,andmeasurementerrorsfordifferentvaluesofb.Thefigureshowsclearlytheeffectofchangingb.Theovershootforset-pointchangesissmallestforb=0,whichisthecasewherethereferenceisonlyintroducedintheintegralterm,andincreaseswithincreasingb.

Theparametercisnormallyzerotoavoidlargetransientsinthecontrolsignalduetosuddenchangesintheset-point.

6.4DifferentParameterizations

ThePIDalgorithmgivenbyEquation（6.1）canberepresentedbythetransferfunction

6.7

6.8

6.9

AninteractingcontrolleroftheformEquationD6.8Ethatcorrespondstoanon-interactingcontrollercanbefoundonlyif

Theparametersarethengivenby

6.10

Thenon-interactingcontrollergivenbyE