PID外文资料.docx
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PID外文资料
PIDcontroller
Aproportional–integral–derivativecontroller(PIDcontroller)isageneric.controlloopfeedbackmechanismwidelyusedinindustrialcontrolsystems.APIDcontrollerattemptstocorrecttheerrorbetweenameasuredprocessvariableandadesiredsetpointbycalculatingandthenoutputtingacorrectiveactionthatcanadjusttheprocessaccordingly.
ThePIDcontrollercalculation(algorithm)involvesthreeseparateparameters;theProportional,theIntegralandDerivativevalues.TheProportionalvaluedeterminesthereactiontothecurrenterror,theIntegraldeterminesthereactionbasedonthesumofrecenterrorsandtheDerivativedeterminesthereactiontotherateatwhichtheerrorhasbeenchanging.Theweightedsumofthesethreeactionsisusedtoadjusttheprocessviaacontrolelementsuchasthepositionofacontrolvalveorthepowersupplyofaheatingelement.By"tuning"thethreeconstantsinthePIDcontrolleralgorithmthePIDcanprovidecontrolactiondesignedforspecificprocessrequirements.Theresponseofthecontrollercanbedescribedintermsoftheresponsivenessofthecontrollertoanerror,thedegreetowhichthecontrollerovershootsthesetpointandthedegreeofsystemoscillation.Someapplicationsmayrequireusingonlyoneortwomodestoprovidetheappropriatesystemcontrol.Thisisachievedbysettingthegainofundesiredcontroloutputstozero.APIDcontrollerwillbecalledaPI,PD,PorIcontrollerintheabsenceoftherespectivecontrolactions.PIcontrollersareparticularlycommon,sincederivativeactionisverysensitivetomeasurementnoise,andtheabsenceofanintegralvaluemaypreventthesystemfromreachingitstargetvalueduetothecontrolaction.
1.Controlloopbasics
Afamiliarexampleofacontrolloopistheactiontakentokeepone'sshowerwaterattheidealtemperature,whichtypicallyinvolvesthemixingoftwoprocessstreams,coldandhotwater.Thepersonfeelsthewatertoestimateitstemperature.Basedonthismeasurementtheyperformacontrolaction:
usethecoldwatertaptoadjusttheprocess.Thepersonwouldrepeatthisinput-outputcontrolloop,adjustingthehotwaterflowuntiltheprocesstemperaturestabilizedatthedesiredvalue.
Feelingthewatertemperatureistakingameasurementoftheprocessvalueorprocessvariable(PV).Thedesiredtemperatureiscalledthesetpoint(SP).Theoutputfromthecontrollerandinputtotheprocess(thetapposition)iscalledthemanipulatedvariable(MV).Thedifferencebetweenthemeasurementandthesetpointistheerror(e),toohotortoocoldandbyhowmuch.Asacontroller,onedecidesroughlyhowmuchtochangethetapposition(MV)afteronedeterminesthetemperature(PV),andthereforetheerror.ThisfirstestimateistheequivalentoftheproportionalactionofaPIDcontroller.TheintegralactionofaPIDcontrollercanbethoughtofasgraduallyadjustingthetemperaturewhenitisalmostright.Derivativeactioncanbethoughtofasnoticingthewatertemperatureisgettinghotterorcolder,andhowfast,andtakingthatintoaccountwhendecidinghowtoadjustthetap.Makingachangethatistoolargewhentheerrorissmallisequivalenttoahighgaincontrollerandwillleadtoovershoot.Ifthecontrollerweretorepeatedlymakechangesthatweretoolargeandrepeatedlyovershootthetarget,thiscontrolloopwouldbetermedunstableandtheoutputwouldoscillatearoundthesetpointineitheraconstant,growing,ordecayingsinusoid.Ahumanwouldnotdothisbecauseweareadaptivecontrollers,learningfromtheprocesshistory,butPIDcontrollersdonothavetheabilitytolearnandmustbesetupcorrectly.Selectingthecorrectgainsforeffectivecontrolisknownastuningthecontroller.
Ifacontrollerstartsfromastablestateatzeroerror(PV=SP),thenfurtherchangesbythecontrollerwillbeinresponsetochangesinothermeasuredorunmeasuredinputstotheprocessthatimpactontheprocess,andhenceonthePV.VariablesthatimpactontheprocessotherthantheMVareknownasdisturbancesandgenerallycontrollersareusedtorejectdisturbancesand/orimplementsetpointchanges.Changesinfeedwatertemperatureconstituteadisturbancetotheshowerprocess.
Intheory,acontrollercanbeusedtocontrolanyprocesswhichhasameasurableoutput(PV),aknownidealvalueforthatoutput(SP)andaninputtotheprocess(MV)thatwillaffecttherelevantPV.Controllersareusedinindustrytoregulatetemperature,pressure,flowrate,chemicalcomposition,speedandpracticallyeveryothervariableforwhichameasurementexists.Automobilecruisecontrolisanexampleofaprocesswhichutilizesautomatedcontrol.
Duetotheirlonghistory,simplicity,wellgroundedtheoryandsimplesetupandmaintenancerequirements,PIDcontrollersarethecontrollersofchoiceformanyoftheseapplications.
2.PIDcontrollertheory
ThePIDcontrolschemeisnamedafteritsthreecorrectingterms,whosesumconstitutesthemanipulatedvariable(MV).Hence:
wherePout,Iout,andDoutarethecontributionstotheoutputfromthePIDcontrollerfromeachofthethreeterms,asdefinedbelow.
2.1.Proportionalterm
Theproportionaltermmakesachangetotheoutputthatisproportionaltothecurrenterrorvalue.TheproportionalresponsecanbeadjustedbymultiplyingtheerrorbyaconstantKp,calledtheproportionalgain.
Theproportionaltermisgivenby:
Where
Pout:
Proportionaloutput
Kp:
ProportionalGain,atuningparameter
e:
Error=SP−PV
t:
Timeorinstantaneoustime(thepresent)
Ahighproportionalgainresultsinalargechangeintheoutputforagivenchangeintheerror.Iftheproportionalgainistoohigh,thesystemcanbecomeunstable(SeethesectiononLoopTuning).Incontrast,asmallgainresultsinasmalloutputresponsetoalargeinputerror,andalessresponsive(orsensitive)controller.Iftheproportionalgainistoolow,thecontrolactionmaybetoosmallwhenrespondingtosystemdisturbances.
Intheabsenceofdisturbances,pureproportionalcontrolwillnotsettleatitstargetvalue,butwillretainasteadystateerrorthatisafunctionoftheproportionalgainandtheprocessgain.Despitethesteady-stateoffset,bothtuningtheoryandindustrialpracticeindicatethatitistheproportionaltermthatshouldcontributethebulkoftheoutputchange.
2.2.Integralterm
Thecontributionfromtheintegraltermisproportionaltoboththemagnitudeoftheerrorandthedurationoftheerror.Summingtheinstantaneouserrorovertime(integratingtheerror)givestheaccumulatedoffsetthatshouldhavebeencorrectedpreviously.Theaccumulatederroristhenmultipliedbytheintegralgainandaddedtothecontrolleroutput.Themagnitudeofthecontributionoftheintegraltermtotheoverallcontrolactionisdeterminedbytheintegralgain,Ki.
Theintegraltermisgivenby:
Iout:
Integraloutput
Ki:
IntegralGain,atuningparameter
e:
Error=SP−PV
τ:
Timeinthepastcontributingtotheintegralresponse
Theintegralterm(whenaddedtotheproportionalterm)acceleratesthemovementoftheprocesstowardssetpointandeliminatestheresidualsteady-stateerrorthatoccurswithaproportionalonlycontroller.However,sincetheintegraltermisrespondingtoaccumulatederrorsfromthepast,itcancausethepresentvaluetoovershootthesetpointvalue(crossoverthesetpointandthencreateadeviationintheotherdirection).Forfurthernotesregardingintegralgaintuningandcontrollerstability,seethesectiononlooptuning.
2.3Derivativeterm
Therateofchangeoftheprocesserroriscalculatedbydeterminingtheslopeoftheerrorovertime(i.e.itsfirstderivativewithrespecttotime)andmultiplyingthisrateofchangebythederivativegainKd.Themagnitudeofthecontributionofthederivativetermtotheoverallcontrolactionistermedthederivativegain,Kd.
Thederivativetermisgivenby:
Dout:
Derivativeoutput
Kd:
DerivativeGain,atuningparameter
e:
Error=SP−PV
t:
Timeorinstantaneoustime(thepresent)
Thederivativetermslowstherateofchangeofthecontrolleroutputandthiseffectismostnoticeableclosetothecontrollersetpoint.Hence,derivativecontrolisusedtoreducethemagnitudeoftheovershootproducedbytheintegralcomponentandimprovethecombinedcontroller-processstability.However,differentiationofasignalamplifiesnoiseandthusthisterminthecontrollerishighlysensitivetonoiseintheerrorterm,andcancauseaprocesstobecomeunstableifthenoiseandthederivativegainaresufficientlylarge.
2.4Summary
Theoutputfromthethreeterms,theproportional,theintegralandthederivativetermsaresummedtocalculatetheoutputofthePIDcontroller.Definingu(t)asthecontrolleroutput,thefinalformofthePIDalgorithmis:
andthetuningparametersare
Kp:
ProportionalGain-LargerKptypicallymeansfasterresponsesincethe
largertheerror,thelargertheProportionaltermcompensation.Anexcessivelylargeproportionalgainwillleadtoprocessinstabilityandoscillation.
Ki:
IntegralGain-LargerKiimpliessteadystateerrorsareeliminatedquicker.Thetrade-offislargerovershoot:
anynegativeerrorintegratedduringtransientresponsemustbeintegratedawaybypositiveerrorbeforewereachsteadystate.
Kd:
DerivativeGain-LargerKddecreasesovershoot,butslowsdowntransientresponseandmayleadtoinstabilityduetosignalnoiseamplificationinthedifferentiationoftheerror.
3.Looptuning
IfthePIDcontrollerparameters(thegainsoftheproportional,integralandderivativeterms)arechosenincorrectly,thecontrolledprocessinputcanbeunstable,i.e.itsoutputdiv