中英文文献翻译PID控制器.docx
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中英文文献翻译PID控制器
附件1:
外文原文
PIDcontroller
ZuoXinandSunJinming
（ResearchInstituteofAutomation.UniversityofPetroleum,Belting102249,China）
ReceivedApril2,2005
Abstract:
Performaneeassessmentofaproportional-integral-derivative（PID）controllerisconduetedusingthePIDachievableminimumvarianeeasabenchmarkWhentheprocessmodelisunknownwecarlestimatetheP^D-achievableminimumvarianeeandthecorrespondingparametersbyroutineclosed-loopoperationdataSimulationresultsshowthattheprocessoutputvarianeeisreducedbyretuningcontrollerparameters
Keywords：
PerformaneeassessmentPIDcontrol,minimumvarianee
Aproportional-ntegral-derivativeeontroller（PIDeontroller）isageneric.controlloopfeedbackmechanismwidelyusedinindustrialeontrolsystems.APIDeontrollerattemptstocorrecttheerrorbetweenameasuredprocessvariableandadesiredsetpointbycalculatingandthenoutputtingacorrectiveactionthatcanadjusttheprocessaccordingly.
ThePIDeontrollercalculation（algorithm）invoIvesthreeseparateparameters;theProportional,theIntegralandDerivativevalues.TheProportionalvaluedeterminesthereactiontothecurrenterror,theIntegraldeterminesthereactionbasedonthesumofrecenterrorsandtheDerivativedeterminesthereactiontotherateatwhichtheerrorhasbeenchanging.Theweightedsumofthesethreeactionsisusedtoadjusttheprocessviaaeontrolelementsuchasthepositionofaeontrolvalveorthepowersupplyofaheatingelement.By"tuning"thethreeeonstantsinthePIDeontrolleralgorithmthePIDcanprovideeontrolactiondesignedforspecificprocessrequirements.Theresponseoftheeontrollercanbedescribedintermsoftheresponsivenessoftheeontrollertoanerror,thedegreetowhichtheeontrollerovershootsthesetpointandthedegreeofsystemoscillation.NotethattheuseofthePIDalgorithmforeontroldoesnotguaranteeoptimaleontrolofthesystemorsystemstability.
Someapplicationsmayrequireusingonlyoneortwomodestoprovidetheappropriatesystemcontrol.Thisisachievedbysettingthegainofundesiredcontroloutputstozero.APIDcontrollerwillbecalledaPI,PD,PorIcontrollerintheabseneeoftherespectivecontrolactions.PIcontrollersareparticularlycommon,sincederivativeactionisverysensitivetomeasurementnoise,andtheabsenceofanintegralvaluemaypreventthesystemfromreachingitstargetvalueduetothecontrolaction.
Note:
Duetothediversityofthefieldofcontroltheoryandapplication,manynamingconventionsfortherelevantvariablesareincommonuse.
1.Controlloopbasics
Afamiliarexampleofacontrolloopistheactiontakentokeepone'sshowerwaterattheidealtemperature,whichtypicallyinvoIvesthemixingoftwoprocessstreams,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.Changesinfeedwatertemperatureconstituteadisturbaneetotheshowerprocess.
Intheory,acontrollercanbeusedtocontrolanyprocesswhichhasameasurableoutput（PV）,aknownidealvalueforthatoutput（SP）andaninputtotheprocess（MV）thatwillaffecttherelevantPV.Controllersareusedinindustrytoregulatetemperature,pressure,flowrate,chemicalcomposition,speedandpracticallyeveryothervariableforwhichameasurementexists.Automobilecruisecontrolisanexampleofaprocesswhichutilizesautomatedcontrol.
Duetotheirlonghistory,simplicity,wellgroundedtheoryandsimplesetupandmaintenancerequirements,PIDcontrollersarethecontrollersofchoiceformanyoftheseapplications.
2.PIDcontrollertheory
Note:
Thissectiondescribestheidealparallelornon-interactingformofthePIDcontroller.ForotherformspleaseseetheSection"AlternativenotationandPIDforms".
ThePIDcontrolschemeisnamedafteritsthreecorrectingterms,whosesumconstitutesthemanipulatedvariable（MV）.Hence:
MV（t）=Pout+/out+Dout.
WherePout,lout,andDoutarethecontributionstotheoutputfromthePIDcontrollerfromeachofthethreeterms,asdefinedbelow.
2.1.Proportionalterm
Theproportionaltermmakesachangetotheoutputthatisproportionaltothecurrenterrorvalue.TheproportionalresponsecanbeadjustedbymultiplyingtheerrorbyaconstantKp,calledtheproportionalgain.
Theproportionaltermisgivenby:
H>ut=Ape（f）
Where
Pout:
Proportionaloutput
Kp:
ProportionalGain,atuningparameter
e:
Error=SP-PV
t:
Timeorinstantaneoustime（thepresent）
ChangeofresponseforvaryingKpAhighproportionalgainresultsinalargechangeintheoutputforagivenchangeintheerror.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:
/out=A'ie（r）dr
Jo
Iout:
Integraloutput
Ki:
IntegralGain,atuningparameter
e:
Error=SP-PV
t:
Timeinthepastcontributingtotheintegralresponse
Theintegralterm（whenaddedtotheproportionalterm）acceleratesthemovementoftheprocesstowardssetpointandeliminatestheresidualsteady-stateerrorthatoccurswithaproportionalonlycontroller.However,sincetheintegraltermisrespondingtoaccumulatederrorsfromthepast,itcancausethepresentvaluetoovershootthesetpointvalue（crossoverthesetpointandthencreateadeviationintheotherdirection）.Forfurthernotesregardingintegralgaintuningandcontrollerstability,seethesectiononlooptuning.
2.3Derivativeterm
Therateofchangeoftheprocesserroriscalculatedbydeterminingtheslopeoftheerrorovertime（i.e.itsfirstderivativewithrespecttotime）andmultiplyingthisrateofchangebythederivativegainKd.Themagnitudeofthecontributionofthederivativetermtotheoverallcontrolactionistermedthederivativegain,Kd.
Thederivativetermisgivenby:
Omit=K（i—
Dout:
Derivativeoutput
Kd:
DerivativeGain,atuningparameter
e:
Error=SP-PV
t:
Timeorinstantaneoustime（thepresent）
Thederivativetermslowstherateofchangeofthecontrolleroutputandthiseffectismostnoticeableclosetothecontrollersetpoint.Hence,derivativecontrolisusedtoreducethemagnitudeoftheovershootproducedbytheintegralcomponentandimprovethecombinedcontroller-processstability.However,differentiationofasignalamplifiesnois
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