外文翻译PID控制器.docx

外文翻译PID控制器.docx

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外文翻译PID控制器

PIDcontroller

FromWikipedia,thefreeencyclopedia

Aproportional–integral–derivativecontroller（PIDcontroller）isageneric.controlloopfeedbackmechanismwidelyusedinindustrialcontrolsystems.APIDcontrollerattemptstocorrecttheerrorbetweenameasuredprocessvariableandadesiredsetpointbycalculatingandthenoutputtingacorrectiveactionthatcanadjusttheprocessaccordingly.

ThePIDcontrollercalculation（algorithm）involvesthreeseparateparameters;theProportional,theIntegralandDerivativevalues.TheProportionalvaluedeterminesthereactiontothecurrenterror,theIntegraldeterminesthereactionbasedonthesumofrecenterrorsandtheDerivativedeterminesthereactiontotherateatwhichtheerrorhasbeenchanging.Theweightedsumofthesethreeactionsisusedtoadjusttheprocessviaacontrolelementsuchasthepositionofacontrolvalveorthepowersupplyofaheatingelement.By"tuning"thethreeconstantsinthePIDcontrolleralgorithmthePIDcanprovidecontrolactiondesignedforspecificprocessrequirements.Theresponseofthecontrollercanbedescribedintermsoftheresponsivenessofthecontrollertoanerror,thedegreetowhichthecontrollerovershootsthesetpointandthedegreeofsystemoscillation.NotethattheuseofthePIDalgorithmforcontroldoesnotguaranteeoptimalcontrolofthesystemorsystemstability.

Someapplicationsmayrequireusingonlyoneortwomodestoprovidetheappropriatesystemcontrol.Thisisachievedbysettingthegainofundesiredcontroloutputstozero.APIDcontrollerwillbecalledaPI,PD,PorIcontrollerintheabsenceoftherespectivecontrolactions.PIcontrollersareparticularlycommon,sincederivativeactionisverysensitivetomeasurementnoise,andtheabsenceofanintegralvaluemaypreventthesystemfromreachingitstargetvalueduetothecontrolaction.

AblockdiagramofaPIDcontroller

Note:

Duetothediversityofthefieldofcontroltheoryandapplication,manynamingconventionsfortherelevantvariablesareincommonuse.

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

Note:

Thissectiondescribestheidealparallelornon-interactingformofthePIDcontroller.ForotherformspleaseseetheSection"AlternativenotationandPIDforms".

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）

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:

ChangeofresponseforvaryingKiWhere

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:

ChangeofresponseforvaryingKdWhere

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.Anexcessivelylargeproportionalgainwillleadtoprocessinstabilityandoscil