PID控制外文翻译Word格式.docx

PID控制外文翻译Word格式.docx

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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

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:

Thederivativetermslowstherateofchangeofthecontrolleroutputandthiseffectismostnoticeableclosetothecontrollersetpoint.Hence,derivativecontrolisusedtoreducethemagnitudeoftheovershootproducedbytheintegralcomponentandimprovethecombinedcontroller-processstability.However,differentiationofasignalamplifiesnoiseandthusthisterminthecontrollerishighlysensitivetonoiseintheerrorterm,andcancauseaprocesstobecomeunstableifthenoiseandthederivativegainaresufficientlylarge.

2.4Summary

Theoutputfromthethreeterms,theproportional,theintegralandthederivativetermsaresummedtocalculatetheoutputofthePIDcontroller.Definingu（t）asthecontrolleroutput,thefinalformofthePIDalgorithmis:

andthetuningparametersare

ProportionalGain-LargerKptypicallymeansfasterresponsesincethe

largertheerror,thelargertheProportionaltermcompensation.Anexcessivelylargeproportionalgainwillleadtoprocessinstabilityandoscillation.

IntegralGain-LargerKiimpliessteadystateerrorsareeliminatedquicker.Thetrade-offislargerovershoot:

anynegativeerrorintegratedduringtransientresponsemustbeintegratedawaybypositiveerrorbeforewereachsteadystate.

Kd:

DerivativeGain-LargerKddecreasesovershoot,butslowsdowntransientresponseandmayleadtoinstabilityduetosignalnoiseamplificationinthedifferentiationoftheerror.

3.Looptuning

IfthePIDcontrollerparameters（thegainsoftheproportional,integralandderivativeterms）arechosenincorrectly,thecontrolledprocessinputcanbeunstable,i.e.itsoutputd