pid控制外文加中文文献可编辑.docx

pid控制外文加中文文献可编辑.docx

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pid控制外文加中文文献可编辑

pid控制外文加中文文献（可编辑）

PIDcontroller

FromWikipediathefreeencyclopedia

Aproportional–integral–derivativecontrollerPIDcontroller

isagenericcontrolloopfeedbackmechanismwidelyusedinindustrialcontrolsystemsAPIDcontrollerattemptstocorrecttheerrorbetweenameasuredprocessvariableandadesiredsetpointbycalculatingandthenoutputtingacorrectiveactionthatcanadjusttheprocessaccordingly

ThePIDcontrollercalculationalgorithminvolvesthreeseparateparameterstheProportionaltheIntegralandDerivativevaluesTheProportionalvaluedeterminesthereactiontothecurrenterrortheIntegraldeterminesthereactionbasedonthesumofrecenterrorsandtheDerivativedeterminesthereactiontotherateatwhichtheerrorhasbeenchangingTheweightedsumofthesethreeactionsisusedtoadjusttheprocessviaacontrolelementsuchasthepositionofacontrolvalveorthepowersupplyofaheatingelementBy"tuning"thethreeconstantsinthePIDcontrolleralgorithmthePIDcanprovidecontrolactiondesignedforspecificprocessrequirementsTheresponseofthecontrollercanbedescribedintermsoftheresponsivenessofthecontrollertoanerrorthedegreetowhichthecontrollerovershootsthesetpointandthedegreeofsystemoscillationNotethattheuseofthePIDalgorithmforcontroldoesnotguaranteeoptimalcontrolofthesystemorsystem

stability

SomeapplicationsmayrequireusingonlyoneortwomodestoprovidetheappropriatesystemcontrolThisisachievedbysettingthegainofundesiredcontroloutputstozeroAPIDcontrollerwillbecalledaPIPDPorIcontrollerintheabsenceoftherespectivecontrolactionsPIcontrollersareparticularlycommonsincederivativeactionisverysensitivetomeasurementnoiseandtheabsenceofanintegralvaluemaypreventthesystemfromreachingitstargetvalueduetothecontrolaction

AblockdiagramofaPIDcontroller

NoteDuetothediversityofthefieldofcontroltheoryandapplicationmanynamingconventionsfortherelevantvariablesareincommonuse

1Controlloopbasics

AfamiliarexampleofacontrolloopistheactiontakentokeeponesshowerwaterattheidealtemperaturewhichtypicallyinvolvesthemixingoftwoprocessstreamscoldandhotwaterThepersonfeelsthewatertoestimateitstemperatureBasedonthismeasurementtheyperformacontrolactionusethecoldwatertaptoadjusttheprocessThepersonwouldrepeatthisinput-outputcontrolloopadjustingthehotwaterflowuntiltheprocesstemperaturestabilizedatthedesiredvalue

FeelingthewatertemperatureistakingameasurementoftheprocessvalueorprocessvariablePVThedesiredtemperatureiscalledthe

setpointSPTheoutputfromthecontrollerandinputtotheprocessthetappositioniscalledthemanipulatedvariableMVThedifferencebetweenthemeasurementandthesetpointistheerroretoohotortoocoldandbyhowmuchAsacontrolleronedecidesroughlyhowmuchtochangethetappositionMVafteronedeterminesthetemperaturePVandthereforetheerrorThisfirstestimateistheequivalentoftheproportionalactionofaPIDcontrollerTheintegralactionofaPIDcontrollercanbethoughtofasgraduallyadjustingthetemperaturewhenitisalmostrightDerivativeactioncanbethoughtofasnoticingthewatertemperatureisgettinghotterorcolderandhowfastandtakingthatintoaccountwhendecidinghowtoadjustthetapMakingachangethatistoolargewhentheerrorissmallisequivalenttoahighgaincontrollerandwillleadtoovershootIfthecontrollerweretorepeatedlymakechangesthatweretoolargeandrepeatedlyovershootthetargetthiscontrolloopwouldbetermedunstableandtheoutputwouldoscillatearoundthesetpointineitheraconstantgrowingordecayingsinusoidAhumanwouldnotdothisbecauseweareadaptivecontrollerslearningfromtheprocesshistorybutPIDcontrollersdonothavetheabilitytolearnandmustbesetupcorrectlySelectingthecorrectgainsforeffectivecontrolisknownastuningthecontroller

IfacontrollerstartsfromastablestateatzeroerrorPVSPthenfurtherchangesbythecontrollerwillbeinresponsetochangesin

othermeasuredorunmeasuredinputstotheprocessthatimpactontheprocessandhenceonthePVVariablesthatimpactontheprocessotherthantheMVareknownasdisturbancesandgenerallycontrollersareusedtorejectdisturbancesandorimplementsetpointchangesChangesinfeedwatertemperatureconstituteadisturbancetotheshowerprocess

IntheoryacontrollercanbeusedtocontrolanyprocesswhichhasameasurableoutputPVaknownidealvalueforthatoutputSPandaninputtotheprocessMVthatwillaffecttherelevantPVControllersareusedinindustrytoregulatetemperaturepressureflowratechemicalcompositionspeedandpracticallyeveryothervariableforwhichameasurementexistsAutomobilecruisecontrolisanexampleofaprocesswhichutilizesautomatedcontrol

DuetotheirlonghistorysimplicitywellgroundedtheoryandsimplesetupandmaintenancerequirementsPIDcontrollersarethecontrollersofchoiceformanyoftheseapplications

2PIDcontrollertheory

NoteThissectiondescribestheidealparallelornon-interactingformofthePIDcontrollerForotherformspleaseseetheSection"AlternativenotationandPIDforms"

ThePIDcontrolschemeisnamedafteritsthreecorrectingtermswhosesumconstitutesthemanipulatedvariableMVHence

wherePoutIoutandDoutarethecontributionstotheoutputfromthe

PIDcontrollerfromeachofthethreetermsasdefinedbelow

21Proportionalterm

TheproportionaltermmakesachangetotheoutputthatisproportionaltothecurrenterrorvalueTheproportionalresponsecanbeadjustedbymultiplyingtheerrorbyaconstantKpcalledtheproportionalgain

Theproportionaltermisgivenby

Where

PoutProportionaloutput

KpProportionalGainatuningparameter

eErrorSPPV

tTimeorinstantaneoustimethepresent

ChangeofresponseforvaryingKpAhighproportionalgainresultsinalargechangeintheoutputforagivenchangeintheerrorIftheproportionalgainistoohighthesystemcanbecomeunstableSeethesectiononLoopTuningIncontrastasmallgainresultsinasmalloutputresponsetoalargeinputerrorandalessresponsiveorsensitivecontrollerIftheproportionalgainistoolowthecontrolactionmaybetoosmallwhenrespondingtosystemdisturbances

IntheabsenceofdisturbancespureproportionalcontrolwillnotsettleatitstargetvaluebutwillretainasteadystateerrorthatisafunctionoftheproportionalgainandtheprocessgainDespitethe

steady-stateoffsetbothtuningtheoryandindustrialpracticeindicatethatitistheproportionaltermthatshouldcontributethebulkoftheoutputchange

comgralterm

ThecontributionfromtheintegraltermisproportionaltoboththemagnitudeoftheerrorandthedurationoftheerrorSummingtheinstantaneouserrorovertimeintegratingtheerrorgivestheaccumulatedoffsetthatshouldhavebeencorrectedpreviouslyTheaccumulatederroristhenmultipliedbytheintegralgainandaddedtothecontrolleroutputThemagnitudeofthecontributionoftheintegraltermtotheoverallcontrolactionisdeterminedbytheintegralgainKi

Theintegraltermisgivenby

ChangeofresponseforvaryingKiWhere

IoutIntegraloutput

KiIntegralGainatuningparameter

eErrorSPPV

τTimeinthepastcontributingtotheintegralresponse

Theintegraltermwhenaddedtotheproportionaltermacceleratesthemovementoftheprocesstowardssetpointandeliminatestheresidualsteady-stateerrorthatoccurswithaproportionalonlycontrollerHoweversincetheintegraltermisrespondingtoaccumulatederrorsfromthepastitcancausethepresentvaluetoovershootthesetpointvalue

crossoverthesetpointandthencreateadeviationintheotherdirectionForfurthernotesregardingintegralgaintuningandcontrollerstabilityseethesectiononlooptuning

23Derivativeterm

TherateofchangeoftheprocesserroriscalculatedbydeterminingtheslopeoftheerrorovertimeieitsfirstderivativewithrespecttotimeandmultiplyingthisrateofchangebythederivativegainKdThemagnitudeofthecontributionofthederivativetermtotheoverallcontrolactionistermedthederivativegainKd

Thederivativetermisgivenby

ChangeofresponseforvaryingKdWhere

DoutDerivativeoutput

KdDerivativeGainatuningparameter

eErrorSPPV

tTimeorinstantaneoustimethepresent

ThederivativetermslowstherateofchangeofthecontrolleroutputandthiseffectismostnoticeableclosetothecontrollersetpointHencederivativecontrolisusedtoreducethemagnitudeoftheovershootproducedbytheintegralcomponentandimprovethecombinedcontroller-processstabilityHoweverdifferentiationofasignalamplifiesnoiseandthusthisterminthecontrollerishighlysensitivetonoiseintheerrortermandcancauseaprocesstobecomeunstableif

thenoiseandthederivativegainaresufficientlylarge

24Summary

TheoutputfromthethreetermstheproportionaltheintegralandthederivativetermsaresummedtocalculatetheoutputofthePIDcontrollerDefiningutasthecontrolleroutputthefinalformofthePIDalgorithmis

andthetuningparametersare

KpProportionalGain-LargerKptypicallymeansfasterresponsesincethe

largertheerrorthelargertheProportionaltermcompensationAnexcessivelylargeproportionalgainwillleadtoprocessinstabilityandoscillation

KiIntegralGain-LargerKiimpliessteadystateerrorsareeliminatedquickerThetrade-offislargerovershootanynegativeerrorintegratedduringtransientresponse