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PID-säädin



Peruskatsaus

PID-säädin(ProportionIntegrationDifferentiation.ProportionIntegrationDifferentiation.Proportion-Integration-DifferentiationController),joka koostuu suhteellisesta yksiköstäP,integralunitIandderivativemittersofthrought,Kposition. ID-ohjaimetsoveltuvat pääasiassa järjestelmiin, joiden peruslineaarisuus ja dynaamiset ominaisuudet eivät muutu ajan myötä.

PIDcontrollerisacommonfeedbackloopcomponentinindustrialcontrolapplications.Thiscontrollercomparesthecollecteddatawithareferencevalue,andthenusesthisdifferencetocalculateanewinputvalue.Thepurposeofthisnewinputvalueistoallowthesystemdatatoreachormaintainthereferencevalue.Differentfromothersimplecontrolcalculations,PIDcontrollercanadjusttheinputvalueaccordingtohistoricaldataandtheoccurrencerateofdifference,whichcanmakethesystemmoreaccurateandmorestable.ItcanbeprovedbymathematicalmethodsthataPIDfeedbackloopcankeepthesystemstablewhenothercontrolmethodsleadtosystemstabilityerrorsorprocessrepetitions.

Palautesilmukka

Ohjaussilmukka koostuu kolmesta osasta:

Themeasurementresultsobtainedbythesystem’ssensors,thecontrollermakesthedecisionandreactsthroughanoutputdevicetocontrolThedeviceobtainsthemeasurementresultfromthesensor,andthensubtractsthemeasurementresultfromthedemandresulttogettheerror.Thenusetheerrortocalculateacorrectionvaluetothesystemastheinputresult,sothatthesystemcaneliminatetheerrorfromitsoutputresult.

InaPIDloop,therearethreealgorithmsforthiscorrectionvalue,eliminatingerrors,averagingpasterrors,andpredictingfutureerrorsthroughchangesinerrors.

Forexample,ifawatertankisprovidingwaterforaplant,thewaterinthistankneedstobekeptatacertainheight.Asensorwillbeusedtochecktheheightofthewaterinthetank,sothatthemeasurementresultisobtained.Thecontrollerwillhaveafixeduserinputvaluetoindicatetherequiredwatersurfaceheightofthewatertank,assumingthisvalueistomaintain65%ofthewatervolume.Theoutputdeviceofthecontrollerwillbeconnectedtoamotor-controlledwatervalve.Openingthevalvewillfillthewatertank,andclosingthevalvewillreducetheamountofwaterinthewatertank.Thecontrolsignalofthisvalveisthevariablewecontrol,anditisalsotheinputofthissystemtokeepthewatertankfixed.

PIDcontrollercanbeusedtocontrolanyvariablethatcanbemeasuredandcontrolled.Forexample,itcanbeusedtocontroltemperature,pressure,flow,chemicalcomposition,speedandsoon.Thecruisecontrolfunctiononacarisanexample.

SomecontrolsystemsconnectseveralPIDcontrollersinseries,orchainthemintoanetwork.Inthiscase,amaincontrollermayoutputresultsforothercontrols.Acommonexampleisthecontrolofmotors.Wewilloftenneedthemotortohaveacontrolledspeedandstopatacertainposition.Inthisway,asub-controllermanagesthespeed,butthespeedofthissub-controllerismanagedbythemaincontrollerthatcontrolsthepositionofthemotor.

Combinationandseriescontrolareverycommoninchemicalprocesscontrolsystems.

Theory

PIDisnamedafteritsthreecorrectionalgorithms.Allthreealgorithmsuseadditiontoadjustthecontrolledvalue.Infact,mostoftheseadditionoperationsbecomesubtractionoperationsbecausetheaddendisalwaysnegative.Thesethreealgorithmsare:

Osuus-Virran ohjaamiseksi virhearvo kerrotaan negatiivisella vakiollaP(osuus)ja sitten ennalta määrättyLisää .Esimerkiksi sähkövahvistimen säätimen asteikko on10° C,ja sen ennalta määrätty arvo on20 °C.Sillointulostaa100% 10 °C:ssa, 50% 15 °C:ssa ja 10% 19 °C:ssa.Huomaa, että jos virhe on0,säätimen lähtö on0.

Integration-Tocontrolthepast,theerrorvalueisthesumoftheerrorsinthepastperiodoftime,andthenmultipliedbyanegativeconstantI,andthencomparedwiththepredeterminedvalueadd.IFindtheaverageerrorbetweentheoutputresultofthesystemandthepredeterminedvaluefromtheaverageerrorvalueinthepast.Asimpleproportionalsystemwilloscillateandchangebackandfortharoundapredeterminedvaluebecausethesystemcannoteliminateredundantcorrections.Byaddinganegativeaverageerrorratiovalue,theaveragesystematicerrorvaluewillalwaysdecrease.Therefore,intheend,thePIDloopsystemwillbesetatapredeterminedvalue.

Johdannainen-Jos haluat hallita tulevaisuutta, laske virheenensimmäinen johdannainen, kerro se negatiivisella vakiollaD ja lisää lopuksi ennalta määrättyyn arvoon. Tämän johdannaisen ohjaus reagoi järjestelmän muutoksiin. parametrit ovat myös siitä syystä, että PID:tä kutsutaan ennustettavaksi ohjaimeksi.D parametrit ovat erittäin hyödyllisiävähentämäänlyhytaikaisia ​​ohjaimenmuutoksia. Käytännössä jotkut hitaat järjestelmät eivät välttämättä vaadiD-parametria. Ammattimaisemmissa ehdoissa PID-ohjain voidaan kutsua suodattimeksi taajuusalueen pääjärjestelmässä. ohjausjärjestelmän syöttöarvo heilahtelee toistuvasti, mikä voi aiheuttaa sen, että järjestelmä saavuttaa aina esiasetetun arvon.

Ohjauslaki

Vaikka erityyppisillä ohjaimilla on erilaisia ​​rakenteita ja periaatteita, on olemassa vain kolmeperussäätölakia: suhteellinen(P)ohjaus, integraalinen(I)ohjausJa johdannainen(D)ohjaus.Näitä ohjauslakeja voidaankäyttääyksin,mutta)yhteydessä tai yhteiskäytössä. tional-integral(PI)ohjaus,suhteellinen -integraalijohdannainen (PID) ohjaus jne.

Suhteellinen (P)ohjaus

Singleproportionalcontrolisalsocalled"differencecontrol",theoutputchangeisproportionaltothedeviationoftheinputcontroller,Thegreaterthedeviation,thegreatertheoutput.Inpracticalapplications,thedegreeofproportionalityshouldbedeterminedaccordingtothespecificsituation.Toolargeaproportionality,tooweakcontroleffect,isnotconducivetothesystemtoovercomedisturbances,themarginistoolarge,thecontrolqualityispoor,andthereisnocontroleffect;theproportionalityistoosmall,Thecontroleffectistoostrong,itiseasytocausethestabilityofthesystemtodeteriorateandcauseoscillation.

Forthecontrolledobjectwithsensitiveresponseandstrongamplificationability,inordertoimprovethestabilityofthesystem,theproportionalityshouldbeslightlylarger;forthecontrolledobjectwithslowresponseandweakamplificationability,theproportionalThedegreecanbeselectedtobesmallertoimprovethesensitivityoftheentiresystemandtoreducetheresidualsaccordingly.

Pureproportionalcontrolissuitableforoccasionswherethedisturbanceissmall,thehysteresisissmall,theloadchangeissmall,therequirementsarenothigh,andacertainmarginisallowed.Theuseofproportionalcontrollawinindustrialproductionismorecommon.

Suhteellisen integraalin (PI) ohjaus

Proportionalcontrollawisthemostbasicandmostcommonlyusedoneofthebasiccontrollaws.ItsgreatestadvantageisControlistimelyandrapid.Aslongasthereisadeviation,thecontrollerimmediatelytakescontrol.However,thedisadvantageofnotbeingabletofinallyeliminatetheresiduallimitsitsusealone.Thewaytoovercometheresidualistoaddintegralcontrolonthebasisofproportionalcontrol.

Theoutputoftheintegralcontrollerisproportionaltotheintegraloftheinputdeviationovertime.The"points"heremeans"accumulation".Theoutputoftheintegralcontrollerisnotonlyrelatedtothemagnitudeoftheinputdeviation,butalsorelatedtothetimethedeviationexists.Aslongasthedeviationexists,theoutputwillcontinuetoaccumulate(theoutputvalueisgettinglargerorsmaller),andtheaccumulationwillstopuntilthedeviationiszero.Therefore,integralcontrolcaneliminateresiduals.Theintegralcontrollawisalsocalledthenon-differencecontrollaw.

Thesizeoftheintegraltimecharacterizesthestrengthofintegralcontrol.Thesmallertheintegraltime,thestrongerthecontroleffect;onthecontrary,theweakerthecontroleffect.

Althoughintegralcontrolcaneliminatetheresidualerror,ithasthedisadvantageofnottimelycontrol.Becausetheaccumulationofintegraloutputisgradual,thecontroleffectitproducesalwayslagsbehindthechangeofthedeviation,andtheinfluenceofinterferencecannotbeovercomeintimeandeffectively,anditisdifficulttostabilizethecontrolsystem.Therefore,inpractice,integralcontrolisgenerallynotusedalone,butcombinedwithproportionalcontroltoformproportionalintegralcontrol.Inthisway,theadvantagesofthetwoareusedtomakeupforeachother,whichnotonlyhastherapidandtimelyeffectofproportionalcontrol,butalsohastheabilityofintegralcontroltoeliminatetheresidualerror.Therefore,proportionalintegralcontrolcanachieveamoreidealprocesscontrol.

Proportionalintegralcontrolleristhemostwidelyusedcontroller,whichismostlyusedinthecontrolsystemofliquidlevel,pressure,flow,etc.inindustrialproduction.Sincetheintroductionofintegralactioncaneliminatetheresidualerror,makeupfortheshortcomingsofpureproportionalcontrol,andobtainbettercontrolquality.Buttheintroductionofintegralactionwillmakethestabilityofthesystemworse.Forcontrolsystemswithlargeinertialag,trytoavoidusingthem.

Suhteellisen johdannaisen (PD) ohjaus

Proportionalintegralcontrolisnotidealforthecontrolledobjectwithtimelag.Theso-called"timelag"refersto:whenthecontrolledobjectisdisturbed,thecontrolledvariabledoesnotchangeimmediately,butthereisatimedelay,suchasacapacitylag,whentheproportionalintegralcontrolappearssluggishanduntimely.Forthisreason,peopleimagined:Canthecorrespondingcontrolactionbemadeaccordingtothechangingtrendofthedeviation?Justlikeexperiencedoperators,theycanchangethevalveopeningaccordingtothemagnitudeofthedeviation(proportionaleffect),andcanpredictthesituationthatwilloccuraccordingtothespeedofthedeviationchange,andcarryoutexcessivecontrolinadvanceto"preventproblemsbeforetheyoccur.".Thisisthedifferentialcontrollawwith"advanced"controlfunction.Theoutputofthederivativecontrollerdependsonthespeedatwhichtheinputdeviationchanges.

Thedifferentialoutputisonlyrelatedtothechangespeedofthedeviation,andhasnothingtodowiththesizeofthedeviationandwhetherthedeviationexistsornot.Ifthedeviationisafixedvalue,nomatterhowlarge,aslongasitdoesnotchange,theoutputchangemustbezero,andthecontrollerhasnocontroleffect.Thelongerthederivativetime,thelongerthederivativeoutputismaintained,sothestrongerthederivativeaction;otherwise,theweaker.Whenthederivativetimeis0,thereisnoderivativecontroleffect.Inthesameway,theselectionofthedifferentialtimealsoneedstobedeterminedaccordingtotheactualsituation.

Thecharacteristicsofthedifferentialcontrolfunctionare:rapidaction,withadvancedadjustmentfunction,whichcaneffectivelyimprovethecontrolqualityofthecontrolledobjectwithalargetimelag;butitcannoteliminatetheresidual,especiallyfortheconstantdeviationinputThereisnocontroleffectatall.Therefore,thedifferentialcontrollawcannotbeusedalone.

Thecombinationofproportionalanddifferentialactionisfasterthanpureproportionalaction.Especiallyforobjectswithlargecapacitylag,theamplitudeofdynamicdeviationcanbereduced,controltimecanbesaved,andcontrolqualitycanbesignificantlyimproved.

PID-ohjaus

Themostidealcontrolistheproportional-integral-derivativecontrollaw.Itcombinestheadvantagesofthethree:boththeproportionalactionistimelyandrapid,theintegralactioncaneliminatetheresidualerror,andthedifferentialactionhastheadvancedcontrolfunction.

Whenthedeviationstepoccurs,thederivativewillactimmediatelytosuppressthisleapofdeviation;theratioalsoplaysaroleineliminatingthedeviation,sothatthedeviationrangeisreduced,becausetheproportionaleffectislastingandeffective.Themaineffectofthecontrollaw,sothatthesystemcanbemorestable;andtheintegraleffectgraduallyovercomestheresidualerror.Aslongasthecontrolparametersofthethreefunctionsareselectedproperly,theadvantagesofthethreecontrollawscanbefullyutilizedandamoreidealcontroleffectcanbeobtained.

Virheenkorjausmenetelmä

Suhteellisuuskertoimen säätö

Suhteellisuuskertoimen säätöalue on yleensä 0,1--100.

Ifthegainvalueis0.1,thePIDregulatoroutputchangestoone-tenthofthedeviationvalue.Ifthegainvalueis100,theoutputofthePIDregulatorchangestoonehundredtimesthedeviationvalue.

Itcanbeseenthatthelargerthevalue,thegreaterthegaineffectproducedbytheratio.Intheinitialadjustment,chooseasmallervalue,andthenslowlyincreaseituntilthesystemfluctuationissmallenough,andthenadjusttheintegralordifferentialcoefficient.AtoolargePvaluewillcausethesystemtobeunstableandcontinuetooscillate;atoosmallPvaluewillmakethesystemunresponsive.Theappropriatevalueshouldenablethesystemtohavesufficientsensitivitybutnottoosensitive.Thedelayforacertainperiodoftimeshouldbeadjustedbytheintegrationtime.

Adjustmentoftheintegralcoefficient

Thedefinitionoftheintegraltimeconstantisthetimethatthedeviationcausestheoutputtoincrease.Iftheintegrationtimeissetto1second,thetimerequiredfora100%outputchangeis1second.Intheinitialadjustment,settheintegrationtimelonger,andthenslowlyadjustituntilthesystemisstable.

Adjustmentofthedifferentialcoefficient

Thedifferentialvalueistherateofchangeofthedeviationvalue.Forexample,iftheinputdeviationvaluechangeslinearly,aconstantadjustmentamountissuperimposedontheoutputsideoftheregulator.Mostcontrolsystemsdonotneedtoadjustthederivativetime.Becauseonlysystemswithtimelagneedtoaddthisparameter.Ifsuperfluousandaddingthisparameter,thecontrolofthesystemwillbeaffected.Iftheidealcontrolrequirementisstillnotreceivedthroughtheadjustmentoftheproportionalandintegralparameters,thederivativetimecanbeadjusted.Intheinitialadjustment,setthiscoefficienttoasmallvalue,andthenslowlyincreaseituntilthesystemisstable.

Parametertuning

PIDcontrollerparametertuningisthecorecontentofcontrolsystemdesign.Itdeterminestheproportionalcoefficient,integraltimeandderivativetimeofthePIDcontrolleraccordingtothecharacteristicsofthecontrolledprocess.TherearemanymethodsforPIDcontrollerparametertuning,whichcanbesummarizedintotwocategories:Oneisthetheoreticalcalculationtuningmethod.Itismainlybasedonthemathematicalmodelofthesystemtodeterminethecontrollerparametersthroughtheoreticalcalculations.Thecalculateddataobtainedbythismethodmaynotbedirectlyusable,andmustbeadjustedandmodifiedthroughactualengineering.Thesecondistheengineeringtuningmethod,whichmainlyreliesonengineeringexperienceandiscarriedoutdirectlyinthetestofthecontrolsystem,andthemethodissimpleandeasytomaster,andiswidelyusedinengineeringpractice.TheengineeringtuningmethodsofPIDcontrollerparametersmainlyincludecriticalproportionmethod,responsecurvemethodandattenuationmethod.Thethreemethodshavetheirowncharacteristics.Thecommonpointisthattheypassthetest,andthenadjustthecontrollerparametersaccordingtotheengineeringexperienceformula.However,nomatterwhichmethodisused,thecontrollerparametersobtainedneedtobeadjustedandperfectedinactualoperation.Thecriticalratiomethodisgenerallyusednow.ThestepsfortuningPIDcontrollerparametersusingthismethodareasfollows:(1)First,pre-selectashortenoughsamplingperiodforthesystemtowork;(2)Onlyaddproportionalcontrollinksuntilthesystemhascriticaloscillationsinitsstepresponsetotheinput.Writedowntheproportionalamplificationfactorandcriticaloscillationperiodatthistime;(3)Underacertaindegreeofcontrol,theparametersofthePIDcontrollercanbecalculatedbyformulas.

Adaptiivinen hallinta

Ensinnäkin, selvitä mikä on mukautuva ohjaus

Intheproductionprocess,inordertoimproveproductquality,increaseoutput,saverawmaterials,productionmanagementandTheproductionprocessisalwaysinoptimalworkingcondition.Therefore,anoptimalcontrolmethodisproduced,whichiscalledadaptivecontrol.Inthiskindofcontrol,thesystemisrequiredtobeabletoautomaticallyadjustthesystemaccordingtothechangesinthemeasuredparameters,theenvironmentandthecostofrawmaterials,sothatthesystemisinthebeststateatanytime.Adaptivecontrolincludesthreelinks:performanceestimation(discrimination),decision-makingandmodification.Itisthedevelopmentdirectionofthemicrocomputercontrolsystem.However,becausethecontrollawisdifficulttograsp,therearestillsomedifficultproblemstopromote.

Addingadaptivepidcontrolbringssomeintelligentfeatures,whichcanadapttochangesinexternalconditionslikeacreature.

On myös itseoppimisjärjestelmä, joka tekee siitä älykkäämmän.

Säätimen suorituskyky

PID-ohjauksen ongelmat

Therearedocumentsthatpointoutthat60%ofcontrollersintheactualindustryhaveperformanceproblems.Intheindustrialprocess,thereasonsforthepoorperformanceofthecontrolloopcanbeattributedtooneormoreofthefollowingsituations:1)Thecontrollerispoorlytunedandlacksmaintenance.Thereasonsforthissituationinclude:thecontrollerhasneverbeentunedoristunedbasedonamismatchmodel,oranimpropertypeofcontrollerhasbeenused.Intheindustrialprocessautomaticcontrolsystem,morethan90%ofthecontrollersarePIDtypecontrollers,evenifothercontrollersmaybeusedinsomecases,betterperformancemaybeobtained.Infact,themostcommoncauseofpoorcontrolloopperformanceisthelackofmaintenanceofthecontroller.Afteryearsofoperation,thedynamiccharacteristicsoftheactuatorandthecontrolledobjectmaychangeduetowearandotherreasons.Onlyafewengineersmaintainthecontrolloop,andoperatorsandengineersoftenlackunderstandingofthereasonsforthepoorperformanceofthecontrolloop.

2)Equipmentfailureorunreasonablestructuredesign.Poorcontrolloopperformancemaybecausedbysensororactuatorfailure(suchasexcessivefriction).Ifthedesignoftheindustrialdeviceorthecomponentsofthedeviceisnotreasonable,theproblemmaybemoreserious.Theseproblemscannotbeeffectivelysolvedbyre-tuningthecontroller.

3)Lackorinsufficientfeedforwardcompensation.Ifhandledimproperly,externaldisturbanceswilldeterioratetheperformanceoftheloop.Therefore,whenthedisturbanceismeasurable,itisrecommendedtouseFeedforvvardControl(FFC)tocompensateforthedisturbance.

4)Thecontrolstructuredesignisunreasonable.Inappropriateinput/outputpairing,ignoringthemutualcouplingbetweensystemvariables,CompetingControllers,insufficientdegreesoffreedom,strongnonlinearity,andlackofcompensationforlargetimedelaysmayallleadtocontrolstructureproblems.

PID-suorituskyvyn arviointi

ExistingdocumentshavepointedoutthatitisfeasibletoestimatetheminimumvariancethatcanbeachievedbyPIDcontrolwithconventionaloperatingdatainaknownprocess;forPIDcontrol,itcanbeachievedbyusingPIDAstheevaluationbenchmark,theevaluationresultsaremorereasonable;thePIDcontrollerparametersestimatedafterfittingthemodelcansignificantlyreducetheprocessoutputvariance.

Controlperformancemonitoring/assessment(CPM/CPA)forcontrolsystemsisoneofthemostconcernedresearchdirectionsintheworldofprocesscontrol.ControllerperformancemonitoringandevaluationcanbetracedbacktotheworkofAstrom(1967),DeVrieWu(1978)andothersinthe1960sand1970s;by1970,Box,Jenkins(1976),Astrominimumvariancecontrol(minimumvariancecontrol),MVC);In1989,Harris(1989)usedtheminimumvariancecontroltoevaluatethevarianceperformanceoftheSISOsystem,whichmadethisfieldhavepioneeringresultsandnewgoalsinrandomperformancemonitoringandevaluation.Sincethen,CPM/CPAtechnologyhasattractedtheattentionandresearchofalargenumberofcontroltheoryscholarsandhasachievedrapiddevelopment.Throughtheeffortsofpredecessors,thistechnologyhasdevelopedintoacross-integratedtechnologyinvolvingcontroltheory,systemidentification,signalprocessing,probabilityandstatistics,etc.Itisusuallyreferredtoastheperformancemonitoringandevaluationofthecontrolloop,andtheperformancemonitoringandevaluationofthecontroller.Evaluation,performanceevaluation,etc.

InordertosolvetheproblemofPIDcontrollerloopperformancedegradationcausedbysystemtime-varyingintheindustrialsystem,LiuXiaoyanofZhejiangUniversityputforwardthePIDaccessibilityevaluationbenchmarkproposedbyEdgar.Amethodforperformanceevaluation,optimizationandmonitoringofPIDcontrollers,namely:PIDloopevaluationoptimizationalgorithm.Thealgorithmusestheclosed-loopinputandoutputdataofthesystemtoperformonlineslidingwindowidentification,usestheMVC(MinimumVarianceControl)-basedPIDminimumvarianceaccessibilitycriteriontoevaluatetheperformanceofthePIDcontroller,andcalculatestheoptimalPIDcontrollerparametersinthesenseoftheminimumvariance;Comparethetheoreticalminimumvariancewiththeoutputvarianceasthestart-stopthresholdforonlineoptimizationofthePIDsystem.Simulationhasproveditseffectiveness.

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