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1、PIDControlTheoryThemeaningofcontrolisusuallytotracksomethingbasedontheerrorbetweenthedesiredtargetandactualdata.Invelocitycruisecontrolofvehicleasanexample,ifyousetthetargetvelocityas60mph,thecruisecontrollerwilloperatetokeepthattargetvelocitybasedonthedifferencebetweenthetarge
2、tvelocityandactualvehiclevelocity.PIDcontrolisatheorytobeabletoachievethiskindofcontrolchallenges.Thiscontroltheoryisoneoftheclassiccontrols,whichissimple,easytoimplement,andcheep.Ifweassumethattheactualvelocityofthecarcanbemeasured,theerrorcanbecalculatedeasilybytarget-actualv
3、elocity.Mostcontroltheoryusetheerrortotrackthereference,speciallyPIDcontroltheoryusesthiserrormultipliedbyproportional,derivative,andintegralgaintotrackthetarget.Inthiscase,proportionalgainisP,derivativegainisD,andintegralgainisI,thuswecallthiscontroller"PIDcontroller".Pgainusu
4、allyinfluenceshowfastthesystemcanresponse,Disusedtoreducethemagnitudeoftheovershoot,andIisusedtoeliminatethesteady-stateerror.Butthereisnooptimalsolutioninthiscontroller.Forexample,ifPIDarecombinedtogether,thecombinationofPIDgainsaffectsthesystemresponsenotaffectindependently.T
5、husthereisnosolutiontofindtheoptimalgainsousuallyPIDgainsarespecifiedbytuning.Asaresultofthisfeature,PIDcontrollerismostlyusedinLinear-TimeInvariant(LTI)systemandSingle-InputSingle-Output(SISO)systemnotinnon-linearandcomplexMulti-InputMulti-Output(MIMO)system.Totunethesystemres
6、ponse,usuallythesystemspecificationissetatthefirst.Theneachgainistunedtosatisfythesystemresponsespecificationdefinedsuchaspercentovershoot,risingtime,settlingtime,andsoon.Inthissection,wewillexperiencewhatPIDcontrolleris,usingMATLABandfinallywewillimplementthiscontrollertocontr
7、olCart-InvertedCranesystemviaSISOtoolboxinMATLAB.ContentsMATLABEXAMPLEClosedLoopSystemTransferFunctionProportionalControllerP+DerivativeControllerP+IntegralControllerSummaryclcclearallcloseallMATLABEXAMPLEInchapter1-NXTMotorIdentification,wederivedmotortransferfunctionviasystem
8、identificationmethod.Herewewillusethistransferfunction