PIDTHEORYContentsWhat’sPIDPIDconceptPIDadvantagePIDtheoryExampleComplexcontrolloopWhat’sPIDcontrolsystem?Onecontrolsystemcomprisescontroller,sensor,executerunit,objectandI/Ounit.Forthedifferentcontrolsystem,sensor,executeraredifferent.

Pressure,temperature,level,flowandsoon…PIDcontrolsystemusePIDalgorithmtorealizecontrol.Close-loopcontrolsystemThebasicfunctionofclosed-loopcontrolistomaintainaprocesscharacteristic(temperature,flow,pressure,speed,torque)atadesiredvalue.Theprocesscandeviatefromthisdesiredsetpoint(SP)valueasaresultofchangingmaterial,loadrequirements,interactionwithotherprocesses,andsoon.Theactualconditionoftheprocesscharacteristicmeasuredistheprocessvariable(PV).Thedeviationofthemeasuredprocessvariablefromthedesiredsetpointistheerror(E).Theformulaforprocesserroristhus:E=SP–PVOnceanerrorisdetermined,thefunctionofthecontrolloopistooutputacontrolvariabletotheprocesstoforcetheerrorEtozero.Level

transmitterLevelcontrollerSetpointExecutervalveLevelcontrolloopPIDconceptionP:ProportionI:Integral∫

D:DerivativeThecontrollerusethreetypesalgorithmtorealizethecontrolfunction,PIDThecontrollercalculatestheintegralandderivativeoftheerrorbetweentheprocessvariableandsetpointthengeneratesacontroleffortbyaddingthosetwoquantitiestotheerroritself.Auserchoosesthetuningparameters—proportionalgain(P),integralgain(I)andderivativegain(D)—togivemoreorlessweighttoeachterm,therebyadjustingthecontroller'sperformance.PIDalgorithmTheformulaOutput=P*Input+I*∫+D*d/d(t)Coefficient:P=Kp

I=Ki/Ti

D=Kd·TdP,I,DfunctionP:Proportion

controlthesimplestcontrolformat.Output=P*InputSteady-state

error

I:Integral

controlOutput=I*∫I=Ki/TiSystem

with

Steady-state

Error

Ti:value↑,function↑，speedD:Derivativecontrolpre-actmodeOutput=D*d/d(t)D=Kd·Td

Kd:value↓,function↑,precision

“three-modecontrol”canincludeone,two,orthreeterms,ormodes,ofcontrol.Three-modecontrolisknownasPID,whichrepresentsproportional,integral,andderivative.proportionalcontrolactionprovidesacontroloutputcomponentproportionaltothevalueoftheinstantaneouserror.Integralcontrolaction(alsoknownasresetaction)providesacontroloutputcomponentproportionaltothesummationoftheerroroveraperiodoftime.Derivativecontrolaction(alsoknownasrateaction)providesacontroloutputcomponentproportionaltotherateofchangeoftheerror.PIDtheoryThederivativeactionwasknownasthepre-actmodebecausethederivativetermseemedtoactpreemptively,acceleratingthecontroller'scorrectiveeffortsbeyondwhattheproportionaltermcouldmanageonitsown.Earlyusersincreasedordecreasedthedegreeofpreemptive(derivative)actionbyselectingalargerorsmallerpre-acttime.Today'sPIDvendorstypicallydescribeacontroller'sderivativeactionasitsrate.

Integralactionwasoriginallyknownasautomaticresetbecausetheintegraltermseemedtoautomaticallyadjustthesetpointtotheexactvaluerequiredtoeliminatethesteady-stateoffsetcausedbytheproportionalterm(see“TheThreeFacesofPID,”ControlEngineering,March2007formoreonthiscuriousphenomenon).Someusersstillspecifythe

resettimewhentuningaController'sintegralaction,butahigherresettimecorrespondstolessintegralaction,notmore.

Alternately,thedegreeofintegralactionissometimesspecifiedintermsoftheresetrate,whichistheinverseoftheresettimeandentirelyunrelatedtothederivativerate.Confusing“reset”and“resetrate”leadstoincreasedintegralactionwhentheuserwantsless,andviceversa.

Likewise,theproportionalgaininsomePIDcontrollersisspecifiedintermsofitsinverseknownastheproportionalband.Moreprecisely,theproportionalbandis100dividedbytheproportionalgainsothatitrepresentsthepercentchangeintheerrorsignalnecessarytocauseafull-scalechangeintheproportionalterm'soutput.Confusing“proportionalband”with“proportionalgain”leadstodecreasedproportionalactionwhentheuserwantsmore,andviceversa.Negativefeedback:outputandinputarereversedirection(normally)Positivefeedback:outputandinputaresamedirectionFeedback-:Negativefunctioninput↑output↓P-

+:Positivefunctioninput↑output↑P+

NegativefunctionandpositivefunctionComplexcontrolloopCascadecontrolloopProportioncontrolloopSplintcontrolloopSelectioncontrolloopPIDadvantagePIDisthemostwidelycontrolsystemintheproject.Simpleconfiguration,HighstabilityHighreliabilitySimpleoperationClose-loopcontrolsystemClose-loopcontrolsystemTheoutputwillfeedbacktotheinput.Negativefeedback:outputandinputarereversedirectionPositivefeedback:outputandinputaresamedirection(normally)Open-loopcontrolsystemOpen-loopcontrolsystemTheoutputisnoinfluencewiththeinput.Deadband:Acontrollerequippedwithadeadbandwilldonothinguntilthecalculatedcontroleffortchangesbymorethanasetamount.Thispreventsthecontroller