6/6/2015 DerivativeControlExplained|ControlNotes

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LevelControlLoopsHowtoFillaContainer

DerivativeControlExplained

May3,2010

Whendoingonsiteservicesortraining,Iamoftenasked:WhenshouldoneusethederivativecontrolmodeofaPIDcontroller?Althoughthereisnoblack&whitedivisionbetweenwhentouseitornot,Ihaveafewguidelinesthatshouldhelpyourdecision.ButletstakeastepbackfirstandreviewthederivativecontrolmodeanditsroleinaPIDcontroller.

Figure1.PIDController

6/6/2015 DerivativeControlExplained|ControlNotes

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WhatisDerivative?Youcanthinkofderivativecontrolasacrudepredictionoftheerrorinfuture,basedonthecurrentslopeoftheerror.Howfarintothefuture?Thatswhatthederivativetime(Td)isfor.Itisthepredictionhorizon.(Derivativecontrolactuallyusesextrapolation,notprediction.Buthey,weallunderstandhowpredictionworks,soIlljustgowiththat.)Oncethederivativemodehaspredictedthefutureerror,itaddsanadditionalcontrolactionequaltoControllerGain*FutureError.

Forexample,iftheerrorchangesatarateof2%perminute,andthederivativetimeTd=3minutes,thepredictederroris6%.IftheControllerGain,Kc=0.2,thenthederivativecontrolmodewilladdanadditional0.2*6%=1.2%tothecontrolleroutput.

YoudontAbsolutelyNeedDerivativeThefirstpointtoconsiderwhenthinkingaboutusingderivativeisthataPIDcontrolloopwillworkjustfinewithoutthederivativecontrolmode.Infact,theoverwhelmingmajorityofcontrolloopsinindustryuseonlytheproportionalandintegralcontrolmodes.Proportionalgivesthecontrolloopanimmediateresponsetoanerror,andtheintegralmodeeliminatestheerrorinthelongerterm.Hencenoderivativeisneeded.

WhyUseDerivativeThederivativecontrolmodegivesacontrolleradditionalcontrolactionwhentheerrorchangesconsistently.Italsomakestheloopmorestable(uptoapoint)whichallowsusingahighercontrollergainandafasterintegral(shorterintegraltimeorhigherintegralgain).

Thesehavetheeffectofreducingthemaximumdeviationofprocessvariablefromsetpointiftheprocessreceivesandexternaldisturbance.Foratypicaltemperaturecontrolloop,youcanexpecta20%reductioninthemaximumdeviation.Figure2showshowaloopwithderivative(PID)controlrecoversquickerfromadisturbancewithlessdeviationthanaloopwithPorPIcontrol.

Figure2.PversusPIversusPIDcontrol.

Obviouslyyoudontwanttousederivativetospeedupaloopifthecontrolobjectiveisslowresponse,likeasurgetank,forexample.Butforloopswherefastresponseistheobjective,derivativecouldhelp.Butdoreadonforinformationonwhennottousederivative.

NoisyPVUsingthederivativecontrolmodeisabadideawhentheprocessvariable(PV)hasalotofnoiseonit.Noiseissmall,random,rapidchangesinthePV,andconsequentlyrapidchangesintheerror.Becausethederivativemodeextrapolatesthecurrentslopeoftheerror,itishighlyaffectedbynoise(Figure3).YoucouldtrytofilterthePVsoyoucanusederivative,aslongasyourfiltertimeconstantisshorterthan1/5ofyourderivativetime.

6/6/2015 DerivativeControlExplained|ControlNotes

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Figure3.EffectofNoiseonDerivative.

ProcessDynamicsOndeadtimedominantprocesses,PIDcontroldoesnotalwaysworkbetterthanPIcontrol(itdependsonwhichtuningmethodyouuse).Ifthetimeconstant(tau)isequaltoorlongerthanthedeadtime(td),likeinFigure4,PIDcontroleasilyoutperformsPIcontrol.

Figure4.ProcessDynamics.

TemperatureandLevelLoopsTemperaturecontrolloopsnormallyhavesmoothmeasurementsandlongtimeconstants.Theprocessvariableofatemperaturelooptendstomoveinthesamedirectionforalongtime,soitsslopecanbeusedforpredictingfutureerror.Sotemperatureloopsareidealcandidatesforusingderivativecontrolifneeded.Levelmeasurementscanbeverynoisyonboilingliquidsorgasseparationprocesses.However,ifthelevelmeasurementissmooth,levelcontrolloopsalsolendthemselvesverywelltousingderivativecontrol(exceptforsurgetanksandaveraginglevelcontrolwhereyoudontneedthespeed).

FlowControlLoopsFlowcontrolloopstendtohavenoisyPVs(dependingontheflowmeasurementtechnologyused).Theyalsotendtohaveshorttimeconstants.Andtheynormallyactquitefastalready,sospeedisnotanissue.Thesefactorsallmakeflowcontrolloopspoorcandidatesforusingderivativecontrol.

PressureControlLoopsPressurecontrolloopscomeintwoflavors:liquidandgas.Liquidpressurebehavesverymuchlikeflowloops,soderivativeshouldnotbeused.Gaspressureloopsbehavemoreliketemperatureloops(someevenbehavelikelevelloops/integratingprocesses),makingthemgoodcandidatesforusingderivativecontrol.

FinalWordsDerivativecontroladdsanotherdimensionofcomplexitytocontrolloops.Itdoeshaveitsbenefits,butonlyinspecialcases.Ifaloopdoesnotabsolutelyneedderivativecontrol,dontbotherwithit.However,ifyouhavealagdominantloopwithasmoothprocessvariablethatneedseverybitof

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speeditcanget,goforthederivative.

Tolearnmoreaboutcontrollersandtuning,contactOptiControlstoforonsiteprocesscontroltraining.

Staytuned!JacquesSmutsAuthorofthebookProcessControlforPractitioners

Postedin3.PIDControllers| Tags:ControllerTuning,DerivativeControl

4ResponsestoDerivativeControlExplained

GarcierLaCamppiello:June14,2012at4:17pm

Iusedthisasarefresherreviewandfounditveryhelpful.YouhavedoneafinejobatdescribingthederivativecontrolmodeandIrecommendittoallreaders.IamanInstrumentationTechnicianformerlywithAlyeskaPipelineServiceCo.,Alaska,retiredbutstillfunctional.

Thankyou,

abdulwahab:February7,2013at1:27pm

nice,iamveryhappytolearnthis

Sivasankar:April17,2013at1:11pm

Reallyusefulsinceimaninstengineer,havinglongtimedoubtaboutusageofderivativecontrolisearchedlotndidntconvinceanyanswersbuthereireallygotwatiwanted..thanksalot.

Osama:December31,2014at4:36pm

VeryHelpful.Explanationisclearandreallyoneofthebestpostsonthissubject.GoodjobThanksalot

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