Smith Pred Ref Semi

10/28/2015 OvercomingprocessdeadtimewithaSmithPredictor|ControlEngineering

http://www.controleng.com/singlearticle/overcomingprocessdeadtimewithasmithpredictor/8c727a1371eb45011801350175606812.html 1/4

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02/17/2015

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OvercomingprocessdeadtimewithaSmithPredictorAcontrollerequippedwithanaccurateprocessmodelcanignoredeadtime.Deadtimegenerallyoccurswhenmaterialistransportedfromtheactuatorsitetothesensormeasurementlocation.Untilthematerialreachesthesensor,thesensorcannotmeasureanychangeseffectedbytheactuator.VanceVanDoren,PhD,PE

Forthepurposesoffeedbackcontrol,deadtimeisthedelaybetweentheapplicationofacontroleffortanditsfirsteffectontheprocessvariable.Duringthatinterval,theprocessdoesnotrespondtothecontroller'sactivityatall,andanyattempttomanipulatetheprocessvariablebeforethedeadtimehaselapsedinevitablyfails.

Deadtimegenerallyoccurswhenmaterialistransportedfromthesiteoftheactuatortoanotherlocationwherethesensortakesitsreading.Notuntilthematerialhasreachedthesensorcananychangeseffectedbytheactuatorbedetected.

Consider,forexample,therollingmillshowninthe"SimplifiedDeadtimeExample"whichproducesacontinuoussheetofsomematerialatarateofV(inchespersecond).Afeedbackcontrollerusesapistontomodifythegapbetweenapairofreducingrollersthatsqueezethematerialintothedesiredthickness.ThedeadtimeinthisprocessiscausedbytheseparationSbetweentherollersandthethicknessgage.

Thecontrollerinthisexamplecancomparethecurrentthicknessofthesheet(theprocessvariable,PV)withthedesiredthickness(thesetpoint,SP)andgenerateanoutput(CO),butitmustwaitatleastD=S/Vsecondsforthethicknesstochange.Ifitexpectsaresultanysooner,itwilldeterminethatitslastcontrolefforthadnoeffectandwillcontinuetoapplyeverlargercorrectionstotherollersuntilthesensorbeginstoseethethicknesschanginginthedesireddirection.Bythattime,however,itwillbetoolate.Thecontrollerwillhavealreadyovercompensatedfortheoriginalthicknesserror,perhapstothepointofcausinganevenlargererrorintheoppositedirection.

Howbadlythecontrollerovercompensatesdependsonhowaggressivelyitistunedandonthedifferencebetweentheactualandtheassumeddeadtime.Thatis,ifthecontrollerassumesthatthedeadtimeismuchshorterthanisactuallythecase,itwillspendamuchlongertimeincreasingitsoutputbeforesuccessfullyeffectingachangeintheprocessvariable.Ifthecontrolleristunedtobeparticularlyaggressive,therateatwhichitincreasesitsoutputduringthatintervalwillbeespeciallyhigh,andtheresultingovercompensationwillbeparticularlysevere.

Detuningthecontroller

Thepreferredmethodforcuringadeadtimeproblemistophysicallymodifytheprocesstoreducedeadtime.Intherollingmillexample,thiscouldbeaccomplishedbymovingthethicknessgageclosertotherollersorbyrunningthesheetatahighervelocity.

Butifdeadtimecannotbecuredbyrelocatingthesensororspeedinguptheprocess,itssymptomscanstillbeaddressedbymodifyingthecontrolalgorithm.Thesimplestmethodistodetunethecontrollertoslowitsresponserate.Adetunedcontrollerwillnothavetimetoovercompensateunlessdeadtimeisparticularlylong.

Theintegratorinaproportionalintegralderivative(PID)controllerisparticularlysensitivetodeadtime.Bydesign,itsfunctionistocontinuerampingupthecontroller'soutputsolongasthereisanerrorbetweenthesetpointandtheprocessvariable.Inthepresenceofdeadtime,theintegratorworksovertime.ZieglerandNicholsdeterminedthatthebestwaytodetuneaPIDcontrollertohandleadeadtimeofDsecondsistoreducetheintegraltuningconstantbyafactorofD2.TheyalsofoundthattheproportionaltuningconstantshouldbereducedbyafactorofD.Thederivativetermisunaffectedbydeadtimesinceitonlycomesintoplayaftertheprocessvariablehasbeguntomove.

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Detuningcanrestorestabilitytoacontrolloopthatsuffersfromchronicovercompensation,butitwouldnotevenbenecessaryifthecontrollercouldfirstbemadeawareofthedeadtime,andthenendowedwiththepatiencetowaititout.ThatisessentiallywhathappensinthefamousSmithPredictorcontrolstrategyproposedbyOttoSmithin1957.

Removingdeadtimefromtheloop

Smith'sstrategyisshowninthe"SmithPredictor"blockdiagram.Itconsistsofanordinaryfeedbackloopplusaninnerloopthatintroducestwoextratermsdirectlyintothefeedbackpath.Thefirsttermisanestimateofwhattheprocessvariablewouldlooklikeintheabsenceofanydisturbances.Itisgeneratedbyrunningthecontrolleroutputthroughaprocessmodelthatintentionallyignorestheeffectsofdisturbances.Ifthemodelisotherwiseaccurateinrepresentingthebehavioroftheprocess,itsoutputwillbeadisturbancefreeversionoftheactualprocessvariable.

Themathematicalmodelusedtogeneratethedisturbancefreeprocessvariableconsistsoftwoelementshookedupinseries.Thefirstelementrepresentsalloftheprocessbehaviornotattributabletodeadtime.Thesecondelementrepresentsnothingbutthedeadtime.Thedeadtimefreeelementisgenerallyimplementedasanordinarydifferentialordifferenceequationthatincludesestimatesofalltheprocessgainsandtimeconstants.Thesecondelementofthemodelissimplyatimedelay.Thesignalthatgoesintoitcomesoutdelayed,butotherwiseunchanged.

ThesecondtermthatSmith'sstrategyintroducesintothefeedbackpathisanestimateofwhattheprocessvariablewouldlooklikeintheabsenceofbothdisturbancesanddeadtime.Itisgeneratedbyrunningthecontrolleroutputthroughthefirstelementoftheprocessmodel(thegainsandtimeconstants),butnotthroughthetimedelayelement.Itthuspredictswhatthedisturbancefreeprocessvariablewilleventuallylooklikeoncethedeadtimehaselapsed,hencetheexpressionSmithPredictor.

Subtractingthedisturbancefreeprocessvariablefromtheactualprocessvariableyieldsanestimateofthedisturbances.Byaddingthisdifferencetothepredictedprocessvariable,Smithcreatedafeedbackvariablethatincludesthedisturbances,butnotthedeadtime.

Sowhat?

Thepurposeofallthesemathematicalmanipulationsisbestillustratedbythe"SmithPredictorRearranged"blockdiagram.ItshowstheSmithPredictorwiththesameblocksarrangedtoyieldthesamemathematicalresults,onlycomputedinadifferentorder.ThisarrangementmakesiteasiertoseethattheSmithPredictoreffectivelyestimatestheprocessvariable(includingbothdisturbancesanddeadtime)byaddingtheestimateddisturbancesbackintothedisturbancefreeprocessvariable.Theresultisafeedbackcontrolsystemwiththedeadtimeoutsideoftheloop.

TheSmithPredictorworkstocontrolthemodifiedfeedbackvariable(thepredictedprocessvariablewithdisturbancesincluded)ratherthantheactualprocessvariable.Ifitissuccessfulindoingso,andiftheprocessmodeldoesindeedmatchtheprocess,thenthecontrollerwillsimultaneouslydrivetheactualprocessvariabletowardsthesetpoint,whetherthesetpointchangesoraloaddisturbstheprocess.Thedeadtimebecomesirrelevant.

Unfortunately,intherealworld,thosearebigifs.Itiscertainlyeasierforthecontrollertomeetitsobjectiveswithouthavingtodealwiththedeadtime,butitisnotalwaysasimplemattertogeneratetheprocessmodelsrequiredtomakethisstrategywork.Eventheslightestmismatchbetweentheprocessandthemodelcancausethecontrollertogenerateanoutputthatsuccessfullymanipulatesthemodifiedfeedbackvariable,butdrivesofftheactualprocessvariableintooblivion.TherehavebeenseveralfixesproposedtoimproveonthebasicSmithPredictor,butdeadtimeremainsaparticularlydifficultcontrolproblem.

VanceVanDoren,PhD,PE,isacontributingcontentspecialistforControlEngineering.



Postacomment

Loginorcreateanaccounttosubmityourcommentforthisarticle.

Ahmed,OH,Egypt,02/18/1510:47PM:

itisdeepknowledgeofcontrollerandmeaningofdeedtime.

LARRY,WA,UnitedStates,02/19/1509:53PM:

Greatjobpointingoutthepotentialbenefitswithoutminimizingthepotentialhazards.Theapplicationexamplewasagoodone,andhasahiddenhazardtomakemattersworse:thematerialbalanceforarollingprocessmeansthatrepositioningthedriverollerchangesthetravelrateattheoutputside,sothatthe"timedelay" isnotexactlyconstant.Theclassic"SmithPredictorfilter,"asimplementedinthe1950s,usedanalognonminimumphasefilters,whichoftenweresubjecttosensitivityandstabilitylimitations.We have options today to use the same architecturemodel, but replacing the Smith Predictor filter part of theprocessmodelwithdigitaldelaylinesanddigital filters.However,appropriatetuningofthesecanstillbetricky.Whyisthereneverafreelunch?

WILLIAM,CA,UnitedStates,04/07/1512:28PM:

It seems one can also view the Smith Predictor as "feedforward control", where the controller output is simply anothermeasured "input disturbance" which the feedforward equation responds to in an attempt to keep the thickness (controlledvariable)fromchanging.Ifthepredictor's"plantmodel"isperfect,itseemsitwouldsimplycounterthecontrolactionuntilonedeadtimehaspassed.Withtoday'sdigitalcontrollers,itseemsasimplerapproachisthataftereachcontrolchange,waitonedeadtimebeforeactingonthesensorsignal(i.e.commonsense).ThismightberealizedbysimplysettingthePLCcycletime(ortasktime)tomatchthedeadtime.

Tom,NonUS/NotApplicable,Australia,04/07/1509:06PM:

AlsorefertoF.G.Shinskey:PIDdeadtimecontrolofdistributedprocesses.

Glenn,Canada,04/11/1512:52PM:

AgoodarticleandtimelyformeasIjustdesignedandcommissioned3MSP(ModifiedSmithPredictor)controllerslastweek.MSP'shavebeencommoninthepaperindustrysincethe1980's.AnMSPpredictstheeffectoftheprocesstimeconstantinaddition to the dead time. The final controller is simply gain X predicted error divided by process gain. If significantmodelmismatchispossible,Ioftenaddcompensationforuncertainty.Thesecontrollersareverysimpletodesignandimplementandworkwellwithbothimprovedstabilityandspeed.

VanceVanDoren,PhD,PE,isacontributingcontentspecialistforControlEngineering.Keyconcepts:

Deadtimeinaprocesscancauseacontrollertooverreacttoadisturbanceorsetpointchange.Ifitisn'tpracticaltowaitforatimeintervaltopass,therearetechniquesdesignedtomakechangesmorequickly.

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Readmoreoncontrolstrategyandlooptuningbelow.

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