CHE E 446 Process Dynamics and Control Chical Engineering.ppt

chee434/821processcontroliisomereviewmaterial,winter2006instructor:m.guayta:v.adetola,introduction,inthechemicalindustry,thedesignofacontrolsystemisessentialtoensure:goodprocessoperationprocesssafetyproductqualityminimizationofenvironmentalimpact,introduction,whatisthepurposeofacontrolsystem?“tomaintainimportantprocesscharacteristicsatdesiredtargetsdespitetheeffectsofexternalperturbations.”,control,plant,processingobjectivessafetymake$environment.,perturbationsmarketeconomyclimateupsets.,introduction,plant,control,whatconstitutesacontrolsystem?combinationofprocesssensors,actuatorsandcomputersystemsdesignedandtunedtoorchestratesafeandprofitableoperation.,introduction,processdynamics:studyofthetransientbehaviorofprocessesprocesscontroltheuseofprocessdynamicsfortheimprovementofprocessoperationandperformanceortheuseofprocessdynamicstoalleviatetheeffectofundesirable(unstable)processbehaviors,introduction,whatdowemeanbyprocess?aprocess,p,isanoperationthattakesaninputoradisturbanceandgivesanoutputinput:(u)somethingthatyoucanmanipulatedisturbance:(d)somethingthatcomesasaresultofsomeoutsidephenomenonoutput:(y)anobservablequantitythatwewanttoregulate,u,d,y,p,informationflow,examples,stirredtankheater,m,tin,w,q,t,w,tin,w,q,t,process,inputs,output,examples,thespeedofanautomobile,forceofengine,friction,inputs,output,frictionengine,speed,process,examples,e.g.landingonmars,examples,e.g.milliroboticslaparoscopicmanipulators,introduction,processaprocess,p,isanoperationthattakesaninputoradisturbanceandgivesanoutputinput:(u)somethingthatyoucanmanipulatedisturbance:(d)somethingthatcomesasaresultofsomeoutsidephenomenonoutput:(y)anobservablequantitythatwewanttoregulate,u,d,y,p,informationflow,control,whatiscontrol?toregulateofaprocessoutputdespitetheeffectofdisturbancese.g.drivingacarcontrollingthetemperatureofachemicalreactorreducingvibrationsinaflexiblestructuretostabilizeunstableprocessese.g.ridingabikeflightofanairplaneoperationofanuclearplant,benefitsofcontrol,economicbenefitsquality(wastereduction)variancereduction(consistency)savingsinenergy,materials,manpoweroperability,safety(stability)performanceefficiencyaccuracyroboticsreliabilitystabilizabilitybicycleaircraftnuclearreactor,control,acontrollerisasystemdesignedtoregulateagivenprocessprocesstypicallyobeysphysicalandchemicalconservationlawscontrollerobeyslawsofmathematicsandlogic(sometimesintelligent)e.g.-ridingabike(humancontroller)-drivingacar-automaticcontrol(computerprogrammedtocontrol),process,controller,whatisacontroller?,blockrepresentations,blockdiagramsaremodelsofthephysicalsystems,process,systemphysicalboundary,transferoffundamentalquantities,mass,energyandmomentum,inputvariables,outputvariables,physical,operation,abstract,control,acontrolledprocessisasystemwhichiscomprisedoftwointeractingsystems:e.g.mostcontrolledsystemsarefeedbackcontrolledsystemsthecontrollerisdesignedtoprovideregulationofprocessoutputsinthepresenceofdisturbances,process,controller,outputs,disturbances,action,observation,monitor,intervene,introduction,whatisrequiredforthedevelopmentofacontrolsystem?1.theplant(e.g.sppofnylon),water,steam,gasmake-up,vent,nylon,blower,dehumidifier,reheater,reliefpot,heater,introduction,whatisrequired?1.processunderstandingrequiredmeasurementsrequiredactuatorsunderstanddesignlimitations2.processinstrumentationappropriatesensorandactuatorselectionintegrationincontrolsystemcommunicationandcomputerarchitecture3.processcontrolappropriatecontrolstrategy,example,cruisecontrol,controller,friction,process,speed,engine,humanorcomputer,classicalcontrol,controlismeanttoprovideregulationofprocessoutputsaboutareference,r,despiteinherentdisturbancesthedeviationoftheplantoutput,e=(r-y),fromitsintendedreferenceisusedtomakeappropriateadjustmentsintheplantinput,u,process,controller,classicalfeedbackcontrolsystem,d,y,u,r,e,+,-,control,processisacombinationofsensorsandactuatorscontrollerisacomputer(oroperator)thatperformstherequiredmanipulationse.g.classicalfeedbackcontrolloop,y,r,e,a,c,p,m,d,computer,actuator,process,sensor,-,+,examples,drivinganautomobile,y,e,a,c,p,m,driver,automobile,-,+,steering,r,visualandtactilemeasurement,desiredtrajectoryr,actualtrajectoryy,examples,stirred-tankheater,tin,w,q,t,w,heater,tc,thermocouple,y,e,a,c,p,m,controller,tank,-,+,heater,thermocouple,tin,w,tr,examples,measuret,adjustqcontroller:q=k(tr-t)+qnominalwhereqnominal=wc(t-tin)q:isthispositiveornegativefeedback?,tin,w,t,e,a,c,p,m,controller,tank,-,+,heater,thermocouple,feedbackcontrol,tr,examples,measureti,adjustq,a,p,c,m,ti,qi,dq,q,+,+,feedforwardcontrol,controlnomenclature,identificationofallprocessvariablesinputs(affectprocess)outputs(resultofprocess)inputsdisturbancevariablesvariablesaffectingprocessthatareduetoexternalforcesmanipulatedvariablesthingsthatwecandirectlyaffect,controlnomenclature,outputsmeasuredspeedofacarunmeasuredaccelerationofacarcontrolvariablesimportantobservablequantitiesthatwewanttoregulatecanbemeasuredorunmeasured,controller,manipulated,disturbances,process,control,other,example,t,l,t,wi,ti,wc,tci,wc,tco,wo,to,h,variableswi,wo:tankinletandoutletmassflowsti,to:tankinletandoutlettemperatureswc:coolingjacketmassflowpc:positionofcoolingjacketinletvalvepo:positionoftankoutletvalvetci,tco:coolingjacketinletandoutlettemperaturesh:tankliquidlevel,po,pc,example,variablesinputsoutputsdisturbancesmanipulatedmeasuredunmeasuredcontrolwititciwchwotopcpo,task:classifythevariables,processcontrolandmodeling,indesigningacontroller,wemustdefinecontrolobjectivesdevelopaprocessmodeldesigncontrollerbasedonmodeltestthroughsimulationimplementtorealprocesstuneandmonitor,model,controller,y,u,r,e,d,process,design,implementation,controlsystemdevelopment,defineobjectives,developaprocessmodel,designcontrollerbasedonmodel,testbysimulation,implementandtune,monitorperformance,controldevelopmentisusuallycarriedoutfollowingtheseimportantsteps,oftenaniterativeprocess,basedonperformancewemaydecidetoretune,redesignorremodelagivencontrolsystem,controlsystemdevelopment,objectives“whatarewetryingtocontrol?”processmodeling“whatdoweneed?”mechanisticand/orempiricalcontrollerdesign“howdoweusetheknowledgeofprocessbehaviortoreachourprocesscontrolobjectives?”whatvariablesshouldwemeasure?whatvariablesshouldwecontrol?whatarethebestmanipulatedvariables?whatisthebestcontrollerstructure?,controlsystemdevelopment,implementandtunethecontrolledprocesstestbysimulationincorporatecontrolstrategytotheprocesshardwaretheoryrarelytranscendstorealitytuneandre-tunemonitorperformanceperiodicretuningandredesignisoftennecessarybasedonsensitivityofprocessormarketdemandsstatisticalmethodscanbeusedtomonitorperformance,processmodeling,motivation:developunderstandingofprocessamathematicalhypothesisofprocessmechanismsmatchobservedprocessbehaviorusefulindesign,optimizationandcontrolofprocesscontrol:interestedindescriptionofprocessdynamicsdynamicmodelisusedtopredicthowprocessrespondstogiveninputtellsushowtoreact,processmodeling,whatkindofmodeldoweneed?dynamicvs.steady-statesteady-statevariablesnotafunctionoftimeusefulfordesigncalculationdynamicvariablesareafunctionoftimecontrolrequiresdynamicmodel,processmodeling,whatkindofmodeldoweneed?experimentalvstheoreticalexperimentalderivedfromtestsperformedonactualprocesssimplermodelformseasiertomanipulatetheoreticalapplicationoffundamentallawsofphysicsandchemistrymorecomplexbutprovidesunderstandingrequiredindesignstages,processmodeling,dynamicvs.steady-statestepchangeininputtoobservestartingatsteady-state,wemadeastepchangethesystemoscillatesandfindsanewsteady-statedynamicsdescribethetransitorybehavior,0,50,100,150,200,250,300,40,45,50,55,60,65,output,time,steady-state1,steady-state2,processmodeling,empiricalvs.mechanisticmodelsempiricalmodelsonlylocalrepresentationoftheprocess(noextrapolation)modelonlyasgoodasthedatamechanisticmodelsrelyonourunderstandingofaprocessderivedfromfirstprinciplesobservinglawsofconservationofmassenergymomentumusefulforsimulationandexplorationofnewoperatingconditionsmaycontainunknownconstantsthatmustbeestimated,processmodeling,empiricalvsmechanisticmodelsempiricalmodelsdonotrelyonunderlyingmechanismsfitspecificfunctiontomatchprocessmathematicalfrenchcurve,processmodeling,linearvsnonlinearlinearbasisformostindustrialcontrolsimplermodelform,easytoidentifyeasytodesigncontrollerpoorprediction,adequatecontrolnonlinearrealitymorecomplexanddifficulttoidentifyneedstate-of-the-artcontrollerdesigntechniquestodothejobbetterpredictionandcontrolinexistingprocesses,wereallyondynamicmodelsobtainedfromexperimentsusuallyofanempiricalnaturelinearinnewapplications(ordifficultproblems)focusonmechanisticmodelingdynamicmodelsderivedfromtheorynonlinear,processmodeling,generalmodelingprocedureidentifymodelingobjectivesenduseofmodel(e.g.control)identifyfundamentalquantitiesofinterestmass,energyand/ormomentumidentifyboundariesapplyfundamentalphysicalandchemicallawsmass,energyand/ormomentumbalancesmakeappropriateassumptions(simplify)ideality(e.g.isothermal,adiabatic,idealgas,nofriction,incompressibleflow,etc,)writedownenergy,massandmomentumbalances(developthemodelequations),processmodeling,modelingprocedurecheckmodelconsistencydowehavemoreunknownsthanequationsdetermineunknownconstantse.g.frictioncoefficients,fluiddensityandviscositysolvemodelequationstypicallynonlinearordinary(orpartial)differentialequationsinitialvalueproblemscheckthevalidityofthemodelcomparetoprocessbehavior,processmodeling,forcontrolapplications:modelingobjectivesistodescribeprocessdynamicsbasedonthelawsofconservationofmass,energyandmomentumthebalanceequation1.massbalance(stirredtank)2.energybalance(stirredtankheater)3.momentumbalance(carspeed),rateofaccumulationoffundamentalquantity,flowin,flowout,rateofproduction,=,-,+,processmodeling,applicationofamassbalanceholdingtankmodelingobjective:controloftanklevelfundamentalquantity:massassumptions:incompressibleflow,h,f,fin,processmodeling,totalmassinsystem=rv=rahflowin=rfinflowout=rftotalmassattimet=rah(t)totalmassattimet+dt=rah(t+dt)accumulationrah(t+dt)-rah(t)=dt(rfin-rf),processmodeling,modelconsistency“canwesolvethisequation?”variables:h,r,fin,f,a5constants:r,a2inputs:fin,f2unknowns:h1equations1degreesoffreedom0thereexistsasolutionforeachvalueoftheinputsfin,f,processmodeling,solveequationspecifyinitialconditionsh(0)=h0andintegrate,processmodeling,energybalanceobjective:controltanktemperaturefundamentalquantity:energyassumptions:incompressibleflowconstanthold-up,m,tin,w,q,t,w,processmodeling,underconstanthold-upandconstantmeanpressure(smallpressurechanges)balanceequationcanbewrittenintermsoftheenthalpiesofthevariousstreamstypicallyworkdoneonsystembyexternalforcesisnegligibleassumethattheheatcapacitiesareconstantsuchthat,processmodeling,aftersubstitution,sincetrefisfixedandweassumeconstantr,cpdividebyrcpv,processmodeling,resultingequation:modelconsistencyvariables:t,f,v,tin,q,cp,r7constants:v,cp,r3inputs:f,tin,q3unknown:t1equations1thereexistsauniquesolution,processmodeling,assumefisfixedwheret=v/fisthetankresidencetime(ortimeconstant)iffchangeswithtimethenthedifferentialequationdoesnothaveaclosedformsolution.productf(t)t(t)makesthisdifferentialequationnonlinear.solutionwillneednumericalintegration.,processmodeling,asimplemomentumbalanceobjective:controlcarspeedquantity:momentumassumption:frictionproportionaltospeed,momentumout,=,sumofforcesactingonsystem,momentumin,rateofaccumulation,-,+,forceofengine(u),friction,speed(v),processmodeling,forcesare:forceoftheengine=ufriction=bvbalance:totalmomentum=mvmodelconsistencyvariables:m,v,b,u4constants:m,b2inputs:u1unknownsv1,processmodeling,gravitytankobjectives:heightofliquidintankfundamentalquantity:mass,momentumassumptions:outletflowisdrivenbyheadofliquidinthetankincompressibleflowplugflowinoutletpipeturbulentflow,h,l,f,fo,processmodeling,frommassandmomentumbalances,asystemofsimultaneousordinarydifferentialequationsresultslinearornonlinear?,processmodeling,modelconsistencyvariablesfo,a,ap,v,h,g,l,kf,r9constantsa,ap,g,l,kf,r6inputsfo1unknownsh,v2equations2modelisconsistent,solutionofodes,mechanisticmodelingresultsinnonlinearsetsofordinarydifferentialequationssolutionrequiresnumericalintegrationtogetsolution,wemustfirst:specifyallconstants(densities,heatcapacities,etc,)specifyallinitialconditionsspecifytypesofperturbationsoftheinputvariablesfortheheatedstirredtank,specifyr,cp,andvspecifyt(0)specifyq(t)andf(t),inputspecifications,studyofcontrolsystemdynamicsobservethetimeresponseofaprocessoutputinresponsetoinputchangesfocusonspecificinputs1.stepinputsignals2.rampinputsignals3.pulseandimpulsesignals4.sinusoidalsignals5.random(noisy)signals,commoninputsignals,1.stepinputsignal:asustainedinstantaneouschangee.g.unitstepinputintroducedattime1,commoninputsignals,2.rampinput:asustainedconstantrateofchangee.g.,commoninputsignals,3.pulse:aninstantaneoustemporarychangee.g.fastpulse(unitimpulse),commoninputsignals,3.pulses:e.g.rectangularpulse,commoninputsignals,4.sinusoidalinput,commoninputsignals,5.randominput,solutionofodesusinglaplacetransforms,processdynamicsandcontrol,linearodes,forlinearodes,wecansolvewithoutintegratingbyusinglaplacetransformsintegrateouttimeandtransformtolaplacedomain,multiplication,y(s)=g(s)u(s),integration,commontransforms,usefullaplacetransforms1.exponential2.cosine,commontransforms,usefullaplacetransforms3.sine,commontransforms,operators1.derivativeofafunctionf(t)2.integralofafunctionf(t),commontransforms,operators3.delayedfunctionf(t-t),commontransforms,inputsignals1.constant2.step3.rampfunction,commontransforms,inputsignals4.rectangularpulse5.unitimpulse,laplacetransforms,finalvaluetheoremlimitations:initialvaluetheorem,solutionofodes,wecancontinuetakinglaplacetransformsandgenerateacatalogueoflaplacedomainfunctions.seesemtable3.1thefinalaimisthesolutionofordinarydifferentialequations.exampleusinglaplacetransform,solveresult,solutionoflinearodes,stirred-tankheater(withconstantf)takinglaplacetogetbacktotimedomain,wemustspecifylaplacedomainfunctionsq(s),tin(s)takeinverselaplace,linearodes,notes:theexpressiondescribesthedynamicbehavioroftheprocessexplicitlythelaplacedomainfunctionsmultiplyingt(0),tin(s)andq(s)aretransferfunctions,+,+,+,tin(s),q(s),t(0),t(s),laplacetransform,assumetin(t)=sin(wt)thenthetransferfunctiongivesdirectlycannotinvertexplicitly,butifwecanfindaandbsuchthatwecaninvertusingtables.needpartialfractionexpansiontodealwithsuchfunctions,linearodes,wedealwithrationalfunctionsoftheformr(s)=p(s)/q(s)wheredegreeofqdegreeofpq(s)iscalledthecharacteristicpolynomialofthefunctionr(s)theorem:everypolynomialq(s)withrealcoefficientscanbefactoredintotheproductofonlytwotypesoffactorspowersoflinearterms(x-a)nand/orpowersofirreduciblequadraticterms,(x2+bx+c)m,partialfractionexpansions,1.q(s)hasrealanddistinctfactorsexpandas2.q(s)hasrealbutrepeatedfactorexpanded,partialfractionexpansion,heavisideexpansionforarationalfunctionoftheformconstantsaregivenbynote:mostapplicabletoq(s)withrealanddistinctroots.itcanbeappliedtomorespecificcases.,partialfractionexpansions,3.q(s)hasirreduciblequadraticfactorsoftheformwherealgorithmforsolutionofodestakelaplacetransformofbothsidesofodesolvefory(s)=p(s)/q(s)factorthecharacteristicpolynomialq(s)performpartialfractionexpansioninverselaplaceusingtablesoflaplacetransforms,transferfunctionmodelsofdynamicalprocesse,processdynamicsandcontrol,transferfunction,heatedstirredtankexamplee.g.theblockiscalledthetransferfunctionrelatingq(s)tot(s),+,+,+,tin(s),q(s),t(0),t(s),processcontrol,timedomain,transferfunctionmodeling,controllerdesignandanalysis,processmodeling,experimentationandimplementation,laplacedomain,abilitytounderstanddynamicsinlaplaceandtimedomainsisextremelyimportantinthestudyofprocesscontrol,transferfunction,orderofunderlyingodeisgivenbydegreeofcharacteristicpolynomiale.g.firstorderprocessessecondorderprocessessteady-statevalueobtaineddirectlye.g.firstorderresponsetounitstepfunctionfinalvaluetheoremtransferfunctionsareadditiveandmultiplicative,transferfunction,effectofmanytransferfunctionsonavariableisadditive,+,+,+,tin(s),q(s),t(0),t(s),transferfunction,effectofconsecutiveprocessesinseriesinmultiplicativetransferfunction,u(s),y2(s),y1(s),deviationvariables,toremovedependenceoninitialconditione.g.removedependencyont(0)transferfunctionsexpressextentofdeviationfromagivensteady-stateprocedurefindsteady-statewritesteady-stateequationsubtractfromlinearodedefinedeviationvariablesandtheirderivativesifrequiredsubstitutetore-expressodeintermsofdeviationvariables,example,jacketedheatedstirredtankassumptions:constanthold-upintankandjacketconstantheatcapacitiesanddensitiesincompressibleflowmodel,f,tin,fc,tcin,fc,tc,f,t,h,nonlinearodes,q:ifthemodeloftheprocessisnonlinear,howdoweexpressitintermsofatransferfunction?a:wehavetoapproximateitbyalinearone(i.e.linearize)inordertotakethelaplace.,f(x0),f(x),x,x0,nonlinearsystems,firstordertaylorseriesexpansion1.functionofonevariable2.functionoftwovariables3.odes,transferfunction,proceduretoobtaintransferfunctionfromnonlinearprocessmodelsfindsteady-stateofprocesslinearizeaboutthesteady-stateexpressintermsofdeviationsvariablesaboutthesteady-statetakelaplacetransformisolateoutputsinlaplacedomainexpresseffectofinputsintermsoftransferfunctions,firstord