化工过程模拟与分析(第十章控制系统建模简介)

第十章过程控制系统建模简介,主要内容为何化工生产过程需要控制？储液罐液面高度的控制；过程控制的基本概念；储液罐动态系统；一些数学概念；一阶动态系统的响应。,Whyusesurgetank？,Streamwihassomesteadydesignflowrate,butinpracticeitvaries,causingproblemsinprocess2.,Propagationofdisturbancesbetweenprocessesisacommonproblem,andacommonsolutionisthesurgetank.,10.1Designingthetank,StepsCharacterizingtheinletstreamSpecifyinglimitsontheoutletstreamMakingasuitableprocessmodeltoconnectinletwithoutlet,（1）Inlet:supposethattheflowswingsby40%overa20-minuteperiod,flowisinkg/handtimeinminutes.,(2)Outlet:thedesiredflowwois10,000kg/h.Letsbehard-nosedandinsistonnovariation.,(3)Processmodel:byinstinctachemicalengineerwritesamaterialbalance.,heightisinm,areainm2,timeinminutes,anddensityinkg/m3.,Protectthetank,Itseemspossiblethatthetankmayoverfloworrundry,Supposethesimplecaseofwiwo=C,Therefore,weshouldprotectourtankwithsomeautomaticprocesscontrolsomethingthatwillmeasurethelevelandtakecorrectiveactionshouldthelevelbecometoohighorlow.,10.2Definitionsinprocesscontrol,process:theequipmentwithinsomeboundary,alongwiththestreamsofmatterandenergythatcrossthatboundary-whatweusuallymeanwhenwethinkofchemicalprocess.Inthisexample,itsthetank,pump,piping,andfluid.,disturbance:achangeimposedontheprocess.Inthisexample,theinputstreamwivarieswithtime.,controlledvariable:somefeatureoftheprocessthatwewouldliketocontrol.Itmaybeastreamcrossingtheboundaryorsomequantitywithin.Wewanttocontrolitbecausethedisturbancemakesitchangewithtime,inawaythatwedontlike.Inthisexample,thecontrolledvariableistheliquidlevel.,setpoint:thedesiredvalueofthecontrolledvariable.Inthisexample,wehavenosetpoint,butwedowanttoconfinethecontrolledvariablebetweenhighandlowlimits.,manipulatedvariable:somefeatureoftheprocessthatweadjustsothatwecanexertinfluenceonthecontrolledvariable.Inmostchemicalprocesses,themanipulatedvariablewillbetheflowrateofastream.Inthisexample,itseemsreasonabletomanipulatetheoutletflow.,finalcontrolelement:adevicethatadjuststhemanipulatedvariable.Ifthemanipulatedvariableisusuallyastream,thefinalcontrolelementisusuallyavalve,referredtoasacontrolvalve.,measuredvariable:mostoften,synonymouswiththecontrolledvariablewemeasureitsothatwecantellhowwellourcontrolschemeisworking.Ofcourse,wemayalsomeasurethemanipulatedvariableandothervariables,aswell.,controller:thedevicethatdetectstheoutputofthesensor,decideshowseriouslythecontrolledvariabledeviatesfromthesetpoint,anddirectsthefinalcontrolelementinresponse.Thecontrollerperformscalculationsbasedonitscontrolalgorithm.,finalcontrolelement:adevicethatadjuststhemanipulatedvariable.Ifthemanipulatedvariableisusuallyastream,thefinalcontrolelementisusuallyavalve,referredtoasacontrolvalve.,transducer:thismaybemorethanyouwantedtoknow.Thecontrollermustbeabletocommunicatewithsensorandfinalelement.Transducersconvertandtransmitsignalstomakethispossible.,Weinstallalevelsensoronthetank,putacontrolvalveatthepumpdischarge,andconnectthetwowithacontroller.,feedbackcontrol,Whenthelevelsensorindicatesapproachtohighorlowlimits,thecontrollercomputesaresponsebyitsalgorithmanddirectsthecontrolvalvetoopenorcloseappropriately.Theoutletflowwomaynotbeconstant,aswewanted,butbysuitablechoiceoftanksizeandcontrolalgorithmwecansignificantlyreduceitsvariability,andhencetheeffectsondownstreamprocesses.,Howcontrol?,10.3Dynamicsystem,Aprocessisatypeofsystem,butsystemismoreabstractandgeneral.1)thesystemboundaryisoftentenuous.2)theinputsandoutputsofasystemneednotbematerialandenergystreams,astheyareforaprocess.3)Systeminputsarethingsthatcauseandoutputsarethingsthatrespond.,Differencebewtweensystemthatis,ifweidentifysomecomponentsystems.,intermediatevariableswithinasystem.Neitherinputsnoroutputsofthemainsystem,theyconnectthecomponentsystems.Intermediatevariablesmaybeusefulinunderstandingandinfluencingoverallsystembehavior.,Single-loopfeedbackcontrol,Fromtheinputs,wechooseamanipulatedvariable(VM)andinstallanappropriatefinalcontrolelement.Themeasurementisfedtothecontroller,whichdecideshowtoadjustVMtokeepVCatthesetpoint.OtherinputsaredisturbancesthataffectVC,andsorequireactionbythecontroller.,Responsetorectangularpulseattimetd,Supposethatattimetd,extraliquidisinjectedintothefeedstream:massMisaddedovertimeintervaltbeforetheinletflowreturnstonormal.,Thepulsewidththasarbitrarilybeensetequaltotheonsettimetd,Thetemporarydisturbancehashadapermanenteffectontheoutput,Responsetoimpulseattimetd,Wedecreasethetimeintervaloffluidinjection,wefinallyarriveataninfiniteflowrateinaninfinitesimaltimeinterval,deliveringextramassMtothefluid.,Responsetostepattimetd,Thedimensionlessunitstepfunctioniszerobeforetdandonethereafter,Responsetosineattimetd,Attimetd,theinletflowbeginstooscillatewithradianfrequency.,10.4Mathreview,Quadraticequation,Forgreaterthanzero,therootsmayberealorcomplex;therealpartswillhavethesamesign.,Complexnumbers,Polarform,Complexnumbers,Eulersformula,Complexnumberanditsconjugates,Usetheconjugatetoeliminatejinthedenominatorofaratio.,Oscillatorybehavior,Supposeavariabley(aliquidlevel,atemperature,achemicalconcentration,aflowrate)oscillatesregularlyintime:,Thephaseanglerepresentsanadvanceinthesignaly(t)withrespecttosomeothersignal.,Phaselagofresponse,First-order,linear,variable-coefficientODE,Weareaddressingsystemsthatvaryintime,soourindependentvariableisalwayst.,Wesolvethisequationbydefiningtheintegratingfactorp(t),y(t)astheresponseofthesystemtoinputdisturbancesKx(t)andy(t0),Forprocesscontrol,ifa(t)isconstant,wecallitthetimeconstant,andKiscalledthegain.,10.5Dynamicbehavioroffirst-orderprocesses,Transientbehavior,forallthevarietyofsystemsinnatureandtechnology,canbedescribedbyaveryfewelements.,Thefirstorderlag:mixedtank,Thecompositionoftheliquidinthetankisuniform,anditisequaltothecompositionoftheoutletstream.,Thetankisarrangedwithlargeoverflow;thustheinletandoutletflowsareessentiallyequalatanytime,andthevolumeisconstant,Mixtank,Considertheflowtobeconstant,buttheinletconcentrationmayvarywithtime,相减,Theprocessmodelintermsofdeviationvariables,indicatedbyanasterisksuperscript：,Theratiooftankvolumetoflowrateclearlytakesonthesignificanceofacharacteristictime,thetimeconstant,Thisequationistheprocessmodelforthemixingtank,showinghowtheoutletconcentrationbehavesforarbitrarydisturbancesintheinlet.,Asthedisturbanceisintroduced,theoutletconcentrationbeginstochange;itgraduallybecomesequaltotheinletconcentration.,Thestepis95%completewhentimeequaltothreetimeconstantshaselapsed,Firstorderreferstotheorderofthegoverningdifferentialequation.Lagreferstothewayinwhichtheoutputlagsbehindtheinput.,Thelagoccursbecausethesystemhasstoragecapacity,andthatcapacitytakestimetofillordepletewhenconditionschange.Inthisproblem,thesystemstoresthedissolvedcomponent.,Steady-stategain,“Gain”expresesthedegreetowhichadynamicsystemamplifiesorattenuatestheinputsignal.,Forthemixingtank,thegainis1,showingthatpermanentdisturbancesaremerelypassedthroughthesystem.,BothtimeconstantandgainareindependentofthesizeofthedisturbanceC.,Writematerialandenergybalancesandotherequationsrequiredtodescribetheprocess(formostprocesscontrolapplications)IdentifyasteadystateoperatingconditiontoserveasareferenceSubstituteTaylorseriesapproximationsaboutthereferenceconditionfornonlineartermsinthemodelSolvethemodelforanyrequiredoperatingparametersatthereferenceconditionSubtractthesteadystateconditionfromthemodelequationstoexpressallvariablesindeviationformArrangetheequationsinstandardform,identifyingdynamicparametersofknownsignificanceSolvefortheoutputvariablesasfunctionsoftheinputsIntroduceparticulardisturbancesandcalculatetheresponses,Howtoanalysisfirstorderlag,10.6Integrator:pumpedoutlettank,Tobestrictaboutplacingaboveequationinstandardform,weshoulddefineagainandatimeconstant,Theresponsetoastepchangeofmagnitudewininletflowattimetdis,Summaryofdisturbanceresponses,Initialconditioniszero;disturbanceisintroducedattimetd,10.7Multiplesysteminputsfrommultipleinletstreams,Considerawell-stirredtankheatedbyanelectricresistanceelementofoutputpowerQ.,Trefisareferencetemperatureforcomputingtheenthalpyoftheflowingstream,PresumingthatflowFisconstantandthephysicalpropertiesarenotafunctionoftemperature,Steadystate,introducingdeviati