Discrete Event Based Simulation and Control of Con

DiscreteEventBasedSimulationandControlofContinuousSystemsErnestoKofmanThesispresentedinpartialfullfilmentoftherequirementsforthedegreeofDoctorenIngenier´ıaDirector:SergioJuncoFacultaddeCienciasExactas,Ingenier´ıayAgrimensuraUniversidadNacionaldeRosarioiiAbstractThisThesisintroducesthefundamentalsandthetheoryofanewwaytoap-proximatedifferentialequationsappliedtonumericalintegrationanddigitalcontrol.Replacingtheclassictimediscretizationwithstatequantization–anapprox-imationapproachalreadyavailableintheliterature–twonewnumericalinte-grationmethodsareintroduced.Duetothiskindofdiscretizationtechnique,theresultingsimulationmodelsarediscreteeventsystemsinsteadofadiscretetimeasinallclassicnumericalmethods.Thisfactyieldsmanypracticalad-vantageslikeanefficientsparsityexploitationandanimportantcomputationalcostreductioninhybridsystemsimulation.Fromatheoreticalpointofview,itisshownthatthemethodscanbean-alyzedascontinuoussystemswithboundedperturbationsandthus,stability,convergenceanderrorboundpropertiesareprovenshowingalsosomeinterest-ingadvantageswithrespecttoclassicapproaches.Theapplicationofthenewfirstordermethodtothediscretizationofcon-tinuouscontrollerswiththeadditionofanasynchronoussamplingschemeallowtodefineanewdigitalcontrolmethodologyinwhichthetimediscretizationisideallyavoided.Asaresult,thisnewtechniqueimprovesconsiderablythedy-namicresponseofdigitalcontrolsystems,reducesthequantizationeffects,thecomputationalcostsandtheinformationtrafficbetweenplantandcontroller.Whenitcomestotheoreticalproperties,thenewcontrolschemecanensurestability,convergenceanderrorboundpropertieswhichcanbeappliedtolinear,nonlinearandtimevaryingcases.Basedontheseproperties,differentdesignalgorithmsarealsoprovided.iiiAcknowledgmentEveryThesisbeginswithamentiontotheDirector.Inthiscase,myacknowl-edgementisnotonyduetoourworkinthelastfouryears.IfIhadnotmetSergio,myworkwouldnotbeeninvolvedwithteachingandresearch(andnowIwouldbeprobablyworkingattheindustry,withagoodsalary,instead).Followingwiththeacademicside,animportantpartofwhatIlearnedduringthelastyears(fromtechnicalandmathematicaldetailstousingLaTeX)isduetoMarimarSeron.ShealsogavetheimpulseIneededtochoosethesubjectofthisThesis.IalsowanttothankJulioBraslavskyforhisremarksandforthereviewofmanytopicswhichthenwerepartofthiswork(mainlythosetopicsrelatedtocontrol).Inthatsense,IalsoowethankstoJuanCarlosG´omezwho,amongmanyotherthings,helpedmewithacarefulrevisionofmorethanonearticlesup-portingthisThesis.ManyoftheideaswhichformpartoftheresultsofthisThesiswereconceivedaftertalkingwithFran¸coisCellier.Besidesthat,hisinvitationtocoauthorhisbookContinuousSystemSimulationwasoneofthemostimportantimpulsesIreceivedtocontinuewiththiswork.IalsowanttomentiontheveryimportanthelpthatIreceivedfromBernieZeigler.Henotonlyrevisedandcollaboratedwiththecorrectionofmyarticlesbuthealsoopenedthedoorsofagreatpartofthesimulationcommunitytomakemyworkknown.AlthoughIwasonlyreferringtothehelpIreceivedintheacademicalsense,itwouldbeunfairtoforgetthefriendshipandallwhatIreceivedfromthesepeopleinthehumanaspect.Nothingofthisworkhadbeendonewithoutthesupportofmyparents,JuliaandHugo.Theygaveme–andtheystilldo–everythingwhatcanbeexpectedregardinglove,advise,helpand–themostimportantthing–thefreedomtochooseandbuildmyownway.WhenImentionmyfamilyImustalsothankQueca,myGrandmother.She,withherknishesandcookies,withherinfinitededicationandwithherexample,isoneofthelightswhichguideeverydayofmylife.Icannotforgetmentioningthesupportofmybrothers,DiegoandMarco,andImustalsothanktheunconditionalfriendshipofMonica(andRami,ofcourse).Idonotwanttoskipamentiontomyfriendsthatalwaysarewithiiiivme,leavingasidethegeographicdistance:Dami´an,Cabeza,Lottar,Dieguito,Mart´ın,Diego,Gast´on,Betty,Momia,Hern´an.Finally,mygreatestthankstoJuliana,forsharingeachmomentofourlifes.Contents1Introduction11.1OutlineoftheThesis.........................21.2OriginalContributions........................51.3RelatedWorksandRelevanceoftheResults............51.4SupportingPublications.......................82QuantizationandDEVS92.1AnIntroductoryExample......................102.2DiscreteEventSystemsandDEVS.................112.3CoupledDEVSmodels........................142.4SimulationofDEVSmodels.....................162.5QuantizedSystemsandDEVS...................182.6IllegitimacyofQuantizedSystems.................212.7DEVSandContinuousSystemsSimulation............253QuantizedStateSystems273.1HystereticQuantization.......................283.2QSS–method.............................293.3TrajectoriesinQSS..........................303.4DEVSmodelofaQSS........................333.5InputsignalsintheQSS–method..................353.6StartupandOutputInterpolation.................383.7Quantization,HysteresisandErrors................394TheoreticalPropertiesofQSS414.1QSSandPerturbationTheory....................424.2ConvergenceofQSS–method....................444.3GeneralStabilityPropertiesofQSS................464.4LTIPerturbedSystems:LyapunovApproach...........494.5LTIPerturbedSystems:NonConservativeApproach.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