欢迎来到天天文库
浏览记录
ID:33455652
大小:620.00 KB
页数:24页
时间:2019-02-26
《dynamic modeling and control of动态建模与控制》由会员上传分享,免费在线阅读,更多相关内容在应用文档-天天文库。
1、Differential-AlgebraicEquation(DAE)SystemsManyphysicalsystemssuchasmultibodyproblemsarenaturallymodeledusingDAEsmomentumequationkinematicconstraintsDifferential-AlgebraicEquation(DAE)ModelingProblemVaporCompressionCycleExample·Dividethemodelintosubsystemsthatcapturethedyna
2、micbehavior·Interconnections(boundaryconditions)aredeterminedbyconstraints·TheobjectiveistoobtainalowordermodelsuitableforcontrolDAEModelingApproachConservationequationsforsubsystemsalwayshavetheform–energyandmassstorage(P,r,etc.)–boundaryconditions()Algebraicconstraintsde
3、terminetheboundaryconditions,SubsystemModelsmassbalance:energybalance:momentum:assumepressurevariationsarenegligible1)lumpedparameter2)approximationofPDEsVaporCompressionCycleModelEnergyandmassstoragePressuredropandmassflowconstraintsImplicitIntegration(Gear,1971)·Replaced
4、erivativesbyfinitedifferenceapproximationssolvefor·Doesnotresultinanexplicitstatespaceformnecessaryforcontrol·Limitedtoarestrictedclassofproblems(index<3)geometricalinterpretationDifferentiationBasedMethods·Differentiatealgebraicconstraintsandsolvefor·Canresultincomplicate
5、ddifferentialequations·SolutionscandriftoffconstraintsStiffDynamicElementMethod(Karnopp,1979)·Requiresgoodphysicalintuition(bondgraphs)·Needveryfastdynamicsforagoodapproximation·Doesn'tguaranteestability(especiallywithcontrol)StiffDynamicElementMethodlowdamping:highlyoscil
6、latorymoredamping:largeerrorSingularPerturbationMethodThestandardsingularperturbationproblem,,AsthesystemundercertainconditionsapproachesthereducedorderDAEsystemDAESolutionapproach:InvertthesingularperturbationmethodtoconvertDAEstoODEsTheSingularPerturbationApproachtoDAEsA
7、dvantagesoverthestiffdynamicelementmethod:Þmoresystematic,fewerparametersÞguaranteeofstabilityÞbetteraccuracyforagivenbandwidthÞmoresuitedforcontroldesignConditionsforConvergenceAssumefastdynamicsoftheform:NeedtoinvestigatethestabilityofaboundarylayerChangetoafasttimescale
8、.AsboundarylayerdynamicsTikhonov’stheorem:Ifyislocallyexponentiallystableforallandthereex
此文档下载收益归作者所有