Model reduction using the genetic algorithmand routh approxi mations

作者:李红星;芦金石;闫红书 刊名:Journal of Systems Engineering and Electronics 上传者:衣琼

【摘要】A new method of model reduction combining the genetic algorithm(GA) with the Routh approximation method is presented. It is suggested that a high order system can be approximated by a low order model with a time delay. The denominator parameters of the reduced order model are determined by the Routh approximation method, then the numerator parameters and time delay are identified by the GA. The reduced order models obtained by the proposed method will always be stable if the original system is stable and produce a good approximation to the original system in both the frequency domain and time domain. Two numerical examples show that the method is computationally simple and efficient.

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1.INTRODUCTIONTheexactanalysisanddesignofhigh-ordersystemsareoftencomplicated.Itisalwaysdesirabletosubsti-tutesuchahigh-ordersystembyasimplifiedsystem.Modelreductionproblemsare,therefore,ofconsider-ableinterestallalong.Itmaybemorerealisticthatmanyrealsystemsareconsideredtocontainpuretimedelays.Whensuchsystemsareapproximatedbyrationalmodels,thisoftenleadsthesemodelstobehighorderforgoodapproximation.Ifapuretimedelayisintroducedintothereduced-ordermodel,theapproximationmightbeimprovedtoagreatextentandtheoriginalsystemcanbedescribedbythemodelwithfewerparameters.Thus,themodelismoreaccuratereflectionofreali-ty.Somemethodsofmodelreductionwithtimedelayhavebeenpresented[1~4].Thereduced-ordermodelsobtainedbythemhavebetterapproximationtotheo-riginalsystemsthanthosewithouttimedelay.InRefs.[1,2],thePad啨approximationtothetimede-layisusedandthentheparametersofthereduced-or-dermodelarecalculatedbythegradient-basedmethod.Itisworthnotingthattheirmethodsexitanonlinearoptimizationproblemandtheoptimizationmethodsbasedonthegradientoftenfailinthesearchforglobaloptimumwhenthesearchspaceisnonlinearintheparameters.Yangetal[3]proposedahybridmethodthatthedenominatorparametersandtimede-layofthereduced-ordermodelaresearchedbytheGAandthenumeratorparametersarecalculatedbytheleast-squaresmethod(LS).Insearchingtheseparameters,theGAandtheLSaredependenteachother,soitincreasesthecomplexityofthealgo-rithm.Itisveryimportantthatastablereduced-ordermodelisobtainedinsimplifyingahigh-ordermodel.Hutton[5]introducedanov

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