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1、IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.48,NO.12,DECEMBER20032203RecursiveIdentificationofHammersteinSystemsWithDiscontinuousNonlinearitiesContainingDead-ZonesJozefVörösAbstract—ThisnotedealswiththerecursiveparameteridentificationofHammersteinsystemswithdiscontinuousnonlineari
2、ties,i.e.,two-segmentpiecewise-linearwithdead-zonesandpreloads.AspecialformoftheHammersteinmodelwiththistypeofnonlinearityisincorporatedintotherecursiveleastsquaresidentificationschemesupplementedwiththeestimationofmodelinternalvariables.Theproposedmethodisillustratedbyexampl
3、es.IndexTerms—Dead-zone,discontinuousnonlinearities,Hammersteinmodel,recursiveidentification.Fig.1.Discontinuousnonlinearitywithdead-zones.I.INTRODUCTIONDiscontinuousnonsmoothnonlinearitiesshowninFig.1(i.e.,two-theestimationofboththeparametersofthelinearblocktransfersegmentpi
4、ecewise-linearwithpreloadsanddeadzones)arecommoninfunctionandthecoefficientsdescribingthenonlinearcharacteristicengineeringpracticeandcanseverelylimittheperformanceofcontrolusingthesysteminputs,outputsandestimatedinternalvariables.systems[7].Theidentificationofsystemsconsisti
5、ngofthediscontin-Illustrativeexamplesareincluded.uousnonlinearitythatis:1)followedor2)precededbyalineardynamicsystemisthereforeofgreatimportance,becauseonlytheknowledgeII.HAMMERSTEINMODELWITHDISCONTINUOUSNONLINEARITYofnonlinearityparametersenablescancelingorreducingtheadverse
6、effectsofthegivennonlinearity.However,onlyfewapproacheshaveTheHammersteinmodelisgivenbythecascadeconnectionofabeenpublisheddealingwiththefirstcaseknownastheHammersteinstaticnonlinearityblockfollowedbyalineardynamicsystemshownsystem[1],[3],[15](althoughdead-zoneexamplescanbefo
7、undininFig.2[4].Letusassumethenonlinearblockcanbecharacterizedbymorepapers,e.g.,[5],[13],andanothertypeofdiscontinuousnonlin-anonsmoothmappingf(1)earityisconsideredin[12]),andonlyoneapproachdealingwiththesecondcaseknownastheWienersystem[16].Inallthesecasesthex(t)=f[u(t)](1)pa
8、rameterestimationwasperformedoffline.Recursiveidentificationmethodsa
