sliding mode boundary control of unstable parabolic pde systems with parameter variations and matched disturbances

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1、2009AmericanControlConferenceFrA05.1HyattRegencyRiverfront,St.Louis,MO,USAJune10-12,2009SlidingModeBoundaryControlofUnstableParabolicPDESystemswithParameterVariationsandMatchedDisturbancesMeng-BiCheng,VericaRadisavljevic,andWu-ChungSu,Member,IEEEAbstract—Thispaperconsidersthestabilizatio

2、nproblemoftodevelopslidingmodeboundarycontrollawsforinfinite-aone-dimensionalunstableheatconductionsystemsubjecttodimensionalsystemswithoutmodeltruncations.Wewillparametricvariationsandboundaryuncertainties.ThissystemadopttheLyapunovapproachtoslidingsurfacedesign[10]ismodeledasaparabolicp

3、artialdifferentialequation(PDE)intothisinfinite-dimensionalsystemversion.AcontinuousandisonlypoweredfromoneboundarywithaDirichlettypeofactuator.BytakingtheVolterraintegraltransformation,weslidingmodeboundarycontrollawisthendesignedtoobtainanominalPDEwithasymptoticstabilitycharacteristicsa

4、chievesystemstabilizationinspiteofsomeboundedsysteminthenewcoordinateswhenanappropriateboundarycontrolparametervariationsandboundaryexogenousdisturbances.inputisapplied.TheassociatedLyapunovfunctioncanthenbeusedfordesigninganinfinite-dimensionalslidingsurface,Thevariablestructurecontrol(V

5、SC)methodologyhasonwhichthesystemexhibitsexponentialstability,invariantofbeenappliedtoinfinite-dimensionalsystemsinthedis-theboundedmatcheddisturbance,andisrobustagainstcertaintributedcontrolmechanism[11]–[13]aswellasinthetypesofparametervariations.Acontinuousvariablestructureboundarycont

6、rollawisemployedtoattaintheslidingmodeonboundarycontrolmechanism[14,15].Byutilizingthesemi-theslidingsurface.Theproposedmethodcanbeextendedtogroupoperatortheory,Utkin[12]presentedtheslidingmodeotherparabolicPDEsystemssuchasdiffusion-advectionsystem.discontinuousdistributedcontrolschemefo

7、rtheheatpro-Simulationresultsaredemonstratedandcomparedwiththecessunderthecompactcommutabilityconditionswiththeotheroutstandingback-steppingcontrolschemes.assumptionsofopen-loopstabilityandfullstateaccessability.IndexTerms—Boundarycontrol;chattering,distributed-parameters