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1、INT.J.CONTROL,1984,VOL.40,No.2,421-4:34Slidingcontrollerdesignfornon-linearsystemsJEAN-JACQUESE.SLOTINEtNewresult.sarepresentedOIltheslidingcontrolmethodologyintroducedbySiotineandSastry(l983)toachieveaccuratetrackingforaclassofnon-lineartime-varyingrnultivari
2、ablesystemsinthepresenceofdist.urbencesandparametervariations.Anexplicittrade-offisobtainedbetweentrackingprecisionandrobustnesstomodellinguncertainty:trackingaccuracyissetaccordingtotheextentofparametricun•certaintyandthefrequencyrangeofunmodelleddynamics.The
3、trade-offisfurtherrefinedtoaccountfortime-dependenceofmodeluncertainty.1.IntroductionNewresultsarepresentedontheslidingcontrolmethodologyintroducedbySlotineandSastry(198:3)toachieveaccuratetrackingforaclassofnon•lineartime-varyingsystemsinthepresenceofdisturba
4、ncesandparametervariations.Theclassical'slidingmodecontrol'methodologyhasbeendevelopedessentiallyintheliteraturefromtheSovietUnion(see,forexample,Utkin(1978)andreferencescontainedtherein),whereithasbeenusedtostabilizeaclassofnon-linearsystems.However,asdiscuss
5、edbySlotineandSastry(198:3),thismethodologyhasseveralimportantdrawbacks,particularlyhighcontrolauthorityandcontrolchattering.Chatteringisgenerallyundesirableinpractice,sinceitinvolvesextremelyhighcontrolactivity,andfurthermayexcitehigh-frequencydynamicsneglect
6、edinthecourseofmodelling.SiotineandSastry(198:3)showedhowtotransformtheclassicalslidingmodecontrolschemesandachieveaccuratetrackingcontrolforalargeclassofnon-lineartime-varyingsystems,whilemaintainingreasonablecontrolactivity.Inparticular,themethodologyinvolve
7、datrade-offbetweentrackingprecisionandrobustnesstounmodelledhigh-frequencydynamics.Herewequantifytheprecisenatureofthistrade-off,andcompletethemethodologyofSlotineDownloadedby[NewYorkUniversity]at19:4931July2013andSastry(198:3)byshowinghowtoachieveoptimaltrack
8、ingperformancegivenbandwidthrequirementsand(perhapstime-varying)modellingun•certainties.Section2summarizesthemethodologyofSlotineandSastry(198:3)andillustrates,withanexample,thesim
