資源描述：
《multivariable control systems》由會員上傳分享，免費在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、MassachusettsInstituteofTechnologyDepartmentofElectricalEngineeringandComputerScience6.245:MULTIVARIABLECONTROLSYSTEMSbyA.Megretski?StandardLTIFeedbackOptimizationSetup1Thetwomostfrequentlyusedtechniquesofoptimization-basedfeedbackdesignareH2andH-In?nityoptimization.Botharenormallyappliedtowhat
2、canbereferredtoasthestandardLTIfeedbackoptimizationsetup,tobethemainsubjectofdiscussioninthislecture.1.1BasicConceptsTherearethreebasicconceptsbehindthestandardfeedbackoptimizationsetup:thenotionofamulti-input,multi-output(MIMO)lineartime-invariant(LTI)?niteordersystem,thenotionofaninternallyst
3、ablefeedbackinterconnectionoftwoMIMOLTIsystems,andthenotionofasystemnorm.Inaddition,thereisaconceptofwell-posednessoftheresultingoptimizationproblem,whichhastobesatis?ed(otherwisetheavailableoptimizationalgorithmsareguaranteedtobreakdown).1.1.1ComponentsofastandardsetupInordertode?neastandardLT
4、Ifeedbackoptimizationproblem,sketchedonFigure?g:PKstandard,onehastospecifytheplantP,andaperformancemeasure.?cA.Megretski,20041VersionofFebruary4,20042wzPuyK?Figure1.1:StandardLTIfeedbackoptimizationsetupTheplantisa?niteorderlineartime-invariantsystemwithtwoinputs,wandu,andtwooutputs,zandy.Input
5、sandoutputscanbemulti-variable.The?rstinputwiscalleddisturbance,andistypicallyusedtodescribeexternalnoisesandinternalperturbationscausedbynonlinearityanduncertainty.Thesecondinputuiscalledactuator,anddescribestheoutputofthefeedbackcontrollerK(tobedesignedviaoptimization).The?rstoutputziscalledc
6、ost,andrepresentssignalswhichthedesignerwantstobesmall.Finally,thesecondoutputy,usuallyreferredtoassensor,ormeasurement,representsinputofthecontrollerK(tobedesigned).Theperformancemeasurespeci?esaparticularquantitivemeasureof“smallness”forthecostoutputz.Theoptimizationprocesswillaimat?ndinganLT
7、IfeedbacksystemKwhichmakesthefeedbacksystemonFigure?g:PKstandardstable,and“minimizes”theclosedloopsystemfromwtoz.Twomeasures(alsocallednorms)ofhow“l(fā)arge”astableLTIsystemisaremostpopularinfeedbackoptimization:H2normandH-In?nitynorm
