机电一体化系统设计4(离散控制)课件

Lecture4

Discretetimecontrol

LectureoutlineDiscretetimecontrolintroduction,samplingofcontinuoussignalsPurediscretecontroldesignDiscretetimeapproximationofacontinuoustimecontroldesignWritingcodeContinuousvsdiscretetimecontrolDiscretetimecontrolAssumptions/consequencesNewdiscretetimedesignissuesTwodesignconcepts(continuous,discrete,combinationofboth)Selectionofthesamplingrate(s)-akeyissue;performancevscost.Duetothesampling,filteringofsensor(andcontrol)signalsisoftenrequired;thatis,pre-andpostsamplingfilters.Computerimplementationore.g.cascadedcontrolloopsmayleadtomultiratesamplingtobehandledbythereal-timeimplementation.Softwareimplementation;whatdoesacontrolalgorithmlooklikeintermsofprogramcode(programmingadynamicsystem).Analysisoftheeffectsofthetransformationofthecontroldesignfromcontinuoustodiscretetime.Numericinterp.ofdiscrete/continuousSamplingcontinuoustimesignalsFrequencyfoldingNumericexampleofaliasingPre-orantialiasfilteringRealsignalsarenotbandlimited.Highfrequencycomponentsmustbefilteredawaytoavoidaliasing.Fordigital/discretesensorsthealiasingproblemislessaggravating.Theprefilteristypicallyimplementedasananalogfilterwithresistors,capacitorsandanoperationalamplifier.Thefiltershouldbetakenintoaccountincontroldesign.NEVERIMPLEMENTAFEEDBACKLOOPWITHOUTANTIALIASINGFILTERONALLAD-CONVERTERSChoiceofsamplingratessingleratesystemshighsamplingrateiscostlythefrequencyshouldbesetinrelationtothefastestdynamicsintheclosedloopcharacteristics(i.e.bandwidth,rise-time)ofthefeedback,observerormodelfollowing.or4-10samplesperrisetimeSamplingintervalselectionbasedonfreq.LectureoutlineDiscretetimecontrolintroduction,samplingofcontinuoussignalsPurediscretecontroldesignDiscretetimeapproximationofacontinuoustimedesignWritingcodeTwodigitalcontroldesignsituationsModellinganddesigncompletelyindiscretetimefromthestart."Howdoesthecomputerseetheprocess"Agoodreferenceis:ComputerControlledSystems-Theoryanddesign,ThirdeditionÅströmandWittenmarkPrenticeHall,ISBN0-13-314899-8Transformationofanexistingcontinuoustimedesigntodiscretetime."Howdoweapproximateacontinuoustimecontrollersdiff.eq.asgoodaspossibletoadigitalcomputer"Continuoustimedesigntakingcomputercharacteristicsintoaccount.AcombineddesignisoftenusedPurediscretetimecontroldesignTheprocesstobecontrolledisfirstmodelled(continuoustime).Theprocessmodelisthentransformedintoadiscretetimemodel.Thecontroldesign(e.g.poleplacementdesign)isperformedcompletelyinthediscretedomain.(Withnewrulesforpoleplacement).Closedloopanalysisofthedesign,Sensitivityfunctionetc.Someofthephysicalinsightislostwhenleavingthedifferentialequationsinfavourofthedifferenceequations.DiscretetimestatespacemodelIDiscretetimestatespacemodelIIZeroorderholdsamplingDiscretetimeTF-Thez-transformImportantpropertiesofthez-transformTheZ-transformasdiscreteTFPurediscretetimecontroldesignTheprocesstobecontrolledisfirstmodelled(continuoustime).Theprocessmodelisthentransformedintoadiscretetimemodel.Thecontroldesign(e.g.poleplacementdesign)isperformedcompletelyinthediscretedomain.(Withnewrulesforpoleplacement).Closedloopanalysisofthedesign,Sensitivityfunctionetc.Directdiscretetimedesign-anexampleLectureoutlineDiscretetimecontrolintroduction,samplingofcontinuoussignalsPurediscretecontroldesignDiscretetimeapproximationofacontinuoustimedesignWritingcodeTransformationofanexistingdesignThestatefeedbackcontrollerassuchdoesnotneedtobetranslatedtodiscretetime.Thecontrollerisnotadynamicsystembutsimplyasetoffeedbackgains(therearehowevermethodstocompensateforthesampleandholddelay).Assoonasdynamicsareintroducedintothecontroller,i.e.intheformofintegralorderivativeactionatranslationisrequired.TheerrorderivativegainDinaPDcontrollerisanexample.Theobserverisclearlyadynamicsystemwhichalsoneedstranslation.Thetranslationisclearlyrelatedtothesamplingfrequency.Basicallyweareaimingatfindingadiscreteapproximationofthederivative/integralaction,i.eadiscreteapproximationoftheLaplaceoperators(or1/s).DiscretetimeapproximationTransformationofcontinuoustimedesignTransformationofcontinuoustimedesignMappingofpolesThestabilityregioninthecontinuoustimecase(lefthalfplane)correspondstotheunitcircleinthediscretetimecase.SymbolicallycalculatedinMapleFurtherdiscretetimeapproximationsLectureoutlineDiscretetimecontrolintroduction,samplingofcontinuoussignalsPurediscretecontroldesignDiscretetimeapproximationofacontinuoustimedesignWritingcodeTransformingtocodeExample