离散时间控制系统课件

Computer-ControlledSystems1/3/2023CourseInformationTime:13:30-15:10pm,Wednesday 10:00-11:40am,Friday(evenweeks)Venue:综B204References:离散时间控制系统(英文版第2版)，KatsuhikoOgata，机械工业出版社，2004离散时间控制系统(中文版)，KatsuhikoOgata，陈杰，蔡涛等译，机械工业出版社，2006GradingProcedure:in-termevaluationexperimentalresultsfinalpaperexamination.2Chapter1IntroductiontoDiscrete-Time34Contents1-1Introduction1-2DigitalControlSystems1-3QuantizingandQuantizationError1-4DataAcquisition,ConversionandDistributionSystems1-5ConcludingComments41-1IntroductionDigitalControllerArapidincreaseintheuseofdigitalcontrollers5DigitalControllerThetrendisduetoDigitalcontrolcanachieveoptimalperfor-mance,haveDecision-makingcapabilityandflexibilityinthecontrolprogramAvailablityoflow-costdigitalcomputersAdvantagesofdigitalsignals1-1Introduction6TypesofSignalsContinuous-timesignal:AsignaldefinedoveracontinuousrangeoftimeAnalogsignal:AsignaldefinedoveracontinuousrangeoftimewhoseamplitudecanassumeacontinuousrangeofvaluesAcontinuous-timequantizedsignalDiscrete-timesignal:Asignaldefinedonlyatdiscreteinstantsoftime1-1Introduction7Sampled-datasignal:Adiscrete-timesignaliftheamplitudecanassumeacontinuousrangeofvaluesDigitalsignal:Adiscrete-timesignalwithquantizedamplitudeComparisonDiscrete-time,digital,sampleddatasignal(controlsystem)Continuous-time,analogsignal(controlsystem)1-1Introduction81-1Introduction9SystemsDealtWithinThisBookLinearandtimeinvariantDiscrete-TimeControlSystemsoneormorevariablescanchangeonlyatdiscreteinstantsoftime.TheseinstantsmayspecifythetimesatwhichsomephysicalmeasurementisperformedorthememoryofadigitalcomputerisreadoutDescribedinlineardifferenceequationswithconstantcoefficients1-1Introduction101-2DigitalControlSystemsFigure1-2Blockdiagramofadigitalcontrolsystem11S/HandA/D(A/D)Sample-and-Hold(S/H)SamplingProcesses,replaceoriginalcontinuous-timesignalbyasequenceofvaluesatdiscrete-timetimepointsacircuitthatreceivesanaloginputsignalandholdsthissignalataconstantvalueforaspecifiedperiodoftime.Analog-to-DigitalConverter(A/D)Alsocalledanencoder,isadevicethatconvertsananalogsignalintoadigitalsignal,usuallyanumericallycodedsignal.AS/HcircuitisoftenanintegralpartofacommerciallyavailableA/Dconverter.1-2DigitalControlSystems12TypesofSamplingOperationsPeriodicsamplingtk=kT(k=0,1,2,……)Multiple-ordersamplingtk+r-tk=constantMultiple-ratesamplingAdigitalcontrolsystemhavedifferentsam-plingperiodsindifferentfeedbackpathsRandomsamplingtkisarandomvariable1-2DigitalControlSystems13SignalFormsinaDigitalControlSystem1-2DigitalControlSystemsFigure1-3Blockdiagramofadigitalcontrolsystemshowingsignalsinbinaryorgraphicform14D/AandholdDigital-to-AnalogConverter(D/A)Alsocalledadecoder,isadevicethatconvertsadigitalsignalintoansampled-datasignal.Hold1-2DigitalControlSystems15PlantorProcessAplantisanphysicalobjecttobecontrolled.Wecallanyoperationtobecontrolledaprocess.AccuratemodelingisperhapsthemostdifficultpartinthedesignofcontrolsystemTransducerIsadevicethatconvertsaninputsignalintoanoutputsignalofanotherform,suchasadevicethatconvertsapressuresignalintoanvoltageoutput.Analogtransducer,sampled-datatransducer,digitaltransducer1-2DigitalControlSystems16ThemainfunctionsinvolvedinA/Dconversionaresampling,amplitudequantizingandcodingAmplitudequantizingRepresentacontinuousoranalogsignalbyafinitenumberofdiscretestatesiscalledamplitudequantizationCodingorEncodingRepresentasamplevaluebyanumericalcode1-3QuantizingandQuantizationError17QuantizingThestandardnumbersystemisthebinarynumbersystem.Thecodegroupconsistsofnpulseseachindicatingeither‘on’(1)or‘off’(0).Inthecaseofquantizing,n‘on-off’pulsescanrepresent2namplitudelevelsoroutputstates.ThequantizationlevelQ:therangebetweentwoadjacentdecisionpoints:Q=FSR/2n,FSRisthefull-scalerange.MSBisthemostsignificantbit,hasthemostweight(onehalfofthefullscale)LSBistheleastsignificantbit,hastheleastweightLSB=FSR/2n1-3QuantizingandQuantizationError18QuantizationErrorSincedigitaloutputcanassumeonlyafinitenumberoflevels,ananalognumbermustberoundedofftothenearestdigitallevel.Quantizationerrorvariesbetween0and1/2Q.QuantizationerrordependsonfinenessoftheQ,andcanbemadeassmallasdesiredbymakingQsmaller.1-3QuantizingandQuantizationError191-3QuantizingandQuantizationErrorTodeterminethedesiredsizeofthequantizationlevelinagivendigitalcontrolsystem,theengineermusthaveagoodunderstandingoftherelationshipbetweenthesizeofthequantizationlevelandtheresultingerror.20Forananaloginputx(t),theoutputy(t)takesononlyafinitenumberoflevels,whichareintegralmultiplesofthequantizationlevelQ1-3QuantizingandQuantizationErrorFigure1-4(a)Blockdiagramofaquantizeranditsinput-outputcharacteristics21Round-offerrorTheerrorresultingfromneglectingtheremainingdigitsiscalledround-offerror.Quantizationerrorisaround-offerrorThefinerthequantizationlevelis,thesmallertheround-offerror.1-3QuantizingandQuantizationError22Round-offerror1-3QuantizingandQuantizationErrorFigure1-4(b)Analoginputx(t)anddiscreteoutputy(t)23Quantizationnoise:theuncertaintypresentinthequantizationprocess.ForasmallquantizationlevelQ,thequan-zationerrorissimilartothatofnoise.Soquantizationprocessactsasasourceofrandomnoise.Thevarianceofthequantizationnoiseis241-4DataAcquisition,ConversionandDistributionSystemsFigure1-5(a)Blockdiagramofadata-acquisitionsystem;25TransducerAphysicalvariablesuchasposition,velocity,acceleration,temperatureisfirstconvertedintoanelectricalsignal(avoltageorcurrent)AmplifierAmplifiesthevoltageoutputofthetransducerConvertsacurrentsignalintoavoltagesignalBuffersthesignal1-4DataAcquisition,ConversionandDistributionSystems26Low-passfilterAttenuatesthehigh-frequencysignalcomponents,suchasnoise(electronicnoisesarerandominnatureandmaybereducedbylow-passfilters.However,suchcommonelectricalnoisesaspower-lineinterferencearegenerallyperiodicandmaybereducedbymeansofnotchfilters.)AnalogMultiplexingAdevicethatperformsthefunctionoftime-sharinganA/Dconverteramongmanyanalogchannels.1-4DataAcquisition,ConversionandDistributionSystems27IfmanysignalsaretobeprocessedbyasingleA/Dandadigitalcontroller,thentheseinputsignalsmustbefedtothecontrollerthroughamultiplexer.Isamultipleswitchthatsequentiallyswitchesamonginputchannelsinsomeprescribedfashion.Atagiveninstantoftime,onlyoneswitchisinthe“on”position.Whentheswitchisoninagiveninputchannel,theinputsignalisconnectedtotheoutputofthemultiplexerforaspecifiedperiodoftime.1-4DataAcquisition,ConversionandDistributionSystems281-4DataAcquisition,ConversionandDistributionSystems29DemultiplexerSeparatesthecompositeoutputdigitaldatafromthedigitalcontrollerintotheoriginalchannelsSample-and-HoldCircuitsSampler:covertananalogsignalintoatrainofamplitude-modulatedpulses.Holdcircuit:holdthevalueofthesampledpulsesignaloveraspecifiedperiodoftime1-4DataAcquisition,ConversionandDistributionSystems30twooperationmodesThetrackingmode:theswitchisclosed,i.e.,theinputsignalisconnectedTheholdmode:theswitchisopen,i.e.,theinputsignalisdisconnectedWhenthesamplingdurationisnegligible,thesamplermaybeconsideredanidealsampler1-4DataAcquisition,ConversionandDistributionSystems311-4DataAcquisition,ConversionandDistributionSystemsFigure1-7Sample-and-holdcircuit321-4DataAcquisition,ConversionandDistributionSystemsFigure1-8Trackingmodeandholdmode33Analog-to-DigitalConvertersTheprocessbywhichasampledanalogsignalisquantizedandconvertedtoabinarynumber.TypesoffrequentlyusedA/DConvertersSuccessive-approximationtypeIntegratingtypeCountertypeParalleltypeSelectioncriterionsofA/DconvertersConversionspeed,accuracy,sizeandcost1-4DataAcquisition,ConversionandDistributionSystems34CountertypeA/D(thesimplestA/D)ClockpulsesareappliedtothedigitalcounterinsuchawaythattheoutputvoltageoftheD/Aconverter(thatis,partofthefeedbackloopintheA/Dconverter)issteppeduponeleastsignificantbit(LSB)atatime.Thentheoutputvoltageiscomparedwiththeanaloginputvoltageonceforeachpulse.Whentheoutputvoltagehasreachedthemagnitudeoftheinputvoltage,theclockpulsesarestopped.Thecounteroutputvoltageisthenthedigitaloutput.1-4DataAcquisition,ConversionandDistributionSystems35Successive-approximationtype(mostfrequentlyused)Theprincipleis:Thesuccessive-approximationregister(SAR)firstturnsonthemostsignificantbit(halfthemaximum)andcomparesitwiththeanaloginput.Thecomparatordecideswhethertoleavethebitonorturnitoff.Iftheanaloginputvoltageislarger,themostsignificantbitisseton.Next,turnonbit2andthencomparetheanaloginputvoltagewiththree-fourthsofthemaximum.1-4DataAcquisition,ConversionandDistributionSystems36Afterncomparisonsarecompleted,thedigitaloutputofthesuccessive-approximationregisterindicatesallthosebitsthatremainonandproducesthedesireddigitalcode.Thus,thistypeofA/Dconvertersets1biteachclockcycle,andsoitrequiresonlynclockcyclestogeneratenbits,wherenistheresolutionoftheconverterinbits.(Thenumbernofbitsemployeddeterminestheaccuracyofconversion.)Thetimerequiredfortheconversionisapproximately2µsecorlessfora12-bitconversion.1-4DataAcquisition,ConversionandDistributionSystems371-4DataAcquisition,ConversionandDistributionSystemsFigure1-9Schematicdiagramofasuccessive-approximation-typeofA/Dconverter38ErrorsinA/DConvertersTheinput-outputcharacteristicsofA/DConverterschangewithtimeandtemperature.Actualanalog-to-digitalsignalconvertersalwayshavesomeerrors,suchasoffseterror,linearityerror,andgainerror.CommercialconvertersarespecifiedforthreebasictemperaturerangesCommercial(0ºCto70ººC)Industrial(-25ºCto85ººC)Military(-55ºCto125ºC)1-4DataAcquisition,ConversionandDistributionSystems39ErrorsinA/DConverters1-4DataAcquisition,ConversionandDistributionSystemsFigure1-10ErrorsinA/Dconverters(a)offseterror;(b)linearityerror;(c)gainerror40Thereverseofthedata-acquisitionAdata-distributionsystemconsistsofregisters,ademultiplexer,digital-to-analogconverters,andholdcircuits.Itconvertsthesignalindigitalform(binarynumbers)intoanalogform.Theoutputoftheholdcircuitisfedtotheanalogactuator,which,inturn,directlycontrolstheplantunderconsideration.1-4DataAcquisition,ConversionandDistributionSystemsFigure1-5(b)blockdiagramofadatadistributionsystem41Digital-to-AnalogConvertersForthefullrangeofthedigitalinput,thereare2ncorrespondingdifferentanalogvalues,including0.Forthedigital-to-analogconversion,thereisaone-to-onecorrespondencebetweenthedigitalinputandtheanalogoutputTwocommonD/AmethodsWeightedresistors:simpleincircuitconfiguration,butitsaccuracymaynotbeverygoodR-2Rladdernetwork:alittlemorecomplicatedincircuitconfiguration,butismoreaccurate.1-4DataAcquisition,ConversionandDistributionSystems42Weightedresistors1-4DataAcquisition,ConversionandDistributionSystemsFigure1-11SchematicdiagramofaD/Aconverterusingweightedresistors43WeightedresistorsTheinputresistorsoftheoperationalamplifierhavetheirresistancevaluesweightedinabinaryfashion.Whenthelogiccircuitreceivesbinary1,theswitchconnectstheresistortothereferencevoltage;whenthelogiccircuitreceivesbinary0,theswitchconnectstheresistortogroundNoticethat:asthenumberofbitsisincreased,therangeofresistorvaluesbecomeslargeandconsequentlytheaccuracybecomespoor1-4DataAcquisition,ConversionandDistributionSystems44R-2Rladdernetwork1-4DataAcquisition,ConversionandDistributionSystemsFigure1-12n-bitD/AconverterusinganR-2Rladdercircuit45Notethat:withtheexceptionofthefeedbackresistor(whichis3R),allresistorsinvolvedareeitherRor2R.Thismeansthatahighlevelofaccuracycanbeachieved1-4DataAcquisition,ConversionandDistributionSystems46HoldCircuitsFillinthespacesbetweensamplingperiodsandthusroughlyreconstructtheoriginalanalogsignalTheholdcircuit:toextrapolatetheoutputsignalbetweensuccessivepointsaccordingtosomeprescribedmannerZero-order-hold:producesastaircasewaveform1-4DataAcquisition,ConversionandDistributionSystems471-4DataAcquisition,ConversionandDistributionSystemsFigure1-13Outputfromazero-orderhold48First-order-hold:generatesanoutputslopeequaltotheslopeofalinesegmentconnectingpreviousandpresentsamplesandprojectingitfromthevalueofthepresentsample.Moreaccuratelythanazero-orderhold.Iftheslopeoftheoriginalsignaldoesnotchangemuch,thepredictionisgood.If,however,theoriginalsignalreversesitsslope,thenthepredictioniswrong.Andtheoutputgoesinthewrongdirection,thuscausingalargeerrorforthesamplingperiodconsidered.1-4DataAcquisition,ConversionandDistributionSystems491-4DataAcquisition,ConversionandDistributionSystemsFigure1-14Outputfromafirst-orderhold50Interpolativefirst-orderhold:generatesastraight-lineoutputwhoseslopeisequaltothatjoiningtheprevioussamplevalueandthepresentsamplevalue,buttheprojectionismadefromthepredictionpoint.Itsaccuracyisbetterthanthatofotherholdcircuits,butthereisaone-samplingperioddelay.Fromtheviewpointofthestabilityofclosed-loopsystems,suchadelayisnotdesirable,andsotheinterpolativefirst-orderhold(polygonalhold)isnotusedincontrolsystemapplications.1-4DataAcquisition,ConversionandDistributionSystems511-4DataAcquisition,ConversionandDistributionSystemsFigure1-14Outputfromaninterpolativefirst-orderhold(polygonalhold)52DigitalControllersandAnalogControllerAnalogControllersrepresentthevariablesinanequationbycontinuousphysicalquantities.caneasilybedesignedtoservesatisfactoryasnon-decision-makingcontrollersthecostincreasesrapidlyasthecomplexityofthecomputationsincreases1-5ConcludingComments53DigitalControllersoperateonlyonnumbersdecisionmakingisoneoftheirimportantfunctionshandlenonlinearcontrolequationsinvolvingcomplicatedcomputationsorlogicoperationsuseverymuchwiderclassofcontrollawsflexibleinallowingprogrammingchangessuperiorinperformanceandlowerinpricethantheiranalogcounterpartshighlyreliable,andoftencompactandlightweightlesssensitivetonoisesignals1-5ConcludingComments54OutlineoftheBookTheobjectiveofthebook:Understand,analyzeanddesignCCSChapter1:introductorymaterialsChapter2:ztransformtheoryztransformsofelementaryfunctions,importantpropertiesandtheoremsoftheztransform,theinverseztransform,andthesolutionofdifferenceequationsbytheztransformmethodChapter3:zplaneanalysisofdiscrete-timecontrolsystemsImpulsesamplingandreconstructionoforiginalsignalsfromsampledsignals,pulsetransferfunctions,andrealizationofdigitalcontrollersanddigitalfilters1-5ConcludingComments55Chapter4:Designofdiscrete-timecontrolsystemsbyconventionalmethodsmappingbetweenthesplaneandthezplane,stabilityanalysis,transientandsteady-stateresponseanalysis,designbytheroot-locusandfrequencyresponsemethods,andananalyticaldesignmethodChapter5:state-spaceanalysisState-spacerepresentation,thesolutionofdiscrete-timestatespaceequations,andthepulsetransferfunctionmatrix,discretizationofcontinuous-timestate-spaceequationsandLyapunovstabilityanalysisChapter6:Poleplacementandobserverdesigncontrollabilityandobservability,designtechniquesbasedonpoleplacement,fu11-orderstateobserversandminimum-orderstateobservers,thedesignofservosystem1-5ConcludingComments569、静静夜夜四四无无邻邻，，荒荒居居旧旧业业贫贫。。。。12月月-2212月月-22Sunday,December25,202210、雨雨中中黄黄叶叶树树，，灯灯下下白白头头人人。。。。19:14:1619:14:1619:1412/25/20227:14:16PM11、以以我我独独沈沈久久，，愧愧君君相相见见频频。。。。12月月-2219:14:1619:14Dec-2225-Dec-2212、故故人人江江海海别别，，几几度度隔隔山山川川。。。。19:14:1619:14:1619:14Sunday,December25,202213、乍见见翻疑疑梦，，相悲悲各问问年。。。12月月-2212月月-2219:14:1619:14:16December25,202214、他乡乡生白白发，，旧国国见青青山。。。25十二二月20227:14:16下下午19:14:1612月-2215、比不了得得就不比，，得不到的的就不要。。。。十二月227:14下下午12月-2219:14December25,202216、行动出成成果，工作作出财富。。。2022/12/2519:14:16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