离散时间控制系统课件

Computer-ControlledSystems10/2/离散时间控制系统课件第1页CourseInformationTime: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，离散时间控制系统(汉字版)，KatsuhikoOgata，陈杰，蔡涛等译，机械工业出版社，GradingProcedure:in-termevaluationexperimentalresultsfinalpaperexamination.2离散时间控制系统课件第2页Chapter1IntroductiontoDiscrete-Time3离散时间控制系统课件第3页4Contents1-1Introduction1-2DigitalControlSystems1-3QuantizingandQuantizationError1-4DataAcquisition,ConversionandDistributionSystems1-5ConcludingComments4离散时间控制系统课件第4页1-1IntroductionDigitalControllerArapidincreaseintheuseofdigitalcontrollers5离散时间控制系统课件第5页DigitalControllerThetrendisduetoDigitalcontrolcanachieveoptimalperfor-mance,haveDecision-makingcapabilityandflexibilityinthecontrolprogramAvailablityoflow-costdigitalcomputersAdvantagesofdigitalsignals1-1Introduction6离散时间控制系统课件第6页TypesofSignalsContinuous-timesignal:AsignaldefinedoveracontinuousrangeoftimeAnalogsignal:AsignaldefinedoveracontinuousrangeoftimewhoseamplitudecanassumeacontinuousrangeofvaluesAcontinuous-timequantizedsignalDiscrete-timesignal:Asignaldefinedonlyatdiscreteinstantsoftime1-1Introduction7离散时间控制系统课件第7页Sampled-datasignal:Adiscrete-timesignaliftheamplitudecanassumeacontinuousrangeofvaluesDigitalsignal:Adiscrete-timesignalwithquantizedamplitudeComparisonDiscrete-time,digital,sampleddatasignal(controlsystem)Continuous-time,analogsignal(controlsystem)1-1Introduction8离散时间控制系统课件第8页1-1Introduction9离散时间控制系统课件第9页SystemsDealtWithinThisBookLinearandtimeinvariantDiscrete-TimeControlSystemsoneormorevariablescanchangeonlyatdiscreteinstantsoftime.TheseinstantsmayspecifythetimesatwhichsomephysicalmeasurementisperformedorthememoryofadigitalcomputerisreadoutDescribedinlineardifferenceequationswithconstantcoefficients1-1Introduction10离散时间控制系统课件第10页1-2DigitalControlSystemsFigure1-2Blockdiagramofadigitalcontrolsystem11离散时间控制系统课件第11页S/HandA/D(A/D)Sample-and-Hold(S/H)SamplingProcesses,replaceoriginalcontinuous-timesignalbyasequenceofvaluesatdiscrete-timetimepointsacircuitthatreceivesanaloginputsignalandholdsthissignalataconstantvalueforaspecifiedperiodoftime.Analog-to-DigitalConverter(A/D)Alsocalledanencoder,isadevicethatconvertsananalogsignalintoadigitalsignal,usuallyanumericallycodedsignal.AS/HcircuitisoftenanintegralpartofacommerciallyavailableA/Dconverter.1-2DigitalControlSystems12离散时间控制系统课件第12页TypesofSamplingOperationsPeriodicsamplingtk=kT(k=0,1,2,…)Multiple-ordersamplingtk+r-tk=constantMultiple-ratesamplingAdigitalcontrolsystemhavedifferentsam-plingperiodsindifferentfeedbackpathsRandomsamplingtkisarandomvariable1-2DigitalControlSystems13离散时间控制系统课件第13页SignalFormsinaDigitalControlSystem1-2DigitalControlSystemsFigure1-3Blockdiagramofadigitalcontrolsystemshowingsignalsinbinaryorgraphicform14离散时间控制系统课件第14页D/AandholdDigital-to-AnalogConverter(D/A)Alsocalledadecoder,isadevicethatconvertsadigitalsignalintoansampled-datasignal.Holdreconstructtheanalogsignalthathasbeentransmittedasatrainofpulsesamples,i.e.fillinthespacesbetweensamplingperiodsandthusroughlyreconstructtheoriginalanalogsignal1-2DigitalControlSystems15离散时间控制系统课件第15页PlantorProcessAplantisanphysicalobjecttobecontrolled.Wecallanyoperationtobecontrolledaprocess.AccuratemodelingisperhapsthemostdifficultpartinthedesignofcontrolsystemTransducerIsadevicethatconvertsaninputsignalintoanoutputsignalofanotherform,suchasadevicethatconvertsapressuresignalintoanvoltageoutput.Analogtransducer,sampled-datatransducer,digitaltransducer1-2DigitalControlSystems16离散时间控制系统课件第16页ThemainfunctionsinvolvedinA/Dconversionaresampling,amplitudequantizingandcodingAmplitudequantizingRepresentacontinuousoranalogsignalbyafinitenumberofdiscretestatesiscalledamplitudequantizationCodingorEncodingRepresentasamplevaluebyanumericalcode1-3QuantizingandQuantizationError17离散时间控制系统课件第17页QuantizingThestandardnumbersystemisthebinarynumbersystem.Thecodegroupconsistsofnpulseseachindicatingeither‘on’(1)or‘off’(0).Inthecaseofquantizing,n‘on-off’pulsescanrepresent2namplitudelevelsoroutputstates.ThequantizationlevelQ:therangebetweentwoadjacentdecisionpoints:Q=FSR/2n,FSRisthefull-scalerange.MSBisthemostsignificantbit,hasthemostweight(onehalfofthefullscale)LSBistheleastsignificantbit,hastheleastweightLSB=FSR/2n1-3QuantizingandQuantizationError18离散时间控制系统课件第18页QuantizationErrorSincedigitaloutputcanassumeonlyafinitenumberoflevels,ananalognumbermustberoundedofftothenearestdigitallevel.Quantizationerrorvariesbetween0and

1/2Q.QuantizationerrordependsonfinenessoftheQ,andcanbemadeassmallasdesiredbymakingQsmaller.1-3QuantizingandQuantizationError19离散时间控制系统课件第19页1-3QuantizingandQuantizationErrorTodeterminethedesiredsizeofthequantizationlevelinagivendigitalcontrolsystem,theengineermusthaveagoodunderstandingoftherelationshipbetweenthesizeofthequantizationlevelandtheresultingerror.20离散时间控制系统课件第20页Forananaloginputx(t),theoutputy(t)takesononlyafinitenumberoflevels,whichareintegralmultiplesofthequantizationlevelQ1-3QuantizingandQuantizationErrorFigure1-4(a)Blockdiagramofaquantizeranditsinput-outputcharacteristics21离散时间控制系统课件第21页Round-offerrorTheerrorresultingfromneglectingtheremainingdigitsiscalledround-offerror.Quantizationerrorisaround-offerrorThefinerthequantizationlevelis,thesmallertheround-offerror.1-3QuantizingandQuantizationError22离散时间控制系统课件第22页Round-offerror1-3QuantizingandQuantizationErrorFigure1-4(b)Analoginputx(t)anddiscreteoutputy(t)23离散时间控制系统课件第23页Quantizationnoise:theuncertaintypresentinthequantizationprocess.ForasmallquantizationlevelQ,thequan-zationerrorissimilartothatofnoise.Soquantizationprocessactsasasourceofrandomnoise.Thevarianceofthequantizationnoiseis24离散时间控制系统课件第24页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-5(a)Blockdiagramofadata-acquisitionsystem;25离散时间控制系统课件第25页TransducerAphysicalvariablesuchasposition,velocity,acceleration,temperatureisfirstconvertedintoanelectricalsignal(avoltageorcurrent)AmplifierAmplifiesthevoltageoutputofthetransducerConvertsacurrentsignalintoavoltagesignalBuffersthesignal1-4DataAcquisition,ConversionandDistributionSystems26离散时间控制系统课件第26页Low-passfilterAttenuatesthehigh-frequencysignalcomponents,suchasnoise(electronicnoisesarerandominnatureandmaybereducedbylow-passfilters.However,suchcommonelectricalnoisesaspower-lineinterferencearegenerallyperiodicandmaybereducedbymeansofnotchfilters.)AnalogMultiplexingAdevicethatperformsthefunctionoftime-sharinganA/Dconverteramongmanyanalogchannels.1-4DataAcquisition,ConversionandDistributionSystems27离散时间控制系统课件第27页IfmanysignalsaretobeprocessedbyasingleA/Dandadigitalcontroller,thentheseinputsignalsmustbefedtothecontrollerthroughamultiplexer.Isamultipleswitchthatsequentiallyswitchesamonginputchannelsinsomeprescribedfashion.Atagiveninstantoftime,onlyoneswitchisinthe“on”position.Whentheswitchisoninagiveninputchannel,theinputsignalisconnectedtotheoutputofthemultiplexerforaspecifiedperiodoftime.1-4DataAcquisition,ConversionandDistributionSystems28离散时间控制系统课件第28页1-4DataAcquisition,ConversionandDistributionSystems29离散时间控制系统课件第29页DemultiplexerSeparatesthecompositeoutputdigitaldatafromthedigitalcontrollerintotheoriginalchannelsSample-and-HoldCircuitsSampler:covertananalogsignalintoatrainofamplitude-modulatedpulses.Holdcircuit:holdthevalueofthesampledpulsesignaloveraspecifiedperiodoftime1-4DataAcquisition,ConversionandDistributionSystems30离散时间控制系统课件第30页twooperationmodesThetrackingmode:theswitchisclosed,i.e.,theinputsignalisconnectedTheholdmode:theswitchisopen,i.e.,theinputsignalisdisconnectedWhenthesamplingdurationisnegligible,thesamplermaybeconsideredanidealsampler1-4DataAcquisition,ConversionandDistributionSystems31离散时间控制系统课件第31页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-7Sample-and-holdcircuit32离散时间控制系统课件第32页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-8Trackingmodeandholdmode33离散时间控制系统课件第33页Analog-to-DigitalConvertersTheprocessbywhichasampledanalogsignalisquantizedandconvertedtoabinarynumber.TypesoffrequentlyusedA/DConvertersSuccessive-approximationtypeIntegratingtypeCountertypeParalleltypeSelectioncriterionsofA/DconvertersConversionspeed,accuracy,sizeandcost1-4DataAcquisition,ConversionandDistributionSystems34离散时间控制系统课件第34页CountertypeA/D(thesimplestA/D)ClockpulsesareappliedtothedigitalcounterinsuchawaythattheoutputvoltageoftheD/Aconverter(thatis,partofthefeedbackloopintheA/Dconverter)issteppeduponeleastsignificantbit(LSB)atatime.Thentheoutputvoltageiscomparedwiththeanaloginputvoltageonceforeachpulse.Whentheoutputvoltagehasreachedthemagnitudeoftheinputvoltage,theclockpulsesarestopped.Thecounteroutputvoltageisthenthedigitaloutput.1-4DataAcquisition,ConversionandDistributionSystems35离散时间控制系统课件第35页Successive-approximationtype(mostfrequentlyused)Theprincipleis:Thesuccessive-approximationregister(SAR)firstturnsonthemostsignificantbit(halfthemaximum)andcomparesitwiththeanaloginput.Thecomparatordecideswhethertoleavethebitonorturnitoff.Iftheanaloginputvoltageislarger,themostsignificantbitisseton.Next,turnonbit2andthencomparetheanaloginputvoltagewiththree-fourthsofthemaximum.1-4DataAcquisition,ConversionandDistributionSystems36离散时间控制系统课件第36页Afterncomparisonsarecompleted,thedigitaloutputofthesuccessive-approximationregisterindicatesallthosebitsthatremainonandproducesthedesireddigitalcode.Thus,thistypeofA/Dconvertersets1biteachclockcycle,andsoitrequiresonlynclockcyclestogeneratenbits,wherenistheresolutionoftheconverterinbits.(Thenumbernofbitsemployeddeterminestheaccuracyofconversion.)Thetimerequiredfortheconversionisapproximately2µsecorlessfora12-bitconversion.1-4DataAcquisition,ConversionandDistributionSystems37离散时间控制系统课件第37页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-9Schematicdiagramofasuccessive-approximation-typeofA/Dconverter38离散时间控制系统课件第38页ErrorsinA/DConvertersTheinput-outputcharacteristicsofA/DConverterschangewithtimeandtemperature.Actualanalog-to-digitalsignalconvertersalwayshavesomeerrors,suchasoffseterror,linearityerror,andgainerror.CommercialconvertersarespecifiedforthreebasictemperaturerangesCommercial(0ºCto70ºC)Industrial(-25ºCto85ºC)Military(-55ºCto125ºC)1-4DataAcquisition,ConversionandDistributionSystems39离散时间控制系统课件第39页ErrorsinA/DConverters1-4DataAcquisition,ConversionandDistributionSystemsFigure1-10ErrorsinA/Dconverters(a)offseterror;(b)linearityerror;(c)gainerror40离散时间控制系统课件第40页Thereverseofthedata-acquisitionAdata-distributionsystemconsistsofregisters,ademultiplexer,digital-to-analogconverters,andholdcircuits.Itconvertsthesignalindigitalform(binarynumbers)intoanalogform.Theoutputoftheholdcircuitisfedtotheanalogactuator,which,inturn,directlycontrolstheplantunderconsideration.1-4DataAcquisition,ConversionandDistributionSystemsFigure1-5(b)blockdiagramofadatadistributionsystem41离散时间控制系统课件第41页Digital-to-AnalogConvertersForthefullrangeofthedigitalinput,thereare2ncorrespondingdifferentanalogvalues,including0.Forthedigital-to-analogconversion,thereisaone-to-onecorrespondencebetweenthedigitalinputandtheanalogoutputTwocommonD/AmethodsWeightedresistors:simpleincircuitconfiguration,butitsaccuracymaynotbeverygoodR-2Rladdernetwork:alittlemorecomplicatedincircuitconfiguration,butismoreaccurate.1-4DataAcquisition,ConversionandDistributionSystems42离散时间控制系统课件第42页Weightedresistors1-4DataAcquisition,ConversionandDistributionSystemsFigure1-11SchematicdiagramofaD/Aconverterusingweightedresistors43离散时间控制系统课件第43页WeightedresistorsTheinputresistorsoftheoperationalamplifierhavetheirresistancevaluesweightedinabinaryfashion.Whenthelogiccircuitreceivesbinary1,theswitchconnectstheresistortothereferencevoltage;whenthelogiccircuitreceivesbinary0,theswitchconnectstheresistortogroundNoticethat:asthenumberofbitsisincreased,therangeofresistorvaluesbecomeslargeandconsequentlytheaccuracybecomespoor1-4DataAcquisition,ConversionandDistributionSystems44离散时间控制系统课件第44页R-2Rladdernetwork1-4DataAcquisition,ConversionandDistributionSystemsFigure1-12n-bitD/AconverterusinganR-2Rladdercircuit45离散时间控制系统课件第45页Notethat:withtheexceptionofthefeedbackresistor(whichis3R),allresistorsinvolvedareeitherRor2R.Thismeansthatahighlevelofaccuracycanbeachieved1-4DataAcquisition,ConversionandDistributionSystems46离散时间控制系统课件第46页HoldCircuitsFillinthespacesbetweensamplingperiodsandthusroughlyreconstructtheoriginalanalogsignalTheholdcircuit:toextrapolatetheoutputsignalbetweensuccessivepointsaccordingtosomeprescribedmanner

Zero-order-hold:producesastaircasewaveform1-4DataAcquisition,ConversionandDistributionSystems47离散时间控制系统课件第47页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-13Outputfromazero-orderhold48离散时间控制系统课件第48页First-order-hold:generatesanoutputslopeequaltotheslopeofalinesegmentconnectingpreviousandpresentsamplesandprojectingitfromthevalueofthepresentsample.Moreaccuratelythanazero-orderhold.Iftheslopeoftheoriginalsignaldoesnotchangemuch,thepredictionisgood.If,however,theoriginalsignalreversesitsslope,thenthepredictioniswrong.Andtheoutputgoesinthewrongdirection,thuscausingalargeerrorforthesamplingperiodconsidered.1-4DataAcquisition,ConversionandDistributionSystems49离散时间控制系统课件第49页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-14Outputfromafirst-orderhold50离散时间控制系统课件第50页Interpolativefirst-orderhold:generatesastraight-lineoutputwhoseslopeisequaltothatjoiningtheprevioussamplevalueandthepresentsamplevalue,buttheprojectionismadefromthepredictionpoint.Itsaccuracyisbetterthanthatofotherholdcircuits,butthereisaone-samplingperioddelay.Fromtheviewpointofthestabilityofclosed-loopsystems,suchadelayisnotdesirable,andsotheinterpolativefirst-orderhold(polygonalhold)isnotusedincontrolsystemapplications.1-4DataAcquisition,ConversionandDistributionSystems51离散时间控制系统课件第51页1-4DataAcquisition,ConversionandDistributionSystemsFigure1-14Outputfromaninterpolativefirst-orderhold(polygonalhold)52离散时间控制系统课件第52页DigitalControllersandAnalogControllerAnalogControllersrepresentthevariablesinanequationbycontinuousphysicalquantities.caneasilybedesignedtoservesatisfactoryasnon-decision-makingcontrollersthecostincreasesrapidlyasthecomplexityofthecomputationsincreases1-5ConcludingComments53离散时间控制系统课件第53页DigitalCo