離散時(shí)間控制系統(tǒng)課件

Computer-ControlledSystems10/2/離散時(shí)間控制系統(tǒng)課件第1頁CourseInformationTime:13:30-15:10pm,Wednesday 10:00-11:40am,Friday(evenweeks)Venue:綜B204References:離散時(shí)間控制系統(tǒng)(英文版

第2版)，KatsuhikoOgata，機(jī)械工業(yè)出版社，離散時(shí)間控制系統(tǒng)(漢字版)，KatsuhikoOgata，陳杰，蔡濤等譯，機(jī)械工業(yè)出版社，GradingProcedure:in-termevaluationexperimentalresultsfinalpaperexamination.2離散時(shí)間控制系統(tǒng)課件第2頁Chapter1IntroductiontoDiscrete-Time3離散時(shí)間控制系統(tǒng)課件第3頁4Contents1-1Introduction1-2DigitalControlSystems1-3QuantizingandQuantizationError1-4DataAcquisition,ConversionandDistributionSystems1-5ConcludingComments4離散時(shí)間控制系統(tǒng)課件第4頁1-1IntroductionDigitalControllerArapidincreaseintheuseofdigitalcontrollers5離散時(shí)間控制系統(tǒng)課件第5頁DigitalControllerThetrendisduetoDigitalcontrolcanachieveoptimalperfor-mance,haveDecision-makingcapabilityandflexibilityinthecontrolprogramAvailablityoflow-costdigitalcomputersAdvantagesofdigitalsignals1-1Introduction6離散時(shí)間控制系統(tǒng)課件第6頁TypesofSignalsContinuous-timesignal:AsignaldefinedoveracontinuousrangeoftimeAnalogsignal:AsignaldefinedoveracontinuousrangeoftimewhoseamplitudecanassumeacontinuousrangeofvaluesAcontinuous-timequantizedsignalDiscrete-timesignal:Asignaldefinedonlyatdiscreteinstantsoftime1-1Introduction7離散時(shí)間控制系統(tǒng)課件第7頁Sampled-datasignal:Adiscrete-timesignaliftheamplitudecanassumeacontinuousrangeofvaluesDigitalsignal:Adiscrete-timesignalwithquantizedamplitudeComparisonDiscrete-time,digital,sampleddatasignal(controlsystem)Continuous-time,analogsignal(controlsystem)1-1Introduction8離散時(shí)間控制系統(tǒng)課件第8頁1-1Introduction9離散時(shí)間控制系統(tǒng)課件第9頁SystemsDealtWithinThisBookLinearandtimeinvariantDiscrete-TimeControlSystemsoneormorevariablescanchangeonlyatdiscreteinstantsoftime.TheseinstantsmayspecifythetimesatwhichsomephysicalmeasurementisperformedorthememoryofadigitalcomputerisreadoutDescribedinlineardifferenceequationswithconstantcoefficients1-1Introduction10離散時(shí)間控制系統(tǒng)課件第10頁1-2DigitalControlSystemsFigure1-2Blockdiagramofadigitalcontrolsystem11離散時(shí)間控制系統(tǒng)課件第11頁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離散時(shí)間控制系統(tǒng)課件第12頁TypesofSamplingOperationsPeriodicsamplingtk=kT(k=0,1,2,…)Multiple-ordersamplingtk+r-tk=constantMultiple-ratesamplingAdigitalcontrolsystemhavedifferentsam-plingperiodsindifferentfeedbackpathsRandomsamplingtkisarandomvariable1-2DigitalControlSystems13離散時(shí)間控制系統(tǒng)課件第13頁SignalFormsinaDigitalControlSystem1-2DigitalControlSystemsFigure1-3Blockdiagramofadigitalcontrolsystemshowingsignalsinbinaryorgraphicform14離散時(shí)間控制系統(tǒng)課件第14頁D/AandholdDigital-to-AnalogConverter(D/A)Alsocalledadecoder,isadevicethatconvertsadigitalsignalintoansampled-datasignal.Holdreconstructtheanalogsignalthathasbeentransmittedasatrainofpulsesamples,i.e.fillinthespacesbetweensamplingperiodsandthusroughlyreconstructtheoriginalanalogsignal1-2DigitalControlSystems15離散時(shí)間控制系統(tǒng)課件第15頁P(yáng)lantorProcessAplantisanphysicalobjecttobecontrolled.Wecallanyoperationtobecontrolledaprocess.AccuratemodelingisperhapsthemostdifficultpartinthedesignofcontrolsystemTransducerIsadevicethatconvertsaninputsignalintoanoutputsignalofanotherform,suchasadevicethatconvertsapressuresignalintoanvoltageoutput.Analogtransducer,sampled-datatransducer,digitaltransducer1-2DigitalControlSystems16離散時(shí)間控制系統(tǒng)課件第16頁ThemainfunctionsinvolvedinA/Dconversionaresampling,amplitudequantizingandcodingAmplitudequantizingRepresentacontinuousoranalogsignalbyafinitenumberofdiscretestatesiscalledamplitudequantizationCodingorEncodingRepresentasamplevaluebyanumericalcode1-3QuantizingandQuantizationError17離散時(shí)間控制系統(tǒng)課件第17頁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離散時(shí)間控制系統(tǒng)課件第18頁QuantizationErrorSincedigitaloutputcanassumeonlyafinitenumberoflevels,ananalognumbermustberoundedofftothenearestdigitallevel.Quantizationerrorvariesbetween0and

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

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