离散时间控制系统ch1

2019/9/5Computer-ControlledSystems2CourseInformationTime:13:30-15:10pm,Wednesday10:00-11:40am,Friday(evenweeks)Venue:综B204References: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，2006GradingProcedure:in-termevaluationexperimentalresultsfinalpaperexamination.344Contents1-1Introduction1-2DigitalControlSystems1-3QuantizingandQuantizationError1-4DataAcquisition,ConversionandDistributionSystems1-5ConcludingComments51-1IntroductionDigitalControllerArapidincreaseintheuseofdigitalcontrollers6DigitalControllerThetrendisduetoDigitalcontrolcanachieveoptimalperfor-mance,haveDecision-makingcapabilityandflexibilityinthecontrolprogramAvailablityoflow-costdigitalcomputersAdvantagesofdigitalsignals1-1Introduction7TypesofSignalsContinuous-timesignal:AsignaldefinedoveracontinuousrangeoftimeAnalogsignal:AsignaldefinedoveracontinuousrangeoftimewhoseamplitudecanassumeacontinuousrangeofvaluesAcontinuous-timequantizedsignalDiscrete-timesignal:Asignaldefinedonlyatdiscreteinstantsoftime1-1Introduction8Sampled-datasignal:Adiscrete-timesignaliftheamplitudecanassumeacontinuousrangeofvaluesDigitalsignal:Adiscrete-timesignalwithquantizedamplitudeComparisonDiscrete-time,digital,sampleddatasignal(controlsystem)Continuous-time,analogsignal(controlsystem)1-1Introduction91-1Introduction10SystemsDealtWithinThisBookLinearandtimeinvariantDiscrete-TimeControlSystemsoneormorevariablescanchangeonlyatdiscreteinstantsoftime.TheseinstantsmayspecifythetimesatwhichsomephysicalmeasurementisperformedorthememoryofadigitalcomputerisreadoutDescribedinlineardifferenceequationswithconstantcoefficients1-1Introduction111-2DigitalControlSystemsFigure1-2Blockdiagramofadigitalcontrolsystem12S/HandA/D(A/D)Sample-and-Hold(S/H)SamplingProcesses,replaceoriginalcontinuous-timesignalbyasequenceofvaluesatdiscrete-timetimepointsacircuitthatreceivesanaloginputsignalandholdsthissignalataconstantvalueforaspecifiedperiodoftime.Analog-to-DigitalConverter(A/D)Alsocalledanencoder,isadevicethatconvertsananalogsignalintoadigitalsignal,usuallyanumericallycodedsignal.AS/HcircuitisoftenanintegralpartofacommerciallyavailableA/Dconverter.1-2DigitalControlSystems13TypesofSamplingOperationsPeriodicsamplingtk=kT(k=0,1,2,…)Multiple-ordersamplingtk+r-tk=constantMultiple-ratesamplingAdigitalcontrolsystemhavedifferentsam-plingperiodsindifferentfeedbackpathsRandomsamplingtkisarandomvariable1-2DigitalControlSystems14SignalFormsinaDigitalControlSystem1-2DigitalControlSystemsFigure1-3Blockdiagramofadigitalcontrolsystemshowingsignalsinbinaryorgraphicform15D/AandholdDigital-to-AnalogConverter(D/A)Alsocalledadecoder,isadevicethatconvertsadigitalsignalintoansampled-datasignal.Holdreconstructtheanalogsignalthathasbeentransmittedasatrainofpulsesamples,i.e.fillinthespacesbetweensamplingperiodsandthusroughlyreconstructtheoriginalanalogsignal1-2DigitalControlSystems16PlantorProcessAplantisanphysicalobjecttobecontrolled.Wecallanyoperationtobecontrolledaprocess.AccuratemodelingisperhapsthemostdifficultpartinthedesignofcontrolsystemTransducerIsadevicethatconvertsaninputsignalintoanoutputsignalofanotherform,suchasadevicethatconvertsapressuresignalintoanvoltageoutput.Analogtransducer,sampled-datatransducer,digitaltransducer1-2DigitalControlSystems17ThemainfunctionsinvolvedinA/Dconversionaresampling,amplitudequantizingandcodingAmplitudequantizingRepresentacontinuousoranalogsignalbyafinitenumberofdiscretestatesiscalledamplitudequantizationCodingorEncodingRepresentasamplevaluebyanumericalcode1-3QuantizingandQuantizationError18QuantizingThestandardnumbersystemisthebinarynumbersystem.Thecodegroupconsistsofnpulseseachindicatingeither‘on’(1)or‘off’(0).Inthecaseofquantizing,n‘on-off’pulsescanrepresent2namplitudelevelsoroutputstates.ThequantizationlevelQ:therangebetweentwoadjacentdecisionpoints:Q=FSR/2n,FSRisthefull-scalerange.MSBisthemostsignificantbit,hasthemostweight(onehalfofthefullscale)LSBistheleastsignificantbit,hastheleastweightLSB=FSR/2n1-3QuantizingandQuantizationError19QuantizationErrorSincedigitaloutputcanassumeonlyafinitenumberoflevels,ananalognumbermustberoundedofftothenearestdigitallevel.Quantizationerrorvariesbetween0and1/2Q.QuantizationerrordependsonfinenessoftheQ,andcanbemadeassmallasdesiredbymakingQsmaller.1-3QuantizingandQuantizationError201-3QuantizingandQuantizationErrorTodeterminethedesiredsizeofthequantizationlevelinagivendigitalcontrolsystem,theengineermusthaveagoodunderstandingoftherelationshipbetweenthesizeofthequantizationlevelandtheresultingerror.21Forananaloginputx(t),theoutputy(t)takesononlyafinitenumberoflevels,whichareintegralmultiplesofthequantizationlevelQ1-3QuantizingandQuantizationErrorFigure1-4(a)Blockdiagramofaquantizeranditsinput-outputcharacteristics22Round-offerrorTheerrorresultingfromneglectingtheremainingdigitsiscalledround-offerror.Quantizationerrorisaround-offerrorThefinerthequantizationlevelis,thesmallertheround-offerror.1-3QuantizingandQuantizationError