机电控制总复习

ProblemsProblemsProblemsProblem3-1ConsiderthegearreducershowninFig.3.1.Letthediameterofthegearoninputshaftbeequaltod1=2.0inandwidthw1=0.5in.Assumethatthegearismadeofmaterialsteelandthatitisasolidframewithoutanyholes.Theoutputgearhasthesamewidthandmaterial,andthegearreductionfrominputtooutputisN=5,(d2=10.0in).Thelengthanddiametersoftheshaftsthatextendtothesidesofthegearsareds1=1.0in,ds2=1.0in.andls1=1.0in,ls2=1.0in.LetusconsiderthatthereisanetloadtorqueofTL2=50lb/inattheoutputshaft.(a)Determinethenetrotaryinertiareflectedontheinputshaftduetotwogearsandtwoshafts.(b)Determinethenecessarytorqueattheinputshafttobalancetheloadtorque.(c)Iftheinputshaftisactuatedbyamotorthatiscontrolledwith1/10degreeaccuracy,whatistheangularpositioningaccuracythatcanbeprovidedattheoutputshaft?ProblemsRegardlessoftheefficiency:22112snetsJJJJJN2411111112222ddJmw412(0.286/386)0.522425.8210lbinsec2411111112222sssssddJml411.0(0.286/386)1.022527.2710lbinsecProblems2422222112222ddJmw4110(0.286/386)0.52220.3637lbinsec2422222112222sssssddJml411.0(0.286/386)1.022527.2710lbinsec2221120.01521lbinsecsnetsJJJJJNProblems,5010lb/in5outineffTTN1110.02degree510outinNProblemsConsideratranslational(linear)positionstagedrivenbyaservomotor(Fig.3.3).Thetravelrangeofthetableis50cm.Therequiredpositionaccuracyofthestageis0.1μm.Assumethatamotor-basedrotaryincrementalencoderisusedforpositionsensing.Whatshouldbetheresolutionoftheencoder,iftheball-screwpitchis0.5rev/mm?Ifthedecodercircuitfortheencodercanhandleencodersignalfrequencyupto1MHz,whatistheimplicationofthisonthemotionlimits?Problem6-2ProblemsFIGURE3.3:Rotary-to-translationalmotionconversionmechanism:lead-screworball-screwwithlinearguidebearings3220.50.1102/20000pxrad20000-lines/rev6max1050rev/sec3000rpm20000wmaxmax50100/0.5wVmmspProblemsConsiderarotarymotionaxisanditsspeedcontrol(i.e.speedcontrolofaspindleofaCNCmachinetoolorspeedcontrolofaprecisionconveyor).Assumethatbothhigh-speed(wmax=3600rpm)andlow-speed(wmin=1rpm)speedcontrolsarerequiredwith0.01rpmregulationaccuracy.(a)Determinespecificationsforatachometertomeetthespeedcontrolrequirements.(b)Selectanopticalincrementalencoderandderivespeedinformationfromthepositionpulsesdigitally.Whatisthespeedestimationaccuracyatminimumspeedifthesamplingperiodis1.0msec?Showhowthespeedestimationcanbeimprovedwithatimeperiodmeasurementtechnique.Whatisthemaximumpulsefrequencyoftheselectedencoderatthemaximumspeed?Problem6-3Problems(a)Thespeed-to-voltagegain,Maximumoutputvoltage,Maximumspeed，Maximumexpectedripplevoltage,(c)Weselecta10000lines/revincrementalencoder.Sothederivedspeedis:vwK0.010.000278%3600max3600vwVKmax/vwVK60/0.001/100006wNNrpmNisthepulsecountin1msec.Thespeedestimationaccuracy:160/0.001/100006rpmProblemsThetimeintervalforapulseat1rpmspeedis:600.006610000smsIfweuseatimeperiodmeasurementwith1-μsecresolution,themeasuredtimewillbe0.006001sor0.005999sec,sothespeedwillbe:11/0.00600160/100000.9998wrpm21/0.00599960/100001.00017wrpmSpeedestimationcanbeimprovedgreatly.Themaximumpulsefrequencyatmaximumspeedis:3600/6010000600000fHzProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsProblemsAssumeazerolappedfour-edgeslidevalvewhichhasa20spool,theradialclearanceis10μ,thevalveopenwidthisfullcircle.Pleasecalculatethethreevalvegainsatzeroposition.（viscousμ=40×10-6m2/s×900kg/m3）kgsmDrWrKccc/10713.1900104032)1010(10201416.3323241162632220smPWCKsdq/106.4900/101010201416.362.02630kgsmKKKcqP221111000104.210713.1106.4ProblemsConsideraDCmotor(orequivalent)motioncontrolsystem.AssumethattheDCbusvoltageavailableisVs=90VDC.ThebackEMFconstantofthemotorisKe=20V/krpm.ThenominalterminalresistanceofthemotorstatorwindingsisR=10Ohm.Determinethemaximumno-loadspeedandthemaximumtorquecapacityatstall(zerospeed)ofthemotorinsteadystate.Problem8-3max901000450020seVwrpmKmax20901.71910002/6010sTVTKNmRProblemsAssumeaelectro-hydraulicpositioncontrolsystemforpureinertialoads,inwhichthehydraulicnaturalfrequencyisωh=3201/s,dampingratioisζh=0.25,Valve’sflowgainiskq=40(cm3/s)/mA,forhydrauliccylinderAp=20cm2,positionfeedbackgainiskf=0.4V/cm,pleasedeterminethevalveofKaifthegainmarginisatleast6dB.Problem11-1vhhK416/0.2532020100.10.410040101000afqhhhhafqKKKAAKAVKKFor6dBgainmargin:ProblemsAnalyzespeedcontrolsystemasshowninfigure.Pleasedrawblockdiagramofthesystemandwritedownitsopen-looptransferfunction.Ifthissystemiscompensatedbyanintegralcontroller,pleasedeterminetheintegralgainifthegainmarginisatleast6dB.Problem11-2+—ValveKq,KcLoadM,BAmplifierCylinderA,VaKuiufuSpeedfeedbackKVProblemsBlockdiagram：Open-looptransferfunction：+—uiufuaKvvK12/22ssAKhhhq12/)(22ssAKKKsGhhhvaqProblemsInwhich:Aftercompensatedbyanintegralcontroller:Forgainmarginof6dB：Hence：)(42MVAEhhhphchMKVABVMEAK4)/()12(/)(22sssA