机械工程师手册,仪器仪表,系统,控制系统,和MEMch11.doc

383CHAPTER11BASICCONTROLSYSTEMSDESIGNWilliamJ.PalmIIIDepartmentofMechanicalEngineeringUniversityofRhodeIslandKingston,RhodeIsland1INTRODUCTION3832CONTROLSYSTEMSTRUCTURE3862.1AStandardDiagram3862.2TransferFunctions3882.3System-TypeNumberandErrorCoefcients3883TRANSDUCERSANDERRORDETECTORS3893.1DisplacementandVelocityTransducers3893.2TemperatureTransducers3913.3FlowTransducers3913.4ErrorDetectors3923.5DynamicResponseofSensors3924ACTUATORS3924.1ElectromechanicalActuators3924.2HydraulicActuators3944.3PneumaticActuators3965CONTROLLAWS3995.1ProportionalControl3995.2IntegralControl4015.3Proportional-plus-IntegralControl4035.4DerivativeControl4045.5PIDControl4056CONTROLLERHARDWARE4056.1FeedbackCompensationandControllerDesign4056.2ElectronicControllers4066.3PneumaticControllers4076.4HydraulicControllers4077FURTHERCRITERIAFORGAINSELECTION4097.1PerformanceIndices4107.2Optimal-ControlMethods4117.3TheZieglerNicholsRules4127.4NonlinearitiesandControllerPerformance4137.5ResetWindup4148COMPENSATIONANDALTERNATIVECONTROLSTRUCTURES4148.1SeriesCompensation4158.2FeedbackCompensationandCascadeControl4158.3FeedforwardCompensation4158.4State-VariableFeedback4178.5PseudoderivativeFeedback4189GRAPHICALDESIGNMETHODS4189.1TheNyquistStabilityTheorem4199.2SystemswithDead-TimeElements4209.3Open-LoopDesignforPIDControl4209.4DesignwiththeRootLocus42110PRINCIPLESOFDIGITALCONTROL42410.1DigitalControllerStructure42510.2DigitalFormsofPIDControl42511UNIQUELYDIGITALALGORITHMS42711.1DigitalFeedforwardCompensation42711.2ControlDesigninthez-Plane42811.3DirectDesignofDigitalAlgorithms43212HARDWAREANDSOFTWAREFORDIGITALCONTROL433RevisedfromWilliamJ.PalmIII,Modeling,AnalysisandControlofDynamicSystems,2nded.,Wiley,2000,bypermissionofthepublisher.Mechanical Engineers Handbook: Instrumentation, Systems, Controls, and MEMS, Volume 2, Third Edition.Edited by Myer KutzCopyright 2006 by John Wiley & Sons, Inc.384BasicControlSystemsDesignFigure1Blockdiagramofthethermostatsystemfortemperaturecontrol.112.1DigitalControlHardware43412.2SoftwareforDigitalControl43612.3EmbeddedControlSystemsandHardware-in-the-LoopTesting43813SOFTWARESUPPORTFORCONTROLSYSTEMDESIGN43813.1SoftwareforGraphicalDesignMethods43813.2SoftwareforControlSystemsSimulation43814FUTURETRENDSINCONTROLSYSTEMS43914.1FuzzyLogicControl44114.2NonlinearControl44114.3AdaptiveControl44114.4OptimalControl442REFERENCES4421INTRODUCTIONThepurposeofacontrolsystemistoproduceadesiredoutput.Thisoutputisusuallyspeciedbythecommandinputandisoftenafunctionoftime.Forsimpleapplicationsinwell-structuredsituations,sequencingdevicesliketimerscanbeusedasthecontrolsystem.Butmostsystemsarenotthateasytocontrol,andthecontrollermusthavethecapabilityofreactingtodisturbances,changesinitsenvironment,andnewinputcommands.Thekeyelementthatallowsacontrolsystemtodothisisfeedback,whichistheprocessbywhichasystemsoutputisusedtoinuenceitsbehavior.Feedbackintheformoftheroom-temperaturemeasurementisusedtocontrolthefurnaceinathermostaticallycontrolledheatingsystem.Figure1showsthefeedbackloopinthesystemsblockdiagram,whichisagraphicalrepresentationofthesystemscontrolstructureandlogic.AnothercommonlyfoundcontrolsystemisthepressureregulatorshowninFig.2.Feedbackhasseveralusefulproperties.Asystemwhoseindividualelementsarenon-linearcanoftenbemodeledasalinearoneoverawiderrangeofitsvariableswiththeproperuseoffeedback.Thisisbecausefeedbacktendstokeepthesystemnearitsreferenceoperationcondition.Systemsthatcanmaintaintheoutputnearitsdesiredvaluedespitechangesintheenvironmentaresaidtohavegooddisturbancerejection.Oftenwedonothaveaccuratevaluesforsomesystemparameterorthesevaluesmightchangewithage.Feedbackcanbeusedtominimizetheeffectsofparameterchangesanduncertainties.Asystemthathasbothgooddisturbancerejectionandlowsensitivitytoparametervariationisrobust.Theapplicationthatresultedinthegeneralunderstandingofthepropertiesoffeed-backisshowninFig.3.TheelectronicampliergainAislarge,butweareuncertainofitsexactvalue.WeusetheresistorsR1andR2tocreateafeedbacklooparoundtheamplierandpickR1andR2tocreateafeedbacklooparoundtheamplierandR1andR2sothatAR2/R11.ThentheinputoutputrelationbecomeseoR1ei/R2,whichisindependent1Introduction385Figure2Pressureregulator:(a)cutawayview;(b)blockdiagram.1Figure3Aclosed-loopsystem.ofAaslongasAremainslarge.IfR1andR2areknownaccurately,thenthesystemgainisnowreliable.Figure4showstheblockdiagramofaclosed-loopsystem,whichisasystemwithfeedback.Anopen-loopsystem,suchasatimer,hasnofeedback.Figure4servesasafocusforoutliningtheprerequisitesforthischapter.ThereadershouldbefamiliarwiththetransferfunctionconceptbasedontheLaplacetransform,thepulsetransferfunctionbasedonthez-transform,fordigitalcontrol,andthedifferentialequationmodelingtechniquesneededtoobtainthem.Itisalsonecessarytounderstandblockdiagramalgebra,characteristicroots,thenal-valuetheorem,andtheiruseinevaluatingsystemresponseforcommoninputslikethestepfunction.AlsorequiredarestabilityanalysistechniquessuchastheRouthcriterion386BasicControlSystemsDesignFigure4Feedbackcompensationofanamplier.Figure5Positioncontrolsystemusingadcmotor.1andtransientperformancespecicationssuchasthedampingratio,naturalfrequencyn,dominanttimeconstant,maximumovershoot,settlingtime,andbandwidth.Theabovematerialisreviewedinthepreviouschapter.TreatmentindepthisgiveninRefs.14.2CONTROLSYSTEMSTRUCTURETheelectromechanicalpositioncontrolsystemshowninFig.5illustratesthestructureofatypicalcontrolsystem.AloadwithaninertiaIistobepositionedatsomedesiredangler.Adcmotorisprovidedforthispurpose.Thesystemcontainsviscousdamping,andadis-turbancetorqueTdactsontheload,inadditiontothemotortorqueT.Becauseofthedisturbance,theangularpositionoftheloadwillnotnecessarilyequalthedesiredvaluer.Forthisreason,apotentiometer,orsomeothersensorsuchasanencoder,isusedtomeasurethedisplacement.Thepotentiometervoltagerepresentingthecontrolledpositioniscomparedtothevoltagegeneratedbythecommandpotentiometer.Thisdeviceenablestheoperatortodialinthedesiredangler.Theamplierseesthedifferenceebetweenthetwopotentiometervoltages.Thebasicfunctionoftheamplieristoincreasethesmallerrorvoltageeuptothevoltagelevelrequiredbythemotorandtosupplyenoughcurrentrequiredbythemotortodrivetheload.Inaddition,theampliermayshapethevoltagesignalincertainwaystoimprovetheperformanceofthesystem.Thecontrolsystemisseentoprovidetwobasicfunctions:(1)torespondtoacommandinputthatspeciesanewdesiredvalueforthecontrolledvariableand(2)tokeepthecontrolledvariablenearthedesiredvalueinspiteofdisturbances.Thepresenceofthefeed-backloopisvitaltobothfunctions.AblockdiagramofthissystemisshowninFig.6.Thepowersuppliesrequiredforthepotentiometersandtheamplierarenotshowninblockdiagramsofcontrolsystemlogicbecausetheydonotcontributetothecontrollogic.2.1AStandardDiagramTheelectromechanicalpositioningsystemtsthegeneralstructureofacontrolsystem(Fig.7).Thisgurealsogivessomestandardterminology.Notallsystemscanbeforcedintothisformat,butitservesasareferencefordiscussion.2ControlSystemStructure387Figure6BlockdiagramofthepositioncontrolsystemshowninFig.5.1Figure7Terminologyandbasicstructureofafeedbackcontrolsystem.1Thecontrollerisgenerallythoughtofasalogicelementthatcomparesthecommandwiththemeasurementoftheoutputanddecideswhatshouldbedone.Theinputandfeedbackelementsaretransducersforconvertingonetypeofsignalintoanothertype.Thisallowstheerrordetectordirectlytocomparetwosignalsofthesametype(e.g.,twovoltages).Notallfunctionsshowupasseparatephysicalelements.TheerrordetectorinFig.5issimplytheinputterminalsoftheamplier.Thecontrollogicelementsproducethecontrolsignal,whichissenttothenalcontrolelements.Thesearethedevicesthatdevelopenoughtorque,pressure,heat,andsoontoinuencetheelementsundercontrol.Thus,thenalcontrolelementsarethemuscleofthesystem,whilethecontrollogicelementsarethebrain.Hereweareprimarilyconcernedwiththedesignofthelogictobeusedbythisbrain.388BasicControlSystemsDesignTheobjecttobecontrolledistheplant.Themanipulatedvariableisgeneratedbythenalcontrolelementsforthispurpose.Thedisturbanceinputalsoactsontheplant.Thisisaninputoverwhichthedesignerhasnoinuenceandperhapsforwhichlittleinformationisavailableastothemagnitude,functionalform,ortimeofoccurrence.Thedisturbancecanbearandominput,suchaswindgustonaradarantenna,ordeterministic,suchasCoulombfrictioneffects.Inthelattercase,wecanincludethefrictionforceinthesystemmodelbyusinganominalvalueforthecoefcientoffriction.Thedisturbanceinputwouldthenbethedeviationofthefrictionforcefromthisestimatedvalueandwouldrepresenttheuncer-taintyinourestimate.SeveralcontrolsystemclassicationscanbemadewithreferencetoFig.7.Aregulatorisacontrolsysteminwhichthecontrolledvariableistobekeptconstantinspiteofdistur-bances.Thecommandinputforaregulatorisitssetpoint.Afollow-upsystemissupposedtokeepthecontrolvariablenearacommandvaluethatischangingwithtime.Anexampleofafollow-upsystemisamachinetoolinwhichacuttingheadmusttraceaspecicpathinordertoshapetheproductproperly.Thisisalsoanexampleofaservomechanism,whichisacontrolsystemwhosecontrolledvariableisamechanicalposition,velocity,oracceler-ation.Athermostatsystemisnotaservomechanism,butaprocesscontrolsystem,wherethecontrolledvariabledescribesathermodynamicprocess.Typically,suchvariablesaretemperature,pressure,owrate,liquidlevel,chemicalconcentration,andsoon.2.2TransferFunctionsAtransferfunctionisdenedforeachinputoutputpairofthesystem.Aspecictransferfunctionisfoundbysettingallotherinputstozeroandreducingtheblockdiagram.TheprimaryorcommandtransferfunctionforFig.7isA(s)G(s)G(s)G(s)C(s)amp(1)V(s)1G(s)G(s)G(s)H(s)ampThedisturbancetransferfunctionisQ(s)G(s)C(s)p(2)D(s)1G(s)G(s)G(s)H(s)ampThetransferfunctionsofagivensystemallhavethesamedenominator.2.3System-TypeNumberandErrorCoefcientsTheerrorsignalinFig.4isrelatedtotheinputas1E(s)R(s)(3)1G(s)H(s)Ifthenal-valuetheoremcanbeapplied,thesteady-stateerrorissR(s)elim(4)ss1G(s)H(s)s0ThestaticerrorcoefcientciisdenedasiclimsG(s)H(s)(5)is03TransducersandErrorDetectors389Table1Steady-StateErroressforDifferentSystem-TypeNumbersR(s)System-TypeNumbern0123Step1/s11骠C0000Ramp1/s2骠1C100Parabola1/s3骠骠1C20AsystemisoftypenifG(s)H(s)canbewrittenassnF(s).Table1relatesthesteady-stateerrortothesystemtypeforthreecommoninputsandcanbeusedtodesignsystemsforminimumerror.Thehigherthesystemtype,thebetterthesystemisabletofollowarapidlychanginginput.Buthighertypesystemsaremoredifculttostabilize,soacompromisemustbemadeinthedesign.Thecoefcientsc0,c1,andc2arecalledtheposition,velocity,andaccelerationerrorcoefcients.3TRANSDUCERSANDERRORDETECTORSThecontrolsystemstructureshowninFig.7indicatesaneedforphysicaldevicestoperformseveraltypesoffunctions.Herewepresentabriefoverviewofsomeavailabletransducersanderrordetectors.ActuatorsanddevicesusedtoimplementthecontrollogicarediscussedinSections4and5.3.1DisplacementandVelocityTransducersAtransducerisadevicethatconvertsonetypeofsignalintoanothertype.Anexampleisthepotentiometer,whichconvertsdisplacementintovoltage,asinFig.8.Inadditiontothisconversion,thetransducercanbeusedtomakemeasurements.Insuchapplications,thetermsensorismoreappropriate.Displacementcanalsobemeasuredelectricallywithalinearvariabledifferentialtransformer(LVDT)orasynchro.AnLVDTmeasuresthelineardis-placementofamovablemagneticcorethroughaprimarywindingandtwosecondarywind-ings(Fig.9).Anacvoltageisappliedtotheprimary.Thesecondariesareconnectedtogetherandalsotoadetectorthatmeasuresthevoltageandphasedifference.Aphasedifferenceof0骠correspondstoapositivecoredisplacement,while180骠indicatesanegativedisplacement.Theamountofdisplacementisindicatedbytheamplitudeoftheacvoltageinthesecondary.Thedetectorconvertsthisinformationintoadcvoltageeo,suchthateo骠Kx.TheLVDTissensitivetosmalldisplacements.Twoofthemcanbewiredtogethertoformanerrordetector.Asynchroisarotarydifferentialtransformer,withangulardisplacementaseithertheinputoroutput.Theyareoftenusedinpairs(atransmitterandareceiver)wherearemoteindicationofangulardisplacementisneeded.Whenatransmitterisusedwithasynchrocontroltransformer,twoangulardisplacementscanbemeasuredandcompared(Fig.10).Theoutputvoltageeoisapproximatelylinearwithangulardifferencewithin骠70骠,sothateo骠K(骠1骠骠2).390BasicControlSystemsDesignFigure8Rotarypotentiometer.1Figure9Linearvariabledifferentialtrans-former.1Figure10Synchrotransmittercontroltransformer.1Displacementmeasurementscanbeusedtoobtainforcesandaccelerations.Forexam-ple,thedisplacementofacalibratedspringindicatestheappliedforce.Theaccelerometerisanotherexample.Stillanotheristhestraingageusedforforcemeasurement.Itisbasedonthefactthattheresistanceofanewirechangesasitisstretched.Thechangeinresistanceisdetectedbyacircuitthatcanbecalibratedtoindicatetheappliedforce.Sensorsutilizingpiezoelectricelementsarealsoavailable.Velocitymeasurementsincontrolsystemsaremostcommonlyobtainedwithatachom-eter.Thisisessentiallyadcgenerator(thereverseofadcmotor).Theinputismechanical(avelocity).Theoutputisageneratedvoltageproportionaltothevelocity.Translational3TransducersandErrorDetectors391velocitycanbemeasuredbyconvertingittoangularvelocitywithgears,forexample.Ta-chometersusingacsignalsarealsoavailable.Othervelocitytransducersincludeamagneticpickupthatgeneratesapulseeverytimeageartoothpasses.Ifthenumberofgearteethisknown,apulsecounterandtimercanbeusedtocomputetheangularvelocity.Thisprincipleisalsoemployedinturbineowmeters.Asimilarprincipleisemployedbyopticalencoders,whichareespeciallysuitablefordigitalcontrolpurposes.Thesedevicesusearotatingdiskwithalternatingtransparentandopaqueelementswhosepassageissensedbylightbeamsandaphotosensorarray,whichgeneratesabinary(onoff)trainofpulses.Therearetwobasictypes:theabsoluteencoderandtheincrementalencoder.Bycountingthenumberofpulsesinagiventimeinterval,theincrementalencodercanmeasuretherotationalspeedofthedisk.Byusingmultipletracksofelements,theabsoluteencodercanproduceabinarydigitthatindicatestheamountofrotation.Hence,itcanbeusedasapositionsensor.Mostencodersgenerateatrainoftransistortransistorlogic(TTL)voltagelevelpulsesforeachchannel.TheincrementalencoderoutputcontainstwochannelsthateachproduceNpulseseveryrevolution.Theencoderismechanicallyconstructedsothatpulsesfromonechannelareshiftedrelativetotheotherchannelbyaquarterofapulsewidth.Thus,eachpulsepaircanbedividedintofoursegmentscalledquadratures.Theencoderoutputconsistsof4Nquadraturecountsperrevolution.Thepulseshiftalsoallowsthedirectionofrotationtobedeterminedbydetectingwhichchannelleadstheother.Theencodermightcontainathirdchannel,knownasthezero,index,ormarkerchannel,thatproducesapulseonceperrevolution.Thisisusedforinitialization.Thegainofsuchanincrementalencoderis4N/2.Thus,anencoderwith1000pulsesperchannelperrevolutionhasagainof636countsperradian.Ifanabsoluteencoderproducesabinarysignalwithnbits,themaximumnumberofpositionsitcanrepresentis2n,anditsgainis2n/2.Thus,a16-bitabsoluteencoderhasagainof216/210,435countsperradian.3.2TemperatureTransducersWhentwowiresofdissimilarmetalsarejoinedtogether,avoltageisgeneratedifthejunc-tionsareatdifferenttemperatures.Ifthereferencejunctioniskeptataxed,knowntem-perature,thethermocouplecanbecalibratedtoindicatethetemperatureattheotherjunctionintermsofthevoltagev.Electricalresistancechangeswithtemperature.Platinumgivesalinearrelationbetweenresistanceandtemperature,whilenickelislessexpensiveandgivesalargeresistancechangeforagiventemperaturechange.Seminconductorsdesignedwiththispropertyarecalledthermistors.Differentmetalsexpandatdifferentrateswhenthetemperatureisincreased.Thisfactisusedinthebimetallicstriptransducerfoundinmosthomethermostats.Twodissimilarmetalsarebondedtogethertoformthestrip.Asthetemperaturerises,thestripcurls,breakingcontactandshuttingoffthefurnace.Thetemper-aturegapcanbeadjustedbychangingthedistancebetweenthecontacts.Themotionalsomovesapointeronthetemperaturescaleofthethermostat.Finally,thepressureofauidinsideabulbwillchangeasitstemperaturechanges.Ifthebulbuidisair,thedeviceissuitableforuseinpneumatictemperaturecontrollers.3.3FlowTransducersAowrateqcanbemeasuredbyintroducingaowrestriction,suchasanoriceplate,andmeasuringthepressuredroppacrosstherestriction.TherelationispRq2,where392BasicControlSystemsDesignFigure11Venturi-typeowmeter.Thediaphragmdisplacementindicatestheowrate.1Rcanbefoundfromcalibrationofthedevice.Thepressuredropcanbesensedbyconvertingitintothemotionofadiaphragm.Figure11illustratesarelatedtechnique.TheVenturi-typeowmetermeasuresthestaticpressuresintheconstrictedandunconstrictedowregions.Bernoullisprinciplerelatesthepressuredifferencetotheowrate.Thispressuredifferenceproducesthediaphragmdisplacement.Othertypesofowmetersareavailable,suchastur-binemeters.3.4ErrorDetectorsTheerrordetectorissimplyadeviceforndingthedifferencebetweentwosignals.Thisfunctionissometimesanintegralfeatureofsensors,suchaswiththesynchrotransmittertra