chapter 2. analysis of linear control systems

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1、2ANALYSISOFLINEARCONTROLSYSTEMS2.1INTRODUCTIONInthisintroductionwegiveabriefdescriptionofcontrolproblemsandofthecontentsofthischapter.Acontrolsystemisadynamicsystemwhichastimeevolvesbehavesinacertainprescribedway,generallywithouthumaninterference.Controltheorydealswiththeanalysisandsynthesisofcontr

2、olsystems.Theessentialcomponentsofacontrolsystem(Fig.2.1)are:(1)theplaizt,whichisthesystemtobecontrolled;(2)oneormoresensors,whichgiveinformationabouttheplant;and(3)thecontroller,the"heart"ofthecontrolsystem,whichcomparesthemeasuredvaluestotheirdesiredvaluesandadjuststheinputvariablestotheplant.Ane

3、xampleofacontrolsystemisaself-regulatinghomeheatingsystem,whichmaintainsatalltimesafairlyconstanttemperatureinsidethehomeeventhoughtheoutsidetemperaturemayvaryconsiderably.Thesystemoperateswithouthumanintervention,exceptthatthedesiredtemperaturemustbeset.Inthiscontrolsystemtheplantisthehomeandthehe

4、atingequipment.Thesensorgenerallyconsistsofatemperaturetransducerinsidethehome,sometimescomplementedbyanoutsidetemperaturetransducer.Thecoi~frollerisusuallycombinedwiththeinsidetemperaturesensorinthethermostat,whichswitchestheheatingequipmentonandoffasnecessary.Anotherexampleofacontrolsystemisatrac

5、kingantenna,whichwithouthumanaidpointsatalltimesatamovingobject,forexample,asatellite.Heretheplantistheantennaandthemotorthatdrivesit.Thesensorcon-sistsofapotentiometerorothertransducerwhichmeasurestheantennadisplacement,possiblyaugmentedwithatachometerformeasuringtheangularvelocityoftheantennashaf

6、t.Thecontrollerconsistsofelectronicequipmentwhichsuppliestheappropriateinputvoltagetothedrivingmotor.Mthoughatfirstglancethesetwocontrolproblemsseemdifferent,uponfurtherstudytheyhavemuchincommon.First,inbothcasestheplantandthecontrolleraredescribedbydifTerentialequations.Consequently,themathematica

7、ltoolneededtoanalyzethebehaviorofthecontrolsystemin119120AnalysisofLinearContrulSyslcmsdesiredvalue-("putoutputcontroller-plant'Fig.2.1.Schemalicrcprcscntationofaconlrolsystem.bothcasesconsistsofthecollecti