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1、CONTROLSYSTEMS,ROBOTICS,ANDAUTOMATION–Vol.III–ControllerDesign-BorisLohmannCONTROLLERDESIGNBorisLohmannInstitutfürAutomatisierungstechnik,UniversitätBremen,GermanyKeywords:StateFeedbackDesign,SISOSystems,StateFeedbackControl,stability,controllability,poleplacement,Ac
2、kermann’sformula,deadbeatcontrolContents1.ObjectivesandStructureofStateFeedbackControl2.Determinationofthepre-compensatorg3.DeterminationoftheControllerk3.1DeterminationbyMatchingofCoefficients3.2DeterminationfromControlCanonicalForm3.3.DeterminationbyTransformtoCont
3、rolCanonicalForm:Ackermann’sFormula3.4.DesignParameters4.Example:InvertedPendulum5.Discrete-TimeStateFeedbackandDead-BeatBehaviorGlossaryBibliographyBiographicalSketchSummaryBasedonthestatevariabledescriptionofdynamicsystemsanditsanalysis,thischapterpresentsapproache
4、stothedesignofclosed-loopcontrol.Alinearweightedsumofstatevariablesisfedbacktothecontrolinputoftheplant,theresultingcontrollawiscalledstatefeedback.Thisallowsthecontrol-systemdesignertoplacealloftheneigenvaluesoftheclosed-loopsystemindesirablelocations,mostlyreferred
5、toaspoleplacementorpoleassignment.Thestabilitycantherebybeassuredandthetransientbehaviorbeadjusted.AfrequentlyuseddesignprocedureisdescribedbyAckermann’sformula.UNESCO–EOLSSAspecialfeatureofdiscrete-timestatefeedbackcontroloccurs,whentheneigenvaluesareplacedattheorig
6、inofthecomplexplane:theinitialstateofthesystemdecaystozeroafteramaximumofSAMPLECHAPTERSnsteps,whichiscalleddead-beatbehavior.1.ObjectivesandStructureofStateFeedbackControlStartingpointisthestatespacedescriptionofadynamicsystemwithonescalarcontrolinputu(t),onescalarco
7、ntroloutputy(t),andthe(n,1)-statevector(orn-vectorofstate)x(t),Statedifferentialequation:xA"()tt=+xb()u()t,(1)TOutputequation:y()tt=cx().(2)©EncyclopediaofLifeSupportSystems(EOLSS)CONTROLSYSTEMS,ROBOTICS,ANDAUTOMATION–Vol.III–ControllerDesign-BorisLohmannBesidethecon
8、trolinput,thesystemisinfluencedfromoutsidebythevectorofinitialvalues,theinitialstatexx()t=.(3)00Inmostcases,theinitialstatewillnotb
