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1、LINEAR-QUADRATICCONTROLOFAMEMSMICROMIRRORUSINGKALMANFILTERINGTHESISJamieP.Schnapp,Capt,USAFAFIT/GE/ENG/11-44DEPARTMENTOFTHEAIRFORCEAIRUNIVERSITYAIRFORCEINSTITUTEOFTECHNOLOGYWright-PattersonAirForceBase,OhioAPPROVEDFORPUBLICRELEASE;DISTRIBUTIONUNLIMITEDTheviewsexpressedi
2、nthisthesisarethoseoftheauthoranddonotreflecttheofficialpolicyorpositionoftheUnitedStatesAirForce,DepartmentofDefense,ortheU.S.Government.ThismaterialisdeclaredaworkoftheU.S.GovernmentandisnotsubjecttocopyrightprotectionintheUnitedStates.AFIT/GE/ENG/11-44LINEAR-QUADRATI
3、CCONTROLOFAMEMSMICROMIRRORUSINGKALMANFILTERINGTHESISPresentedtotheFacultyDepartmentofElectricalEngineeringGraduateSchoolofEngineeringandManagementAirForceInstituteofTechnologyAirUniversityAirEducationandTrainingCommandInPartialFulfillmentoftheRequirementsfortheDegreeofM
4、asterofScienceinElectricalEngineeringJamieP.Schnapp,BSCapt,USAFDecember2011APPROVEDFORPUBLICRELEASE;DISTRIBUTIONUNLIMITEDAFIT/GE/ENG/11-44AbstractThedeflectionlimitationsofelectrostaticflexure-beamactuatorsarewellknown[64].Specifically,asthebeamisactuatedandthegaptraver
5、sed,therestoringforcenecessaryforequilibriumincreasesproportionallywiththedisplacementtofirstorder,whiletheelectrostaticactuatingforceincreaseswiththesquareofthepotentialdifferenceacrossthegap,aswellastheinversesquareofthegap.Equilibrium,andthusstableopen-loopvoltagecon
6、trol,ceasesatone-thirdthetotalgapdistance,leadingtoanunstableactuatorsnap-in.AKalmanFilterisdesignedwithanappropriatelycomplexstatedynamicsmodeltoestimateactuatordeflectionaccuratelygivenvoltageinputandcapacitancemeasurements,whicharethenusedbyaLinearQuadraticcontroller
7、togenerateaclosed-loopvoltagecontrolsignal.Theconstraintsofthelatteraredesignedtomaximizestablecontrolovertheentiregap.ThedesignandsimulationoftheKalmanFilterandcontrollerarepresentedanddiscussed,withstaticanddynamicresponsesanalyzed,asappliedtobasic,100µmby100µmsquare,
8、flexure-beam-actuatedmicromirrorsfabricatedbyPolyMUMPs.Successfulapplicationofthesetechniquesenablesdemonstrat
