Adaptive Control of a MEMS Gyroscope Using Lyapunov Methods

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1、278IEEETRANSACTIONSONCONTROLSYSTEMSTECHNOLOGY,VOL.14,NO.2,MARCH2006BriefPapers_______________________________________________________________________________AdaptiveControlofaMEMSGyroscopeUsingLyapunovMethodsRobertP.Leland,Member,IEEEAbstract—TwoadaptivecontrollersforavibrationalMEMSgy-anautomat

2、icgaincontrolloop,whichadjuststheinputampli-roscopearedescribed.Bothcontrollerstunethedriveaxisnaturaltude.Adaptivecontrolisusedtomaintainthedesiredamplitude.frequencytoapreselectedfrequency,regulatetheamplitudeoftheThird,thequadratureerrormustbecanceled.Couplingbetweendriveaxisvibration,cancelo

3、utquadratureerrorduetostiffnessthedriveandsenseaxesfromstiffnesscoupling,andmisalignedcoupling,anddrivethesenseaxisvibrationtozeroforforce-to-re-balanceoperation.Thefirstcontrollerisbasedonanaveraged,sensorsandactuatorsresultsinvibrationofthesenseaxisthatislowfrequencymodel,andthesecondisbasedont

4、hefullgyroscopenotduetorotation.Adaptivecontrolisusedtocancelthiseffect,model.BothcontrollersaresuccessfullysimulatedfortheBerkeleycalledquadratureerror.Fourth,inforce-to-rebalancemode,theZ-axisgyro.TheLyapunovfunctionusediscriticalinobtainingasenseaxisvibrationisdriventozero.Thecontrolsignaltha

5、tgoodtransientresponse,especiallyfortheforce-to-rebalanceanddoesthisbecomesthemeasurement.Adaptivecontrolisusedautomaticgaincontrolloops.Toimplementthefullmodelcon-trollerwithdisplacementmeasurementsonly,andnovelocitymea-toimplementtherebalanceloop.surements,thecontrollerisapproximated.Aslowsyst

6、emmodelofthegyroscopedynamicswasde-IndexTerms—Adaptivecontrol,Lyapunovmethods,microelec-rivedbythemethodofaveraging.Themethodofaveragingwastromechanicaldevices,perturbationmethods.usedtoanalyzeavibratorygyroscopein[9].ALyapunovbasedadaptivecontrollerwasdesignedusingthisslowsystemmodel.Anenergy-l

7、ikeLyapunovfunctionandPIadaptationlawswereI.INTRODUCTIONusedforrapidconvergenceofthecontrollerparameters.Mis-EMSvibrationalgyroscopesprovidealowcostiner-matchofthedriveandsenseaxisnaturalfrequenciesisallowed,Mtialmeasurement