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1、©FreundPublishingHouseLtd.InternationalJournalofNonlinearSciences&NumericalSimulation,10(4),425-444,April2009ChaoticAnalysisandControlofMicrocandileverswithPDFeedbackUsingDifferentialTransformationMethodCheng-ChiWang1**,Her-TerngYau21DepartmentofMechanicalEng
2、ineering,Far-EastUniversity,Tainan744,Taiwan,ROC.DepartmentofElectricalEngineering,Far-EastUniversity,Tainan744,Taiwan,ROC.AbstractThispaperinvestigatesthenonlineardynamicbehavioroftheprobetipofanatomicforcemicroscopewithaPD(proportional-plus-derivative)feedb
3、ackcontrolusingthedifferentialtransformationmethod(DTM).ThedynamicbehavioroftheprobetipwithPDcontrollawischaracterizedbyreferencetophaseportraits,powerspectra,Poincaremaps,andmaximumLyapunovexponentplotsproducedusingthetime-seriesdataobtainedfromdifferentialt
4、ransformationmethod.Furthermore,thedetailedtransitionsinthedynamicresponseoftheprobetipareexaminedusingbifurcationdiagramsofthetipdisplacementandthetipvelocity,respectively.Theresultsindicatethattheprobetipbehaviorissignificantlydependentonthemagnitudeofthepr
5、oportionalandderivativecontrolgain.Specifically,theprobetipmotionincludessubharmonic,multi-periodic,andchaoticmotion.NumericalresultsshowthatthedynamicbehaviorwillleavechaoticmotiontoperiodicmotionatKp=-0.45inthesteadystatebychangingthecontrolloopgainKvfrom-0
6、.1to-1.0.Furthermore,itisdemonstratedthatthedifferentialtransformationmethodisingoodagreementfortheconsideredsystem.Keywords:Atomicforcemicroscope;PDfeedbackcontrol;Differentialtransformationmethod1.Introductionperformedchaoticmotionunderspecificphysicalcondi
7、tions.Ashhabetal.[7]modeledTheatomicforcemicroscope(AFM)themicrocantileverofanAFMusingasingle-providesapowerfultoolforsurfaceanalysisfrequencymodeapproximationandanalyzedtheapplicationsinthenano-electronics,materialschaoticdynamicsofthecantilever-sampleandbio
8、technologyfields[1-4].Duringoperation,systemusingtheMelnikovmethod.Leeetal.[8]intermolecularforcesbetweentheAFMprobeanalyzedtheeffectsofvanderWaalsandtipandthesamplesurfacecauseadeflectio
