考虑模型不确定性的
基于分解控制直流电机系统的摩擦补偿方法克晶，苏宝库，曾鸣（哈尔滨工业大学控制工程系，黑龙江哈尔滨150001）摘要：针对陀螺漂移测试转台直流力矩电机系统中存在的非线性动态摩擦和电机波动力矩，为提高转台摇摆状态位置跟踪精度，该文基于分解控制的设计方法提出了一种新的鲁棒自适应摩擦补偿方法。该设计具有积分形式的自适应补偿器来补偿常值的可参数化的摩擦模型不确定性，而设计鲁棒补偿器来补偿不可参数化的摩擦模型不确定性。最后综合两种补偿器形成完整的补偿控制律。Lyapunov方法证明了闭环系统全局稳定性和对期望位置信号的渐进跟踪性能，仿真结果证实了该补偿方法对高精度运动曲线跟踪的有效性。
关键词：直流力矩电机；摩擦补偿；分解控制1Introduction
Becauseofefficiency,highreliabilityandeasymaintenance,DCmotorsystemshavebeenwidelyusedinthemotioncontroloftheprecisionmeasurementturntable.FortheexistenceofthenonlinearfrictionforcesandrippleforceintheDCmotorsystems,thetypicalhigh-precisionpositionrequirementoftheturntableisseriouslydegraded[1].Mostofthedynamicbehaviorsoffriction,suchasthepreslidingdisplacement,thefrictionlagandtheStribeckeffect,areresponsiblefortheinabilityofthesystemtoachievesmallsteady-statetrackingerrorsandalsolimitingtheallowableclosed-loopbandwidthinordertoavoidlimitcycling.Therefore,nonlinearfrictionforcesandrippleforceneedtobeeliminatedorrejectedintheDCmotorsystemoftheturntable.
Extensiveresearchoffrictionmodelingandrobustoradaptivefrictioncompensationschemeshasbeenconductedinpastfewyears.Anadaptivecompensatorwasproposedin[2]tohandleCoulombandviscousfrictioncomponentsaswellasStribeckeffectsinthepermanent-magnetlinearmotors.Severaladaptivefrictioncompensationmethods[3-5]havebeendevelopedbasedonthenewdynamicLuGremodelproposedin[6].Basedontherobustnonlinearcontroldesigns[7-8],amodelindependentfrictioncompensationwasproposedthatdidnotrelyonaspecificmodeloffrictionanddidnotrequireestimationoffrictionparameters.In[9],robustcontrollersweredesignedforrobotmanipulatorsinthepresenceofdynamicmodeluncertainties.Whiletheadvantageofadaptivefrictioncompensationcanbereadilyunderstood,itmayencounterdifficultiesfromlackofexcitationandeveninstabilityduetoincompletenessoffrictionmodel.Theproblembecomesworseifthepositiondependencyoffrictionisinvolved.Intheory,arobustcontrollercaneasilycompensateforlowvelocityfriction,sincetheunmodelledlowvelocityfrictionisobviouslybounded.However,highfeedbackgainisappliedinordertosuppressmodeluncertaintiesforhighaccuracy,whichisalwayslimitedbyhardwareissues[10].
Toutilizeadvantagesofvariouscontrolmethods,decompositionbasedcontroldesignapproachwasproposedin[11,12]forrobotmanipulators.Thefundamentalstrategyofthisapproachistodistinguishbetweenuncertainparametersandvariablesofdifferentphysicaltypes,andtodesignaseparatecompensatorforeachofthem,whiletakingintoaccounteachspecificphysicalfeature.Decompositionbasedcontroldesignapproachadvocatestreatingeachtypeofmodeluncertaintywiththemostsuitableandefficientmeans,includingPID,robustandadaptivemethods.Theoverallcontrollerisgeneratedbysynergeticintegrationofthesecompensators.Aproposeddecompositionbasedcontroldesignisappliedtosynthesizethefrictioncompensationschemesin[10].
Inthispaper,anewfrictioncompensationschemeisdevelopedfurtherapplyingthedecompositionbasedcontroldesignapproachtohandlethefrictionmodeluncertaintiesintheDCmotorsystemoftheturntable,andthecompensationfortherippleforceandloadforceisconsideredsimultaneously.Thedesignmotivationistocompensatefortheinfluenceofunknownbutconstantparametricuncertaintycompletelyusinganintegral-typeadaptivecompensator,andonlythenonparametricuncertaintyisdealtwithbyarobustsaturation-basedcompensator.ThepositiontrackingerrorisprovedtobeconvergedtothepredeterminedboundarybyLyapunovmethod.Finally,computersimulationsverifytheeffectivenessoftheproposedschemeforhigh-precisionmotiontrajectorytrackingoftheturntable.
2DynamicModelFormulation
2.1Thesimplifieddcmotorsystemmodelwithfriction
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