Fal函数滤波器的分析及应用

1411201011ELECTRICMACHINESANDCONTROLVol14No11Nov.2010Fal王宇航,姚郁,马克茂(,150080):Fal函数是一种特殊的非线性结构,是自抗扰控制器中扩张状态观测器(ESO)的核心部分提出了Fal函数滤波器,对于噪声有较好的滤波效果,并分析了Fal函数滤波器的滤波特性提出了一种基于Fal函数滤波器的新型ESO,用于处理量测环节带有噪声干扰的情况与扩展一阶状态到ESO的方法以及扩展滤波器方程到ESO的方法相比,该新型ESO无须扩展ESO的阶数,避免了因阶数增加带来的观测误差增大以及参数整定问题数值仿真表明,该新型ESO对于带有量测噪声的系统具有较好的状态跟踪效果:Fal函数;扩张状态观测器;自抗扰控制;滤波器:TP13:A:1007-449X(2010)11-0088-04AnalysisandapplicationofFalfunctionfilterWANGYu-hang,YAOYu,MAKe-mao(ControlandSimulationCenter,HarbinInstituteofTechnology,Harbin150080,China)Abstract:Falfunctionisakindofspecialnonlinearstructure,whichisthekeypartofextendedstateobserverinautodisturbancerejectioncontroller.Falfunctionfilterwasproposed,whichhasgoodfilteringeffectonnoises;moreoverthefilteringcharacteristicsofFalfunctionfilterwasanalyzed.Thenanewtypeextendedstateobserver(ESO)basedonFalfunctionfilterwasproposedtodealwithnonlinearsystemwithmeasurementnoises.ComparingwiththemethodofextendingarankstatetoESOandthatofexten-dingfilterequationtoESO,thisnewmethoddidnotneedextendtherankofESO.Sothetrackingerrorincreasingproblemandtheparametertuningproblemcanbeavoided.Atlas,tthesimulationresultsshowthatthisnewtypeESOhasgoodperformanceofstatestrackingforsystemwithnoisesmeasuremen.tKeywords:Falfunction;extendedstateobserver;autodisturbancerejectioncontro;lfilter:2008-04-01:国家自然科学基金(60674043):王宇航(1980),男,博士,研究方向为飞行器制导与控制非线性系统控制;姚郁(1963),男,博士,教授,博士生导师,研究方向为飞行器制导与控制非线性系统控制;马克茂(1971),男,博士,教授,博士生导师,研究方向为非线性系统控制运动与控制0,,,,[1-2](autodisturbancerejec-tioncontro,lADRC)(ex-tendedstateobserver,ESO),,Fal,,,[3-4]ADRCFal,FalADRCFal:,;,[5],,PID,,Fal,Fal,[6],Fal,Fal,,Fal,FalESO,,,:,ESO,,[7],ESO,[8]ESO,ESO,,FalESO,ESO,,1FalFal11FalFig.1Falfunctionfilterx=kFal(e,a,),e=v-x,y=x(1),Fal(e,a,)=|e|asign(e),|e|e/1-a,|e|,v,k,a0~1,,yv,y=FalFilter(v,k,a,)fal,,,5T10T,Tk,k,,a0~1,a,,kafalx1=x0+w=sin(t)+w,x0,w0003,x12,Fal:k=20,a=03,=001,T=0001x2,x0,3x1,8911:Fal20s+20,x3,44Fig.4Signalthroughthelow-passfilter234,,Fal,,,,Fal,2Fal21Fal1,Fal|e|,|e|,k|e|asign(e)v,e|e|,(1)kFal(e,a,)=ke/1-a,k1=k/1-a,vy:yv=k1/s1+k1/s=k1s+k1=1s/k1+1,,k1,,,,,,,k1,,,Fal,[7]ESO,ESOFal22FalFalFal,Falx=w(x,t)+u,,|w(x,t)|w0,uxu=u(x),u(x)=-kFal(x,a,)|x|,x=-k|x|asign(x)+w(x,t)2x,dx2/dt-2k|x|(|x|a-w0/k)0,|x(t)|(w0/k)1/a,u(x)=-k|x|asign(x)w(x,t)|x||w0/k|1/aa=1(),|x|w0/k,a1(),|x||w0/k|1/a,|x|,x=-kx/1-a+w(x,t),2x,:dx2/dt-2kx2/1-a+2xw(x,t)=-2x2(k/1-a-w(x,t)/x)(2)xk/1-a-w(x,t)/x0,|x||w(x,t)|1-a/k,dx2/dt0w(x,t)|x||w(x,t)|1-a/k3FalESO,,,FalESO,Fal,,ESOESO,[7]x1=-10x31-x1-2cosx1+vx,y=x1+vy(3)vx=sin(10t),vy,x2=-10x31-x1-2cosx1+vx,ESOx1,x2,y0=FalFilter(y,k,a,0),e=z1-y0,z1=z2-01e,z2=02Fal(e,a,1)(4)FalESO,9014z1,z2x1,x2,55FalESOFig.5AnewtypeESOwithFalfunctionfilter,ESO:ESO[7];ESO[8],,67567,FalESO,[7][8],67ESOESO,ESO,,,,ESO,ka,34Fal,,,ESO,FalESO,ESO,ESOESO,ESO,:ESO,,,:[1].[J].,1998,13(1):19-23.HANJingqing.Autodisturbancerejectioncontrolleranditsappl-ication[J].ControlandDecision,1998,13(1):19-23.[2].[J].,1995,10(1):85-88.HANJingqing.Theextendedstateobserverofaclassofuncertainsystem[J].ControlandDecision,1995,10(1):85-88.[3],.[J].,2000,45(13):1373-1379.HUANGY,iHANJingqing.Analysisanddesignofnonlinearcon-tinuoussecondorderextendedstateobserver[J].SciencePaper,2000,45(13):1373-1379.[4]HUANGY,iHANJingqing.Analysisanddesignforthesecondordernonlinearcontinuousextendedstateobserver[J].ChineseScience,2000,45(21):1938-1944.[5]GAOZhiqiang,HUANGY,iHANJingqing.Analternativepara-digmforcontrolsystemdesign[C]Proceedingsofthe40thIEEEConferenceonControlandDecision,December4-7,2001,Or-lando,USA.2001:4578-4585.[6],.[J].,2002,19(4):485-492.(99)9111:Fal[9]BHENDECN,MISHRAS,JAINSK.T-Sfuzzycontrolledactivepowerfilterforloadcompensation[J].IEEETransactiononPowerDelivery,2006,21(3):1459-1465.[10]SHYUKuoKa,iYANGMingJ,iWANGTewe,ietal.T-SfuzzycontrollerdesignbasedonLMIforashuntactivepowerfiltersys-tem[C]//The33rdAnnualConferenceoftheIEEEIndustrialE-lectronicsSociety,November5-8,2007,Taipe,iChina.2007:620-625.[11]TANAKAK,WANGHO.FuzzyControlSystemsDesignandA-nalysis:ALinearMatrixInequalityApproach[M].NewYork:JohnWiliey&SonsInc.,2001.[12]LIANKY,LIOUJJ,HUANGCY.LMI-basedintegralfuzzycontrolofDC-DCconverters[J].IEEETransactiononFuzzySys-tem,2006,14(1):71-80.[13]JIZhicheng,ZHOUYinghuan.StabilizationofaclassoffuzzycontrolsystemsviapiecewisefuzzyLyapunovfunctionapproach[C]//AmericanControlConference,July9-13,NewYork,A-merica.2007:4065-4070.[14]TANAKAK,SUGENOM.Stabilityanalysisanddesignoffuzzycontrolsystems[J].IEEETransactiononFuzzySetsandSys-tems,1992,45(2):135-156.[15]TANAKAK,SUGENOM.Ontheconceptofregulatorandob-serveroffuzzycontrolsystems[J].ProceedingsoftheThirdIEEEConferenceonWorldCongressonComputationalIntelligence,1994,2(3):767-772.(编辑:于智龙)(91)HUANGY,iZHANGWenge.Developmentofautodisturbancere-jectioncontroller[J].ControlTheoryandApplications,2002,19(4):485-492.[7],.[J].,2003,18(1):110-112.SONGJinla,iGANZuoxin.Studyofautodisturbancerejectioncontrolleronfiltering[J].ControlandDecision,2003,18(1):110-112.[8],.[J].,2005,22(6):995-998.LINFe,iSUNHu.Novelextendedstateobserverforuncertainsystemwithmeasuremen