陷波器对系统稳定性影响的分析

:2005-01-16::(1968-),,,,.:1004-3918(2005)04-0582-04李振杰1,韩丰田2,姬中华1(1.,450002;2.,100084):提出了静电支承转子不平衡振动的两种抑制方法:传统陷波器法和通用陷波器法,并对比了两者的优缺点.在保证系统稳定性的前提下,传统陷波器的中心频率受到系统参数的限制,算法实现简单,而通用陷波器的中心频率可以任意选取,算法实现复杂.最后通过计算机仿真得到了验证.:静电支承;陷波器;稳定性:TP11:A,.,,;,;.,.,,..,,,.11.1Fig.1BlockdiagramofthecontrolsystemincludingtheconventionalnotchfilterN(s)=s2+20s2+210s+20(1)N(s)=s2+20s2+210s+20=(s-j0)(s+j0)(s-p)(s+p)(2)p=-10+j01-21j0+10ej,2.,10.1,0.23.第23卷第4期2005年8月河南科学HENANSCIENCEVol23No.4Aug.20052Fig.2Pole/zerolocationsoftheconventionalnotchfilter3Fig.3Blockdiagramofthecontrolsystemincludingthegeneralnotchfilter4Fig.4Pole/zerolocationsofthegeneralnotchfilter:c(t)=[sin(0t)Icos(0t)I]TR-TJTJTRsin(0t)w(t)cos(0t)w(t)dt(3)c+20c=TRw-0TJw(4)N(s)=e(s)Y(s)=(s2+20)(s2I+sA1+A0)-1(5)A1=TRA0=20I-0TJ.(SISO),N(s)=s2+20(s-p)(s-p)p=j0+rej(6)=arg(TR+jTJ)r=12TR+jTJ4.,.TRTJ,,,.3,.:P(s)=2.9191010s2(s+10000)(7)C(s)=11(s+72)(s+727)(s+2)(s+147900)(8)G0(s)=3.21091011(s+72)(s+727)s2(s+10000)(s+2)(s+14790)(9)c=351Hzb=622Hz200Hz.3.1GNO(s)=G0(s)N(s)=3.21091011(s+721)(s+727)s2(s+10000)(s+2)(s+14790)s2+20s2+200s+20(10)1+GNO(s)=0(11)RouthMATLAB,:0328Hz.,200Hz,.,58320058,.3.20=det(I+Nf(s)S(s))=det(s2+20)I+j0s0TR+jTJS(s)(12)U(s)=(sj0TR+jTJ)S(s)U(s)s=j,=diag(1,2,,m),0=det((s2+20)I+j0(ss))=mk=1(s2+20+j0k(s))(13)s.s()::s(0)=j0,=0,mj0.sk()=0=-12k(j0)=-12eig(U(j0))=-12eig(TS(j0))(14)T+TR+jTJK=sk(s)=0=tan,s()=0s.232,kj0s,,:2arg(-12eig(TS(j0)))32(15),0,T,.0=200Hz,(15):TR0,TJ-1.7278TR,,.4,Matlab,bode,5,6.5bodeFig.5Bodediagramoftheopenloopsystemincludingtheconventionalnotchfliter6bodeFig.6Bodediagramoftheopenloopsystemincludingthegeneralnotchfliter:,(0=200Hz),;(0=200Hz),..5,,,,.,,,;584河南科学234,,T,,,.:[1].[D].:,2003.[2],,.[J].,2004,22(3):299-302.[3],,.[J].,2000,13(4):610-615.[4]RaoulHerzog,PhilippBuhler,Conrad,etal.UnbalanceCompensationUsingGeneralizedNotchFilterintheMultivariableFeedbackofMagneticBearings[J].IEEETRANSACTIONSONCONTROLSYSTEMTECHNOLOGY,1996,4(5):580-586.AnalysisofinfluenceofnotchfilteronthesystemstabilityLIZhen-jie1,HANFeng-tian2,JIZhong-hua1(1.SchoolofMechanicalEngineering,ZhengzhouUniversity,Zhengzhou450002,China;2.DepartmentofPrecisionInstrumentsandMechanology,TsinghuaUniversity,Beijing100084,China)Abstract:Twomethods,namelyconventionalnotchfilterandgeneralnotchfilter,ofcontrolofunbalancevibrationforanelectrostaticlevitationsystemarepresentedinthispaper.Theperformanceofthetwowaysiscomparedaswell.Ontheconditionofkeepingthesystemstabilitythecentralfrequencyoftheconventionalnotchfilterisrestrictedbythesystematicparametersanditsalgorithmiseasytorealize,onthecontrarythegeneralnotchfilterisnot,whichareconfirmedthroughsimulationoncomputers.Keywords:electrostaticlevitation;notchfilter;stability58520058