架硅微型机械振动陀螺仪鲁棒控制研究

*1231(210003)2(210096)3(210096),,H∞。,,H∞,。H∞TH70V241.45TP212.1A460.40510.8040120.3040RobustControlforDouble-gimbalVibratoryMEMSGyroscopeFangYuming1LiPu2MaoPansong31(DepartmentofInformationEngineering,NanjingUniversityofPostsandTelecommunications,Nanjing21yyyz,{|ina)2(Departmentof}ec|anicalEngineering,~out|eastUniversity,Nanjing21yy9,{|ina)z(#ey$a%orataryof}E}~of}inistryofEducation,~out|eastUniversity,Nanjing21yy9,{|ina)&bstractA’o(us)H∞*on)’o+s*,-m-.o’),-*on/-n)iona+mo0-+o.o1-’a)iono.23ai4s0ou(+-3gim(a+/i(’a)o’5M6M7g5’os*o1-is1’-s-n)-08T,-s*,-m-is’-a+i2-0(5a.o’*-3(a+an*ing.--0(a*9s*,-m-8T,-’-a+i2a)iono.),isH∞*on)’o+g5’os*o1-is0-mons)’a)-0ina0ou(+-3gim(a+/i(’a)o’5g5’os*o1-:i),1;-’’o’in),-s-ns-a4isna)u’-.’-u-n*58T,-’-su+)ss,o:),a)),-H∞*on)’o+g5’os*o1-1’o/-s)o(-’o(us)in),-na)u’-.’-u-n*5-’’o’in*om1a’ison:i),),-*on/-n)iona+o1-n3+oo1g5’os*o1-8=eyor?s@ou(+-3gim(a+/i(’a)o’5M6M7g5’os*o1-Fo’*-3(a+an*ing*on)’o+Ao(us)H∞*on)’o+B,。M6M7(C,y)D1E2F,GC,(),,Cy,y,y。Cy,,。。。(y),,。D3E4F,G,,CyD2F,。,,y,,D2F,,。。,D5E7F。G26620056*20039,(50305002)H(03IJK510089)。KalmanPreviewControl[5];(Force-balancingfeedbackcontrol[6～7])。y,,y,。,[2]、-[8]。、-,、。,,,[4,9],DSP。,。H∞[10]。H∞2090,,H∞。,Ωz,4,1/6.25;y,,,。22.1[2],,zΩz。(50Hz)(1000Hz),Ωz。(x)(y)[2]:Jx(¨θx+2ξxωxθ·x+ω2xθx)=kdV0υdsinωdt(1)Jy(θ¨y+2ξyωyθ·y+ω2yθy)=-Jxθ·xΩz(2):θx、θyx、y;Jx、Jy、;ωx、ωy、;ξx、ξy、;V0+υdsinωdt,V0》υd,V0;kd:kd=εAx(2lx+bx)/Z20:ε;Ax;lx;bx;z0。ωd=ωx=ωy,,,。、,y[2]:ΔC=εAy(2ly+by)z20θy=ks·θy(3):Ay,ly,by。ΔC,Ωz。2.2[2],--,、。1,:Jx(θ¨x+2ξxωxθ·x+ω2xθx)=kdV0υdsinωdt(4)Jy(θ¨y+2ξyωyθ·y+ω2yθy)=-Jxθ·xΩz+τ(5):τ。V0,:τ=kcV0·u(t)(6)1:u(t),|u(t)|《V0;kc,kc=ks=εAy(2ly+by)z20。2。kV,:Gy(s)=[Jy(s2+2ξyωys+ω2y)]-1、,。29526,,ΔGy(s)。u(t),θyks、kV。:ΔGy(s),C(s),u(t),ΔGy(s)。23H∞[10]。,θy,2Wp(s)θy,zp;u(t),|u(t)|《V0,,Wu(s)u(t),zu;Wdel(s),‖ΔGy(s)‖∞≤|Wdel(s)|,zdel。23H∞。r,r=θy。,rzp、zu、zdel:zp=Wp(s)·θy=Wp(s)·Tθyr(s)·r=Wp(s)·11+kskVkcGy(s)C(s)·r(7)zu=Wu(s)·u(t)=Wu(s)·Tur(s)·r=Wu(s)·-kskVC(s)1+kskVkcGy(s)C(s)·r(8)zdel=Wdel(s)·kcGy(s)·u(t)=Wdel(s)·-kskVkcGy(s)C(s)1+kskVkcGy(s)C(s)·r(9):C(s),:(1):3H∞‖Wp(s)Tθyr(s)‖∞≤1(2):‖Wu(s)Tur(s)‖∞≤1(3)[10]:‖kcWdel(s)Gy(s)Tur(s)‖∞≤1H∞[10]:‖Tzr(s)‖∞========Wp(s)Tθyr(s)Wu(s)Tur(s)kcWdel(s)Gy(s)Tur(s=======)∞≤1(10),z=[zpzuzdel]T=Tzr(s)·r。(10)H∞[10]。Gy(s),ks、kV、kc,Wp(s)、Wu(s)、Wdel(s),MATLABC(s),Gy(s)。4,Ωz=6.28rad/s,:880µm×1500µm×8µm,:380µm×1000µm×8µm,:480µm×1100µm×8µm,1。,xyωx=ωy=9420rad/s(1500Hz),ωd=ωx。,yωy±1%,ωy:1485～1565Hz,x3956,ωd=ωx=9420rad/s,υd=0.5V。H∞。1==========Jx4.1×10-15kg·m2ωx9420rad/sξx====0.0005Jy9.0×10-15kg·m2ωy9420rad/sξy====0.0005ε8.854×10-15F/mly240µmV05====VAy150000µm2bx=by200µmz010====µmAx76000µmkV2.5V/pFlx300µm4.1。、,,,。,Wp(s)、Wdel(s),,,,。Wp(s),。,ωd=ωx=9420rad/s,,θy。:Wp(s)=1×10-7Jy(s2+2·20ξy·ωys+ω2y)(11)4Wp(s)。Wp(s)9420rad/s(1500Hz),,6.25,。(7)、(10),,1/6.25。Wp(s)ξy20,,9420rad/s,,。V0=5V。u(t),,|u(t)|1V。(8)、(10)Wu(s)=0.2。Wdel(s)。y±1%,+1%:ΔG1(s)=-(0.0201ω2y+2ξy·0.01ωy·s)Jy(s2+2ξy·1.01ωys+(1.01ωy)2)-1%:ΔG2(s)=0.0199ω2y+2ξy·0.01ωy·sJy(s2+2ξy·0.99ωy·s+(0.99ωy)2)ΔG1(s)ΔG2(s)5。|Wdel(s)|,,。,|Wdel(s)|:Wdel(s)=1.5×107s2+2·5ξy·ωys+ω2y(12)5,。ΔG1(s)ΔG2(s)(1.01ωy0.99ωy)。4Wp(s)-ΔG1(s)-ΔG2(s)-Wdel(s)5ΔG1(s)、ΔG2(s)Wdel(s),:C(s)=-a(s)b(s):a(s)=5.54·104·s5+4.29·108·s4+9.89·1012·s3+7.57·1016·s2+4.41·1020·s+3.34·1024:49526b(s)=s6+2.43·103·s5+2.67·108·s4+4.37·1011·s3+2.35·1016·s2+1.96·1019·s+6.82·10234.2C(s)2,,Ωz,,6。6,(a)--y,,()()1/6.25。(b)。,,1/5。2、3kVksθy,u(t)。,,Ωz,4,1/6.25。。yωy+1%。7。y+1%,95%!,,x、y。--kVksθy95%。8。y+1%,50%。9。y+1%,50%。,,y+1%,,,,。--6--y7y--y8y5956--y95,,H∞。,Ωz,4,1/6.25;y,,,。1NavidYazdi,FarrokhAyazi,KhalilNajafi.MicromachinedInertialSensors.Proc.IEEE,1998,86(8):1640～1659.2..:,2000.3CenkAcar,SebnemEler,AndreiM.Shkel.Concept,implementationandcontrolofwidebandwidthMEMSgyroscopes.ProceedingsoftheAmericanControlConference,Arington,VA,June25～27,2001,1229～1234.4SungsuPark,RobertoHorowitz.AdaptivecontrolforZ-axisMEMSgyroscopes.ProceedingsoftheAmericanControlConference,Arington,VA,June25～27,2001,1223～1228.5P.B.Ljung.Micromachinedgyroscopewithintegratedelectronics.DoctoralDissertation,Berkeley,CA,1997.6S.Chang,M.Chia,P.Castillo-Borelley,etal..AnelectroformedCMOSintegratedangularratesensor.SensorsandActuators,1998,A66:138～143.7X.Jiang,J.Seeger,M.Kraft.AmonolithicssurfacemicromachinedZ-axisgyroscopewithdigitaloutput.Pro.IEEE2000Symp.VLSICircuits,Honolulu,HI,June2000,16～19.8,,..(),1998,38(11):1～3.9SungsuPark,RobertoHorowitz.AdaptivecontrolfortheconventionalmodelofoperationofMEMSgyroscopes.JournalofMicroelectroMechanicalSystems,2003,12(1):101～108.10.H∞.:,1996.11,..,1997,(4).1975MEMSE-mail:[e-mail]69526