LQR系统最优控制器设计的MATLAB实现及应用

23420058()JournalofShiheziUniversity(NaturalScience)Vol.23No.4Aug.2005:1007-7383(2005)04-0519-03:2005-07-06:(1976-),,,,e-mail:[e-mail]1,2(1,710068;2,222001;):,,QR,MatlabQR,,,:;Riccati;Matlab;:TP27311:ALQR(linearquadraticregulator),,LQRKJ,KQR,QRLQR,LQR,MatlabLQR,1LQRMa-tlab1.1LQR[1,2]:x=Ax+Bu,v=Cxxn@1,um@1:J=Q]t0(xQx+uTRu)dt(1)(1),QR,Qn@n,Rm@mu(1)J,:u=-kx=-R-1BTPx,,PRiccati(ARE):ATP+PA-PBR-1BTP+Q=0Matlablpr()AREP,K11.2QR[1,3],u,ARE,QR,,,QR:1)QR,Q,R2)QR,,R,Q,,R(R=1)3)Q,Q,Q1.3LQRMatlabMatlab,lqr(),:[K,P,E]=lqr(A,B,Q,R),K,PRiccati,EA-BK[1,2]2,,2:#x&x#H&H=00001-(I+ml2)bI(M+m)+Mml20mlbI(M+m)+Mml20m2gl2I(M+m)+Mml20mgl(M+m)I(M+m)+Mml20000x#xH#H+0I+ml2I(M+m)+Mml20mlI(M+m)+Mml2u,y=xH=10000010x#xH#H+00u:M=1.32kg,m=0.07kg,b=0.1NPmPs,l=0.2m,I=0.00093kg#m2,F,x,H,T=0.010s:F,4s,x1s,H50,2%[3]2:x#xH#H=00000-0118180-0145450216727031118180010x#xH#H+011181820415455u;y=xH=10000010x#xH#H+00uLQR2RQ2,R=1,Q=diag(1,0,1,0),Matlab:A=[0100;0-0.18182.67270;0001;0-0.454531.18180];B=[0;1.8182;0;4.5455];C=[1000;0010];D=[0];Q=[1000;0000;0010;0000];R=[1];[k,p,e]=lqr(A,B,Q,R);Ac=[(A-B*k)];Bc=[B];Cc=[C];Dc=[D];[y,x,t]=step(Ac,Bc,Cc,Dc);y1=y(:,1);y2=y(:,2);plot(t,y1,.r:.,t,y2),gridxlabel(.TimePs.,.FontSize.,14)legend(..,..)k=[-1.000,-1.6567,18.6854,3.4594],3,,Q11,,Q11=4500,Q33=110,Matlab,k=[-67.0820,-36.1688,101.8878,20.1743],4,520()23343LQR(),,MatlabMat-labLQR,QR,LQRQR:[1].[M].:,1999.[2],,.[M].:,1997.[3],,.[M].:,1998.[4].PIDMATLAB[M].:,2003.[5].[M].:,2003.TheOptimalControllerDesignofLQRandtheApplicationofMatlabMAJuan-li1,2(1DepartmentofElectronicEngineering,HuaihaiInstituteofTechnology,Lianyungang,Jiangsu222001,China;2DepartmentofAutomaticControl,NorthwesternPolytechnicalUniversity,Xi.an,Shanxi710068,China)Abstract:Inordertomakethedesignedlinearmeetthepracticalproductionrequirementbetter,thispaperrepresentsthebasicprincipleanddesignwaysofLQR,introducessomechoicerulesoftheweightedmatrixQandR.,bymeansofmat-lab,discussestheinfluenceonopticalcontrolsystemcausedbythechangeofparametersQandR,illustratesthatthecontroleffectbasedonthecontrollerdesignwayisbetter,thewayisliabletoreachandrealizethedesigntarget.Keywords:LQR;Riccatiequation;Matlab;weightedmatrix5214:LQRMATLAB