第一次作业1、增广最小二乘辨识模型结构如下所示:其中,a1=-,a2=,b1=,b2=,d1=1,d2=。对其进行MATLAB仿真。解:增广最小二乘辨识程序:>>clearL=60;y1=1;y2=1;y3=1;y4=0;fori=1:L;x1=xor(y3,y4); x2=y1; x3=y2; x4=y3; y(i)=y4; ify(i)>,u(i)=-1;elseu(i)=1;endy1=x1;y2=x2;y3=x3;y4=x4;endfigure(1);subplot(2,1,1);stem(u),gridonv=randn(1,60);subplot(2,1,2);plot(v),gridon;u,v%显示输入信号和噪声信号z=zeros(7,60);zs=zeros(7,60);zm=zeros(7,60);zmd=zeros(7,60);z(2)=0;z(1)=0;zs(2)=0;zs(1)=0;zm(2)=0;zm(1)=0;zmd(2)=0;zmd(1)=0;c0=[]';p0=10^6*eye(7,7);E=;c=[c0,zeros(7,14)];e=zeros(7,15);fork=3:60; z(k)=*z(k-1)-*z(k-2)+*u(k-1)+*u(k-2)+v(k)+v(k-1)+*v(k-2); h1=[-z(k-1),-z(k-2),u(k-1),u(k-2),v(k),v(k-1),v(k-2)]';x=h1'*p0*h1+1;x1=inv(x);k1=p0*h1*x1;d1=z(k)-h1'*c0;c1=c0+k1*d1;zs(k)=-*z(k-1)+*z(k-2)+*u(k-1)+*u(k-2);%系统在M序列的输入下的输出响应zm(k)=[-z(k-1),-z(k-2),u(k-1),u(k-2)]*[c1(1);c1(2);c1(3);c1(4)]; zmd(k)=h1'*c1;e1=c1-c0;e2=e1./c0;e(:,k)=e2;c0=c1; c(:,k)=c1; p1=p0-k1*k1'*[h1'*p0*h1+1];%findp(k)p0=p1;ife2<=Ebreak;endendc,e,%显示被辨识参数及参数收敛情况z,zs,zm%显示输出采样值、系统实际输出值、模型输出值%分离变量a1=c(1,:);a2=c(2,:);b1=c(3,:);b2=c(4,:);d1=c(5,:);d2=c(6,:);d3=c(7,:);ea1=e(1,:);ea2=e(2,:);eb1=e(3,:);eb2=e(4,:);ed1=e(5,:);ed2=e(6,:);ed3=e(7,:);figure(2);%画第二个图形i=1:60;plot(i,a1,'r',i,a2,'r:',i,b1,'b',i,b2,'b:',i,d1,'g',i,d2,'g:',i,d3,'g+')%画出各个被辨识参数title('ParameterIdentificationwithRecursiveLeastSquaresMethod')figure(3);i=1:60;%画出第三个图形plot(i,ea1,'r',i,ea2,'r:',i,eb1,'b',i,eb2,'b:',i,ed1,'g',i,ed2,'g:',i,ed2,'r+')title('IdentificationPrecision')figure(4);subplot(4,1,1);%画出第四个图形,第一个子图i=1:60;plot(i,zs(i),'r')subplot(4,1,2);i=1:60;plot(i,z(i),'g')%第二个子图,画出被辨识系统的采样输出响应subplot(4,1,3);i=1:60;plot(i,zm(i),'b')%第三个子图,画出模型含有噪声的输出响应subplot(4,1,4);i=1:60;plot(i,zs(i),'b')%第四个子图,画出模型去除噪声后的输出响应(1)程序执行结果:u=Columns1through171 -1 -1 -1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 -1Columns18through34-1 -1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1Columns35through51-1 1 1 1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 1Columns52through601
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