广义最小方差自校正控制直接算法

1、%广义最小方差白校正控制(直接算法)考虑如下系统：y(k) -1.7y(k -1) 0.7y(k - 2) = u(k - 4) 0.5u(k - 5)(k) 0.2 (k -1)式中k)为方差为0.1的白噪声。取P(z)=1, R(z)=1, Q(z)= 2，期望输出yr(k)为幅值为10的方波信号。clear all;close all;a=1 -1.7 0.7;b=1 2;c=1 0.2;d=4;na=length(a)-1;nb=length(b)-1;nc=length(c)-1;nf=nb+d-1;ng=na-1;Pw=1;R=1;Q=2; %加权多项式np=length(Pw)-

2、1;nr=length(R)-1;nq=length(Q)-1;L=400;uk=zeros(d+nf,1);yk=zeros(d+ng,1);yek=zeros(nc,1);yrk=zeros(nc,1);xik=zeros(nc,1);%xiek=zeros(nc,1);yr=10*ones(L/4,1);-ones(L/4,1);ones(L/4,1);-ones(L/4+d,1);xi=sqrt(0.1)*randn(L,1);%RELS初值设定thetaek=zeros(na+nb+d+nc,d);P=10A6*eye(na+nb+d+nc);for k=1:Ltime(k)=k;y

3、(k)=-a(2:na+1)*yk(1:na)+b*uk(d:d+nb)+c*xi(k);xik;%递推最小二乘法phie=yk(d:d+ng);uk(d:d+nf);-yek(1:nc);K=P*phie/(1+phie'*P*phie);thetae(:,k)=thetaek(:,1)+K*(y(k)-phie'*thetaek(:,1);P=(eye(na+nb+d+nc)-K*phie')*P;ye=phie'*thetaek(:,d); %最优预测输出估计值% xie=y(k)-phie'*thetae(:,k);% 白噪声估计值%提取辨识参数

4、ge=thetae(1:ng+1,k)'fe=thetae(ng+2:ng+nf+2,k)'ce=1 thetae(ng+nf+3:ng+nf+2+nc,k)'if abs(ce (2) )>0.9ce(2)=sign(ce(2)*0.9;endif fe(1)<0.1fe(1)=0.1;end%e,f,g=singlediophantine(ae,be,ce,d);CQ=conv(ce,Q);FP=conv(fe,Pw);CR=conv(ce,R);GP=conv(ge,Pw);u1=-Q(1)*CQ(2:nc+nq+1)*uk(1:nc+nq)/fe(1

5、)-FP(2:np+nf+1)*uk(1:np+n f);u2=CR*yr(k+d:-1:k+d-min(d,nr+nc);yrk(1:nr+nc-d);u(k)=(u1+u2-GP*y(k);yk(1:np+ng)/(Q(1)*Q(1)/fe(1)+fe(1);%更新数据for i=d:-1:2thetaek(:,i)=thetaek(:,i-1);endthetaek(:,1)=thetae(:,k);for i=d+nf:-1:2uk(i)=uk(i-1);enduk(1)=u(k);for i=d+ng:-1:2yk(i)=yk(i-1);endyk(1)=y(k);for i=nc:

6、-1:2yek(i)=yek(i-1);yrk(i)=yrk(i-1);endif nc>0yek(1)=ye;yrk(1)=yr(k);xik(1)=xi(k);endendfigure(1);subplot(2,1,1);plot(time,yr(1:L),'r:',time,y);xlabel('k');ylabel('y_r(k),y(k)');legend('y_r(k)','y(k)');axis(0 L -20 20);subplot(2,1,2);plot(time,u);xlabel(

7、9;k');ylabel('u(k)');axis(0 L -10 10);figure(2);subplot(211);plot(1:L,thetae(1:ng+1,:),1:L,thetae(ng+nf+3:ng+2+nf+nc,:);xlabel('k');ylabel('参数估计 g,c');legend('g_0','g_1','c_1');axis(0 L -3 4);subplot(212);plot(1:L,thetae(ng+2:ng+2+nf,:);xlabel('k');ylabel('参数估计 f);legend('f_0','f_1&