最小方差调节器和最小方差自校正调节器matlab

%-------------------------------------------------------------------------- %实验三：设计最小方差自校正调节器 %初始化 clear all; close all; %-------------------------------------------------------------------------- %产生白噪声 s=randn(1,200); d=std(s); m=mean(s); s=(s-m)/d; a=0; b=sqrt(1); s=a+b*s; %-------------------------------------------------------------------------- %设置u为一个200行的列向量，且为伪随机信号 u = idinput(200,'prbs'); y(1)=0; y(2)=0; for k=3:15 y(k)=0.9*y(k-1)+u(k-2)+s(k)-0.7*s(k-1); end %-------------------------------------------------------------------------- %递推最小二乘算法 %遗忘因子λ的设置 lambda =0.999; %给定参数的初值θ theta0=[0.01 0.01 0.01 0.01]'; %为了递推计算给出的P(k)初值P(0) p0=10^6*eye(4,4); %开辟内存空间 theta=[theta0,zeros(4,14)]; e=zeros(4,15); for k=3:15 x=[-y(k-1),u(k-2),s(k),s(k-1)]'; k1=p0*x*inv(x'*p0*x+lambda); theta1=theta0+k1*(y(k)-x'*theta0); e1=theta1-theta0; e2=e1/theta0; theta0=theta1; theta(:,k)=theta1; p1=(p0-k1*k1'*(x'*p0*x+lambda))/lambda; p0=p1; %判断是否收敛 if e2<=0.000000005 break; end end theta,e; alpha1=theta(1,:); alpha2=theta(2,:); beta1=theta(3,:); beta2=theta(4,:); q=zeros(1,4); for j=1:4 for i=2:15 if abs(theta(j,i))>0 q(1,j)=theta(j,i) end end end %-------------------------------------------------------------------------- %将辨识出的参数代替调节器参数 u_1=0.0; u_2=0.0; u_3=0.0; y_1=0.0; y_2=0.0; y_3=0.0; e_1=0.0; e_2=0.0; for k=2:1:200 time(k)=k; rin(k)=0; yout(k)=-q(1,1)*y_1+q(1,2)*u_2+q(1,3)*s(k)+q(1,4)*s(k-1); u(k)=-(q(1,1)+q(1,4))*q(1,1)*yout(k)+(q(1,1)+q(1,4))*u_1; u_3=u_2;u_2=u_1;u_1=u(k); y_3=y_2;y_2=y_1;y_1=yout(k); end plot(alpha1,'r') hold on plot(alpha2,'g') hold on plot(beta1,'b') hold on plot(beta2,'y') hold on legend('α1','α2','β1','β2',-1) grid title('参数变化曲线','fontName','楷体_GB2312',... 'fontsize',20) xlabel('样本数量'); ylabel('参数变化'); axis([0 10 -1.5 1.5]) figure(2) plot(time,rin,'b',time,yout,'r'); axis([0 200 -20 20]) grid title('y(k)变化曲线','fontName','楷体_GB2312',... 'fontsize',20) xlabel('时间轴 t(s)'); ylabel('y(k)');