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I implemented the ERLS algorithm, but it don't identify true. would you help me?

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fatemeh abdi
fatemeh abdi 2017-10-13
clear all close all clc
global N delay Ts format long % ======================== system model ========================== % % continuous model
num = [0.00057 , 380]; den = [0.000000021437 , 0.00007633 , 1];
G = tf(num,den); pole(G); zero(G); syms z;
Ts = 0.02e-03;
Gd = c2d(G,Ts) pole(Gd); zero(Gd);
b = Gd.num{1,1}; a = Gd.den{1,1};
% identification parameters teta = [a(2:3),b(2:3)]' N = 800;
% ======================== RLS with step input ========================== %
% Rand_signal = [0.0025*randn(1,N/4) -0.0025*randn(1,N/4) zeros(1, N/2) ] ; % Rand_signal = [0.091*randn(1,200) zeros(1,600) ] ; % figure(1) % plot([0:N-1]*Ts,Rand_signal)
Rand_signal = [0.091*randn(1,N/4) -0.091*randn(1,N/4) zeros(1, N/2) ] ; % Rand_signal = [0.091*randn(1,200) zeros(1,600) ] ; figure(1) plot([0:N-1]*Ts,Rand_signal)
u = 0.126*ones(1,N) + Rand_signal; figure(2) plot([0:N-1]*Ts,u)
y = system_equation(a,b,u);
teta_hat(:,2) = zeros(4,1); % 4 parameters should be identified M=16; H=1; landa= 0.999; L=4; % R = 1e-6*eye(4,4); %sigma*eye(N).eye(N) R=1e-3*eye(4,4);
r = zeros(4,1); %Rh=z h=zeros(L,N); %solution vector alpha=H; %step size m=1;
for t = 3:N
phi = [-y(t-1) -y(t-2) u(t-1) u(t-2)]';
R= landa*R+ phi*phi';
y_hat (t) = phi'*teta_hat(:,t-1);
error(t) = y(t) - phi'*teta_hat(:,t-1);
z = landa*r+error(t)*phi;
r= z; %residual vector
for k=1:1 %itrations [~,p]=max(abs(r)); while abs(r(p))<=alpha/2*R(p,p) && m<=M m=m+1; alpha=alpha/2; end if m>M % number of bits coeffiecient break end h(p,t)=h(p,t)+sign(r(p))*alpha; r=r-sign(r(p))*alpha*R(:,p); end
h;
teta_hat(:,t) = teta_hat(:,t-1) + h(:,t);
end
teta_hat;
plot1(teta,teta_hat,y,y_hat)
error; cost_function_step = 0.5*(error*error'); norm(teta_hat(:,end)-teta); function y = system_equation(a,b,u)
global N delay
y = zeros(1,N);
% initial conditions y(1) = 0; y(2) = -a(2)*y(1); y(3) = -a(2)*y(2)-a(3)*y(1)+b(2)*u(1)+b(1)*u(2);
for i = 4:N y(i) = -a(2)*y(i-1)-a(3)*y(i-2)+b(2)*u(i-1)+b(3)*u(i-2); end
end

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