close all
clear all

%%%%%%%%%%%%%%%%%%%%%%%%%%%
% dados de simula??o
% \dot{x}(t) = -ax(t)+bu(t)
% x = (b/(s+a))u
%%%%%%%%%%%%%%%%%%%%%%%%%%%

a = 5;
b = 3;
num = b;
den = [1 a];
ftx = tf(num,den);
ftx1 = tf([1 0],[1 2 1]);
ftx2 = tf(1,[1 2 1]);
N = 295;
dt = 0.01;
alpha = 0.5;
T = 0:dt:N;
u = 1*ones(1,N/dt+1); 
u = sin(T);
[Y,T] = lsim(ftx,u,T);
Y1 = lsim(ftx1,Y,T);
Y2 = lsim(ftx2,Y,T);
Y3 = lsim(ftx2,u,T);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% algoritmo de identifica??o de par?metros
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Y(1)        = 0;
Erro(1)     = 0;
teta(:,1)   = [0;0];
gamma        = 100*[1 0 ;0 1];
for k = 1:N/dt
    phi1(:,k)   = [-Y2(k);Y3(k)];
    ms         = 1+alpha*phi1(:,k)'*phi1(:,k);
    teta(:,k+1) = teta(:,k) + gamma*dt*((Y1(k)-teta(:,k)'*phi1(:,k))/ms)*phi1(:,k);
    erro(k+1)   = Y1(k)-teta(:,k)'*phi1(:,k);
    
    
end

figure(1)
plot(T,teta,'LineWidth',4)
hold on
plot(T,erro,'LineWidth',4)
legend('Parametro a','Parametro b','Erro')
xlabel('Amostras')
ylabel('Parametro Identificado')
title('Metodo do Gradiente')
ax = gca;
ax.FontSize = 24;

hold off
%saveas(1,'ex2_agosto_2020_ab')