% EESC/USP - SEM 538 - Sistemas de Controle II
% Exemplo Observador - 2018 
%

clear all
%close all
A = [ 0 1; 0 0];
B = [0;1];
C = [1 0];
D = 0;

T0 = 0.1;

S = ss(A,B,C,D);
Sd = c2d(S,T0);
[F,G,C,D]=ssdata(Sd);

%Controlador
p = [0.8+0.25*i;
     0.8-0.25*i];
K = acker(F,G,p);
Fc = F-G*K;

%Observador
p2 = [0.4+0.4*i;
     0.4-0.4*i];
L = acker(F',C',p2)';
Fe = F-L*C;

AA = [F  -G*K; L*C  Fe-G*K];
BB = [0;0;0;0];
CC = [0 0 0 0];
DD= 0;

MF = ss(AA,BB,CC,DD,T0);
[Y,T,X] = lsim(MF,zeros(1,101),[0:0.1:10],[1;0;0;0]) ;

figure
stairs(T,X(:,1:2),'b')
hold on
stairs(T,X(:,3:4),'r')