% EESC/USP - SEM 538 - Sistemas de Controle II
% Exercício - Formas canônicas - 2016
%
close all
clear all

G = tf([1 2],[1 7 12])
figure
step(G)
grid

%Forma Canônica Controlável
Ac = [-7 -12;
    1 0];
Bc= [1; 0];
Cc =[1 2];
Dc=0;

Sc = ss(Ac,Bc,Cc,Dc);
[Yc,t,Xc] = step(Sc,2.5);
figure
subplot(1,2,1)
plot(t,Yc)
ylabel('Y')
grid
subplot(1,2,2)
plot(t,Xc)
ylabel('X')
grid

%Forma Canônica Modal
Am = [-4 0;
    0 -3];
Bm= [1; 1];
Cm =[2 -1];
Dm=0;

Sm = ss(Am,Bm,Cm,Dm);
[Ym,t,Xm] = step(Sm,2.5);
figure
subplot(1,2,1)
plot(t,Ym)
ylabel('Y')
grid
subplot(1,2,2)
plot(t,Xm)
ylabel('Z')
grid


% A,B,C,D para Forma Canônica Controlável

A =[2.0000  -10.0000;
    3.0000   -9.0000];

B =[0.7071;
    0.7071];

C =[-0.7071    2.1213];

D=0;

S = ss(A,B,C,D);
[Y,t,X] = step(S,2.5);
figure
subplot(1,2,1)
plot(t,Y)
ylabel('Y')
grid
subplot(1,2,2)
plot(t,X)
ylabel('X')
grid


[Abar,Bbar,Cbar,t] = ctrbf(A,B,C);
Dbar =0;
Sbar = ss(Abar,Bbar,Cbar,Dbar);
[Ybar,t,Xbar] = step(Sbar,2.5);
figure
subplot(1,2,1)
plot(t,Ybar)
ylabel('Y')
grid
subplot(1,2,2)
plot(t,Xbar)
ylabel('X')
grid