%% Système du 3e ordre 
% stable
sys = tf([1],[0.1 1]);
sys1 = tf([100],[10 1]);
sys2 = tf([1],[0.03 1]);
sys3_bo = sys * sys1 * sys2;
% instable
sys3_bo_i = 3 * sys * sys1 * sys2;
% figures
figure;
bode(sys3_bo);
hold on;
bode(sys3_bo_i); 
grid on;
legend('stable','instable');
figure;
nyquist(sys3_bo);
hold on;
nyquist(sys3_bo_i);
grid on;
legend('stable','instable');

%% Systeme rebouclé
sys3_bf = feedback(sys3_bo, 1);
figure;
bode(sys3_bf); grid on;
figure;
step(sys3_bf); grid on;

%% Correcteur P
Kp = 10;
sys4_bo = sys3_bo*Kp;
figure;
subplot(2,1,1); bode(sys3_bo); grid on;
subplot(2,1,2); bode(sys4_bo); grid on;

sys4_bf = feedback(sys4_bo, 1);
figure;
bode(sys4_bf); grid on;
figure;
step(sys4_bf); grid on;


%% Rebouclage avec 1er ordre
num1 = [Kcapt];
den1 = [0.01 1];
sys_B = tf(num1, den1);
sys_BO2 = sys_bo * sys_B;
figure;
bode(sys_BO2); grid on;

sys_bf2 = feedback(sys_bo, sys_B);
figure;
bode(sys_bf2); grid on;
figure;
step(sys_bf2); grid on;