function Ex2_17

% Example 2.17 in Skogestad.

s = tf('s');
G = 200 / (10*s + 1) / (0.05*s + 1)^2; % plant transfer function
Gd = 100 / (10*s + 1); % disturbance transfer function
M = 1.5; wb = 10; A = 1e-4; % weight parameters
Wp = (s/M + wb) / (s + wb*A); % error sensitivity weight
Wu = 1; % control sensitivity weight
[K, Cl, gamma] = mixsyn(G, Wp, Wu, []); % H-infinity design
% K and Cl are state space objects.
% Compute the closed loop tranfer function from r to y.
L = G * K; % loop transfer function
T = (eye(size(L)) + L)^(-1) * L; % complementary sensitivity
[yu1, tu1] = step(T, 3); % Response to a step in u.
% Compute the closed loop transfer function from d to y.
S = (eye(size(T)) - T) * Gd; % sensivitity
[yd1, td1] = step(S, 3); % Response to a step in d.

% Now repeat all of the above with a different sensitivity weight
Wp = (s/M^(1/2) + wb)^2 / (s + wb*A^(1/2))^2;
[K, Cl, gamma] = mixsyn(G, Wp, Wu, []);
L = G * K;
T = (eye(size(L)) + L)^(-1) * L;
[yu2, tu2] = step(T, 3);
S = (eye(size(T)) - T) * Gd;
[yd2, td2] = step(S, 3);

% Plot the results.
close all; figure;
subplot(2,1,1);
plot(tu1, yu1, tu2, yu2, 'r--'); legend('y_1(t)', 'y_2(t)');
ylabel('reference step response');
subplot(2,1,2);
plot(td1, yd1, td2, yd2, 'r--'); legend('y_1(t)', 'y_2(t)');
ylabel('disturbance step resopnse');
xlabel('time (s)');