%{
ELEC-E8116 Model-based Control Systems
Exercise 7
%}

clearvars;
close all;
clc;

%%
w0=10; % desired closed-loop bandwidth
A=1e-4; % desired disturbance attenuation inside bandwidth
M=1.5 ; % desired bound on hinfnorm(S) & hinfnorm(T)

s=tf('s');
G=200/(10*s+1)/(0.05*s+1)^2;
Gd=100/(10*s+1);
W11=(s/M+w0)/(s+w0*A); % Sensitivity weight 1 (1st order)
W22=((s/sqrt(M)+w0)^2)/((s+w0*sqrt(A))^2); % Sensitivity weight 2 (2nd order)

%%
[K1,CL,GAM,INFO]=mixsyn(G,W11,[],[]);

L1=G*K1; % loop transfer function
S1=inv(1+L1); % Sensitivity
T1=1-S1; % complementary sensitivity
%%
[K2,CL,GAM,INFO]=mixsyn(G,W22,[],[]);

L2=G*K2; % loop transfer function
S2=inv(1+L2); % Sensitivity
T2=1-S2; % complementary sensitivity
%%
%{
For the 2nd order weight the curve increases 40 dB/decade and the slope is 2.
%}
figure(1); clf;
w_range =  logspace(-2,2);
bodemag(S1,'b-', 1/W11, 'r--', w_range)
hold on;
bodemag(S2,'g-.', 1/W22,'c.', w_range)
yline(10^0, '-.')
grid on;
legend('S1','1/W11','S2','1/W22')