# Mixed Sensitivity Problem

I have plant, $$P(s) = \frac{1-s/5}{(s^2 + s/4 +1/4)}$$ I am taking a mixed sensitivity approach for that I have chosen $$V$$,$$W_1$$ and $$W_2$$ as follows:
For bandwidth, $$\omega$$ =1 so I chose M as,
$$M = s^2+ s.\sqrt(2)+1$$
$$D = 1/s^2$$
So, $$V = \frac{s^2+ s.\sqrt(2)+1}{1/s^2}$$
and the remaining values, $$W_1=1$$ and $$W_2=0.1$$
My code is as follows:

s=tf('s');
P = (1-(s/5))/(s^2+s/4+1/4);
M=s^2+sqrt(2)*s+1;
G=[M/s^2 P;
0 0.1 ;
-M/s^2 -P];
G=minreal(ss(G));
nu=1; % u has nu=1 entries
ny=1; % y has ny=1 entries
C=hinfsyn(G,ny,nu); % default rel. tolerance 0.01
K=tf(C) % so

L=P*K;
T=L/(1+L);
% bandwidth(T)  % 0.9963
S=1-T;
figure(1)
bode(T,K*S,P*S,S);
legend('T','KS','PS','S');
grid
figure(2)
step(T,K*S,P*S)
legend('T','KS','PS');
grid


I am not getting and controller $$K$$ for this code. I would really appreciate if you give some suggestion about choosing $$M, W_1, W_2$$ or anything that might help me get a controller $$K$$

• So the problem is you are not getting a controller, the code either crashes or $K$ is empty? or do you not get the desired controller. I advice to use [K, CL, GAM, INFO] = hinfsyn(G, ny, nu). This will give some inside information about the synthesis Apr 16 '21 at 12:24
• Since there is a zero in the $P(s)$, hinfsyn was taking improper function somehow. I rectified the issue by using a user-defined script that addressed the issue of having a zero in the plant transfer function Apr 17 '21 at 13:39