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From: Ashgard on 2 Jun 2010 07:32
Hi,

I have some problems with designing my Hinfinity controller. The plant G can perfectly be controlled using a PI controller, however, when I try to do it with Hinfinity, it simply fails. See code below for details.

So, I was wondering: what are the restrictions of the hinfsyn command? Because I think it is due to restriction in the algorithm that it fails, but I might be wrong...

Advice is highly appreciated.

Thanks in advance
Bob

======== my code =========
num = [1.541 -9.621e-017 -0.003286 1.044e-020 7.742e-007 8.921e-024 -4.307e-011 -2.243e-028];
den = [1 -2.914e-016 -0.003583 5.963e-019 3.367e-006 -1.522e-022 -4.603e-010 8.078e-027 1.513e-014];
G = tf(num,den); % plant
G = ss(G);

figure(1);clf;bode(G,logspace(-20,4,1e2)); % compare plants in bode
figure(2);clf;pzmap(G); % poles and zeros of G

ws = tf([.1 1],[1 .1]); % sensitivity weight
wu = tf(1e-10); % control input weight

systemnames = 'ws wu G';
inputvar = '[r;u]';
outputvar = '[ws;wu;-r+G]';
input_to_wu = '[u]';
input_to_ws = '[-r+G]';
input_to_G = '[u]';
cleanupsysic = 'yes';
Pw = sysic; % weighted system interconnection

[Chinf,cl,gamma,info] = hinfsyn(Pw,1,1); % Hinf controller

systemnames = 'G';
inputvar = '[r;u]';
outputvar = '[G;u;-r+G;r-G]';
input_to_G = '[u]';
cleanupsysic = 'yes';
Pu = sysic; % weighted system interconnection

Thinf = minreal(lft(Pu,Chinf)); % closed loop

% plots
figure(3);clf;bodemag(Thinf(3,1),gamma/ws,{1e-25,1e10});legend('Sinf','gamma/ws');
figure(4);clf;bodemag(Thinf(2,1),gamma/wu,{1e-25,1e10});legend('Rinf','gamma/wu');

% pi controller
Cpi = 5 * tf([0.1 1],[0.1 0]);
Spi = minreal(inv(1+G*Cpi));
Rpi = minreal(C * Spi);
figure(3);clf;bodemag(Thinf(3,1),Spi,{1e-25,1e10});legend('Sinf','Spi');
figure(4);clf;bodemag(Thinf(2,1),Rpi,{1e-25,1e10});legend('Rinf','Rpi');
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