q8.m

Robust自动控制讲义

close all;
% (a)  
s = tf('s'); % Laplace transform variable 's'.
G = (4*s+1)/((s-0.01)*(s^2+0.1*s+1)); % plant to be controlled 
% K = 2.85e5 *(s+0.2)*(s^2  + 0.1*s + 1)/((s+1151)*(s+97.73)*(s+0.25)*(s+0.1324))
K = 3e5 *(s+0.2)*(s^2  + 0.1*s + 1)/((s+1151)*(s+97.73)*(s+0.25)*(s+0.1324))

% Nominal performance test:
L=G*K;  % loop transfer function
S=1/(1+L); % Sensitivity
T=1-S;      % complementary sensitivity
WpS = Wp*S;
% Plot the magnitude of WpS:
figure;
bodemag(WpS);title('|Wp S|');
 
% (b)
 Wi=(2*s+1)/(10*s+2);
 WiT = Wi*T;
 N = [WpS ; WiT];
 figure;
 sigma(N);title('Singular value of N(j\omega)');