red_pend.m

三级倒立摆的稳定

% Controller order reduction
%
omega = logspace(-4,4,100);
K_g = frsp(K,omega);
[Ks,Ku] = sdecomp(K);
[Kb,hsig] = sysbal(Ks);
K1 = hankmr(Kb,hsig,27,'d');
Kred = madd(K1,Ku);
Kred_g = frsp(Kred,omega);
%
% frequency responses of the controllers
figure(1)
vplot('liv,lm',vnorm(K_g),'r-',vnorm(Kred_g),'c--')
grid
tmp1 = 'Maximum singular values of the';
tmp2 = ' controller transfer matrices';
title([tmp1 tmp2])
xlabel('Frequency (rad/sec)')
%legend('Full-order (n = 84) controller', ...
%       'Reduced-order (n = 27) controller',3)
%
% model reduction error (in nu-gap metric)   
K_error = nugap(K,Kred) 
clear Ks Ku Kb K1