mu_pend.m

三级倒立摆的稳定

% mu-analysis of the triple inverted pendulum
% closed-loop system
%
clp_ic = starp(pend_ic,K,6,2);
omega = logspace(-1,4,100);
clp_g = frsp(clp_ic,omega);
%
% robust stability
rob_stab = sel(clp_g,[1:8],[1:8]);
% Mixed perturbations
blkrs = [1 1;1 1;-1 1;-1 1;-1 1;-1 1;-1 1;-1 1];
rbnds = mu(rob_stab,blkrs);
figure(1)
vplot('liv,lm',sel(rbnds,1,1),'r-',sel(rbnds,1,2),'c--')
grid
title('Robust stability')
xlabel('Frequency (rad/s)')
ylabel('mu')
%legend('Upper bound','Lower bound',3)
disp(' ')
disp(['mu-robust stability: ' ...
     num2str(pkvnorm(sel(rbnds,1,1)))])
disp(' ')
%
% nominal performance
nom_perf = sel(clp_g,[9:13],[9:17]);
figure(2)
vplot('liv,m',vnorm(nom_perf),'r-')
grid
title('Nominal performance')
xlabel('Frequency (rad/s)')
%
% robust performance
rob_perf = sel(clp_g,[1:13],[1:17]);
blks = [blkrs;9 5];
rpbnds = mu(rob_perf,blks);
figure(3)
vplot('liv,m',sel(rpbnds,1,1),'r-',sel(rpbnds,1,2),'c--')
grid
title('Robust performance')
xlabel('Frequency (rad/s)')
ylabel('mu')
%legend('Upper bound','Lower bound',4)
disp(' ')
disp(['mu-robust performance: ' ...
     num2str(pkvnorm(sel(rpbnds,1,1)))])
disp(' ')