www.gusucode.com > robust 案例源码程序 matlab代码 > robust/MixedSensitivityH2LoopShapingExample.m
%% Mixed-Sensitivity H2 Loop Shaping % Shape the singular value plots of the sensitivity $S = (I+ GK)^{-1}$ and % complementary sensitivity $T = GK(I+GK)^{-1}$. %% % To do so, find a stabilizing controller _K_ that minimizes the $H_2$ norm % of: %% % % $${T_{{y_1}{u_1}}} \buildrel \Delta \over = \left[ {\begin{array}{*{20}{c}} % {{W_1}S}\\ % {({W_2}/G)T}\\ % {{W_3}T} % \end{array}} \right].$$ % %% % Assume the following plant and weights: % % $$G(s) = \frac{{s - 1}}{{s - 2}},{\rm{ }}{W_1} = \frac{{0.1(s + 1000)}}{{100s + 1}},{\rm{ }}{W_2} = 0.1{\rm{, }}{W_3} = 0.$$ % %% % Using those values, construct the augmented plant P, as illustrated in % the <docid:robust_ref.f10-71923> reference page. % Copyright 2015 The MathWorks, Inc. s = zpk('s'); G = 10*(s-1)/(s+1)^2; G.u = 'u2'; G.y = 'y'; W1 = 0.1*(s+1000)/(100*s+1); W1.u = 'y2'; W1.y = 'y11'; W2 = tf(0.1); W2.u = 'u2'; W2.y = 'y12'; S = sumblk('y2 = u1 - y'); P = connect(G,S,W1,W2,{'u1','u2'},{'y11','y12','y2'}); %% % Use |h2syn| to generate the controller. Note that this system has NMEAS % = 1 and NCON = 1. [K,CL,GAM] = h2syn(P,1,1); %% % Examine the resulting loop shape. L = G*K; S = inv(1+L); T = 1-S; sigmaplot(L,'k-.',S,'r',T,'g') legend('open-loop','sensitivity','closed-loop')