www.gusucode.com > robust 案例源码程序 matlab代码 > robust/PlotWorstCaseGainOfUncertainSystemExample.m
%% Plot Worst-Case Gain of Uncertain System % Plot the worst-case gain of the following system: % % $$sys = \frac{{{s^2} + 3s}}{{{s^2} + 2s + a}}.$$ % % The uncertain parameter _a_ = 2 $\pm$ 1. %% a = ureal('a',2); usys = tf([1 3 0],[1 2 a]); wcsigma(usys) %% % The |Worst| curve identifies the single response within the uncertainty % that yields the highest gain at any frequency. The |Worst-case gain % (upper bound)| curve is the envelope produced by finding the highest gain % within the uncertainty at each frequency. % % The |Worst perturbation| curve identifies the combination of uncertain % elements within the specified range that yields the highest overall gain. % This perturbation corresponds to the |wcu| output of |wcgain|. The % |Worst-case gain| curves show the lower and upper bounds on the % worst-case gain at each frequency. For any perturbation within the % specified uncertainty range, the principal gains (singular values) of the % perturbed system lie below the |Worst-case gain (upper bound)| curve. %% % Focus the plot on the region between 0.1 and 10 rad/s. w = {0.1 10}; wcsigma(usys,w) %% % Examine the effect on the worst-case response of increasing the uncertainty % range. To do this without changing the uncertainty specified in |usys|, % use the |ULevel| option of |wcOptions|. This option scales the normalized % uncertainty by the factor you specify. For example, examine the % worst-case response a 50% greater uncertainty range. opts = wcOptions('ULevel',1.5); wcsigma(usys,w,opts) %% % The plot shows that increasing the uncertainty range substantially % increases the worst-case gain at low frequencies.