www.gusucode.com > robust 案例源码程序 matlab代码 > robust/NormalizedCoprimeStabilityMarginExample.m
%% Normalized Coprime Stability Margin % Consider an unstable first-order plant, |p|, stabilized % by high-gain and low-gain controllers, |cL| and |cH|. %% p = tf(4,[1 -0.001]); cL = 1; cH = 10; %% % Compute the stability margin of the closed-loop system with the low-gain controller. [margL,~] = ncfmargin(p,cL) %% % Similarly, compute the stability margin of the closed-loop system with % the high-gain controller. [margH,~] = ncfmargin(p,cH) %% % The closed-loop systems with low-gain and high-gain controllers have % normalized coprime stability margins of about 0.71 and 0.1, respectively. % This result indicates that the closed-loop system with low-gain % controller is more robust to unstructured perturbations than the system % with the high-gain controller. % % To observe this difference in robustness, construct an uncertain plant, % |punc|, that has an additional 11% unmodeled dynamics % compared to the nominal plant. punc = p + ultidyn('uncstruc',[1 1],'Bound',0.11); %% % Calculate the robust stability of the closed-loop systems formed by the % uncertain plant and each controller. [stabmargL,~] = robstab(feedback(punc,cL)) %% [stabmargH,~] = robstab(feedback(punc,cH)) %% % As expected, the robust stability analysis shows that the closed-loop % system with low-gain controller is more robustly stable in the presence % of the unmodeled LTI dynamics. In fact, this closed-loop system can % tolerate 909% (or 9.09*11%) of the unmodeled dynamics. In contrast, % closed-loop system with the high-gain controller is not robustly stable. % That closed-loop system can only tolerate 90.9% (or 0.909*11%) of the % unmodeled dynamics.