wcdiskmarginplot

Plot the worst-case disk-based gain and phase margins of the following system:

${\mathit{L}}_{\mathrm{unc}}=\frac{1}{{\mathit{s}}^2+\mathit{a}+10}\left(1+0.1\Delta \right)$,

whereais an uncertain real parameter with a nominal value of 1 and a range of 0.2–2, and Δ is a gain-bounded dynamic uncertainty.

a = ureal('a',1,'Range',[.2 2]); Delta = ultidyn('Delta',1); Lunc = tf(1,[1 a 10]) * (1+0.1*Delta); wcdiskmarginplot(Lunc) legend('location','SouthEast')

TheWorst perturbationcurve corresponds to the combination of uncertain elements that yields the smallest disk margin across frequency. This perturbation corresponds to thewcuoutput ofwcdiskmargin.

TheWorst-case margin曲线显示磨破的上下界限t-case margins at each frequency. For any perturbation within the specified uncertainty range, the disk-based gain or phase margins of the perturbed system lie below theWorst-case margin(upper bound) curve. In other words, this curve is the envelope produced by finding the smallest margins within the uncertainty at each frequency. For this system, the lower and upper bounds are close enough to appear identical on the plot. (Seewcdiskmarginfor more information about these bounds.)

Focus the plot on the region between 0.5 and 10 rad/s.

w = {0.5,10}; wcdiskmarginplot(Lunc,w)

Examine the effect on the worst-case margins of increasing the uncertainty range. To do this without changing the uncertainty specified inLunc, use theULeveloption ofwcOptions. This option scales the normalized uncertainty by the factor you specify. For example, examine the worst-case margins for a 50% greater uncertainty range.

opts = wcOptions('ULevel',1.5); wcdiskmarginplot(Lunc,w,opts)

In this case, the gain and phase margins for the worst perturbation reach zero, and the worst margin at any frequency is also zero. This result means that extending the uncertainty range this far encompasses some perturbations that drive the closed-loop systemfeedback(Lunc,1)unstable.

Plot the worst-case disk margins as a function of frequency of a system with the following open-loop response.

a = ureal('a',10,'PlusMinus',[-4,4]); L = tf(25,[1 a a a]);

For the plot, use the default preferences specified in your Control System Toolbox preference, except specify the following attributes:

opts = diskmarginoptions('cstprefs'); opts.FreqUnits ='Hz'; opts.MagScale ='log'; opts.MagUnits ='abs'; opts.grid ='on'; w = {2*pi*1e-3,2*pi*10};% rad/swcdiskmarginplot(L,w,opts)

The plot you obtain might differ in appearance, depending on your current Control System Toolbox preference settings. (SeeToolbox Preferences Editor.)