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Example of multiplicative uncertainty fit

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Enrico Lumetti 2021-08-11 18:59:38 +02:00
parent c535ee08c4
commit 316eb0e1df
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robust/mult_uncertainty.m Normal file
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clear;
s = tf('s');
k = ureal('k', 2.5, 'Range', [2, 3]);
tau = ureal('tau', 2.5, 'Range', [2, 3]);
theta = ureal('theta', 2.5, 'Range', [2, 3]);
% delay is approximated using pade:
% e^(-theta*s) = e^(-theta*s)/2 1 - theta*s/2
% ------------- = --------------
% e^(theta*s)/2 1 + theta*s/2
G = k/(tau*s+1) * (1-theta*s)/2 / ((1+theta*s)/2);
G_nom = k.NominalValue/(tau.NominalValue*s+1);
% G = (1+I_m)G_nom => I_m = (G-G_nom)/G_nom
I_m = (G-G_nom)/G_nom;
% get wcgain
w = logspace(-3, 3, 40);
[wcg, wcu, info] = wcgain(I_m, w);
% fit worst-case magnitude to obtain a closed form of the multiplicative
% uncertainty
data = frd(info.Bounds(:, 2), w);
% use a second-order model
I_m_analytic = tf(fitmagfrd(data, 2));
sigma(I_m, w); hold;
semilogx(w, 20*log10(info.Bounds(:, 2)), 'green');
sigma(I_m_analytic, 'red');
I_m_analytic