From 316eb0e1dfabefc4cb61c2fba1b7ed64adfc57ca Mon Sep 17 00:00:00 2001
From: Enrico Lumetti <enrico.lumetti@gmail.com>
Date: Wed, 11 Aug 2021 18:59:38 +0200
Subject: [PATCH] Example of multiplicative uncertainty fit

---
 robust/mult_uncertainty.m | 34 ++++++++++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 robust/mult_uncertainty.m

diff --git a/robust/mult_uncertainty.m b/robust/mult_uncertainty.m
new file mode 100644
index 0000000..83e5e67
--- /dev/null
+++ b/robust/mult_uncertainty.m
@@ -0,0 +1,34 @@
+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