--- /dev/null
+%% -*- texinfo -*-
+%% Robust control of a mass-damper-spring system.
+%% Type @code{which MDSSystem} to locate,
+%% @code{edit MDSSystem} to open and simply
+%% @code{MDSSystem} to run the example file.
+
+% ===============================================================================
+% Robust Control of a Mass-Damper-Spring System Lukas Reichlin August 2011
+% ===============================================================================
+% Reference: Gu, D.W., Petkov, P.Hr. and Konstantinov, M.M.
+% Robust Control Design with Matlab, Springer 2005
+% ===============================================================================
+
+% Tabula Rasa
+clear all, close all, clc
+
+% ===============================================================================
+% System Model
+% ===============================================================================
+% +---------------+
+% | d_m 0 0 |
+% +-----| 0 d_c 0 |<----+
+% u_m | | 0 0 d_k | | y_m
+% u_c | +---------------+ | y_c
+% u_k | | y_k
+% | +---------------+ |
+% +---->| |-----+
+% | G_nom |
+% u ----->| |-----> y
+% +---------------+
+
+% Nominal Values
+m_nom = 3; % mass
+c_nom = 1; % damping coefficient
+k_nom = 2; % spring stiffness
+
+% Perturbations
+p_m = 0.4; % 40% uncertainty in the mass
+p_c = 0.2; % 20% uncertainty in the damping coefficient
+p_k = 0.3; % 30% uncertainty in the spring stiffness
+
+% State-Space Representation
+A = [ 0, 1
+ -k_nom/m_nom, -c_nom/m_nom ];
+
+B1 = [ 0, 0, 0
+ -p_m, -p_c/m_nom, -p_k/m_nom ];
+
+B2 = [ 0
+ 1/m_nom ];
+
+C1 = [ -k_nom/m_nom, -c_nom/m_nom
+ 0, c_nom
+ k_nom, 0 ];
+
+C2 = [ 1, 0 ];
+
+D11 = [ -p_m, -p_c/m_nom, -p_k/m_nom
+ 0, 0, 0
+ 0, 0, 0 ];
+
+D12 = [ 1/m_nom
+ 0
+ 0 ];
+
+D21 = [ 0, 0, 0 ];
+
+D22 = [ 0 ];
+
+inname = {'u_m', 'u_c', 'u_k', 'u'}; % input names
+outname = {'y_m', 'y_c', 'y_k', 'y'}; % output names
+
+G_nom = ss (A, [B1, B2], [C1; C2], [D11, D12; D21, D22], ...
+ 'inputname', inname, 'outputname', outname);
+
+G = G_nom(4, 4); % extract output y and input u
+
+
+% ===============================================================================
+% Frequency Analysis of Uncertain System
+% ===============================================================================
+
+% Uncertainties: -1 <= delta_m, delta_c, delta_k <= 1
+[delta_m, delta_c, delta_k] = ndgrid ([-1, 0, 1], [-1, 0, 1], [-1, 0, 1]);
+
+% Bode Plots of Perturbed Plants
+w = logspace (-1, 1, 100); % frequency vector
+figure (1)
+
+for k = 1 : numel (delta_m)
+ Delta = diag ([delta_m(k), delta_c(k), delta_k(k)]);
+ G_per = lft (Delta, G_nom);
+ bode (G_per, w)
+ subplot (2, 1, 1)
+ hold on
+ subplot (2, 1, 2)
+ hold on
+endfor
+
+
+% ===============================================================================
+% Mixed Sensitivity H-infinity Controller Design (S over KS Method)
+% ===============================================================================
+% +-------+
+% +--------------------->| W_p |----------> e_p
+% | +-------+
+% | +-------+
+% | +---->| W_u |----------> e_u
+% | | +-------+
+% | | +---------+
+% | | ->| |->
+% r + e | +-------+ u | | G_nom |
+% ----->(+)---+-->| K |----+--->| |----+----> y
+% ^ - +-------+ +---------+ |
+% | |
+% +-----------------------------------------+
+
+% Weighting Functions
+s = tf ('s'); % transfer function variable
+W_p = 0.95 * (s^2 + 1.8*s + 10) / (s^2 + 8.0*s + 0.01); % performance weighting
+W_u = 10^-2; % control weighting
+
+% Synthesis
+K_mix = mixsyn (G, W_p, W_u); % mixed-sensitivity H-infinity synthesis
+
+% Interconnections
+L_mix = G * K_mix; % open loop
+T_mix = feedback (L_mix); % closed loop
+
+% Plotting
+figure (2)
+bode (K_mix) % bode plot
+
+figure (3)
+step (T_mix, 10) % step response for 10 seconds
+
+
+% ===============================================================================
+% H-infinity Loop-Shaping Design (Normalized Coprime Factor Perturbations)
+% ===============================================================================
+
+% Settings
+W1 = 8 * (2*s + 1) / (0.9*s); % precompensator
+W2 = 1; % postcompensator
+factor = 1.1; % suboptimal controller
+
+% Synthesis
+K_ncf = ncfsyn (G, W1, W2, factor); % positive feedback controller
+
+% Interconnections
+K_ncf = -K_ncf; % negative feedback controller
+L_ncf = G * K_ncf; % open loop
+T_ncf = feedback (L_ncf); % closed loop
+
+% Plotting
+figure (4)
+bode (K_ncf) % bode plot
+
+figure (5)
+step (T_ncf, 10) % step response for 10 seconds
+
+% ===============================================================================
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