X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2FMDSSystem.m;fp=octave_packages%2Fcontrol-2.3.52%2FMDSSystem.m;h=92142be756008d481a9cc9a610034c94d62d9264;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05

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+%% -*- 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
+
+% ===============================================================================