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[CreaPhase.git] / octave_packages / control-2.3.52 / Anderson.m

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+%% -*- texinfo -*-
+%% Frequency-weighted coprime factorization controller reduction.
+
+% ===============================================================================
+% Coprime Factorization Controller Reduction     Lukas Reichlin     December 2011
+% ===============================================================================
+% Reference: Anderson, B.D.O.: Controller Reduction: Concepts and Approaches
+%            IEEE Transactions of Automatic Control, Vol. 34, No. 8, August 1989
+% ===============================================================================
+
+% Tabula Rasa
+clear all, close all, clc
+
+% Plant
+A = [ -0.161      -6.004      -0.58215    -9.9835     -0.40727    -3.982       0.0         0.0
+       1.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0
+       0.0         1.0         0.0         0.0         0.0         0.0         0.0         0.0
+       0.0         0.0         1.0         0.0         0.0         0.0         0.0         0.0
+       0.0         0.0         0.0         1.0         0.0         0.0         0.0         0.0
+       0.0         0.0         0.0         0.0         1.0         0.0         0.0         0.0
+       0.0         0.0         0.0         0.0         0.0         1.0         0.0         0.0
+       0.0         0.0         0.0         0.0         0.0         0.0         1.0         0.0     ];
+
+B = [  1.0
+       0.0  
+       0.0  
+       0.0  
+       0.0  
+       0.0  
+       0.0  
+       0.0 ];
+
+C = [  0.0         0.0         6.4432e-3   2.3196e-3   7.1252e-2   1.0002      0.10455     0.99551 ];
+
+G = ss (A, B, C);
+
+% LQG Design
+H = [  0.0         0.0         0.0         0.0         0.55       11.0         1.32       18.0     ];
+
+q1 = 1e-6;
+q2 = 100;   % [100, 1000, 2000]
+
+Q = q1 * H.' * H;
+R = 1;
+
+W = q2 * B * B.';
+V = 1;
+
+F = lqr (G, Q, R)
+L = lqe (G, W, V)
+
+% Coprime Factorization using Balanced Truncation Approximation
+figure (1)
+for k = 8:-1:2
+  Kr = cfconred (G, F, L, k);   % 'method', 'bfsr-bta'
+  T = feedback (G*Kr);
+  step (T, 200)
+  hold on
+endfor
+hold off
+
+% Coprime Factorization using Singular Perturbation Approximation
+figure (2)
+for k = 8:-1:2
+  Kr = cfconred (G, F, L, k, 'method', 'bfsr-spa');
+  T = feedback (G*Kr);
+  step (T, 200)
+  hold on
+endfor
+hold off
+
+% Frequency-Weighted Coprime Factorization using BTA
+figure (3)
+for k = 8:-1:2
+  Kr = fwcfconred (G, F, L, k);
+  T = feedback (G*Kr);
+  step (T, 300)
+  hold on
+endfor
+hold off