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

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+%% -*- texinfo -*-
+%% Frequency-weighted controller reduction.
+
+% ===============================================================================
+% Frequency Weighted Controller Reduction       Lukas Reichlin      December 2011
+% ===============================================================================
+% Reference: Madievski, A.G. and Anderson, B.D.O.
+%            Sampled-Data Controller Reduction Procedure
+%            IEEE Transactions of Automatic Control
+%            Vol. 40, No. 11, November 1995
+% ===============================================================================
+
+% Tabula Rasa
+clear all, close all, clc
+
+% Plant
+Ap1 = [  0.0         1.0
+         0.0         0.0     ];
+
+Ap2 = [ -0.015       0.765
+        -0.765      -0.015   ];
+
+Ap3 = [ -0.028       1.410
+        -1.410      -0.028   ];
+
+Ap4 = [ -0.04        1.85
+        -1.85       -0.04    ];
+
+Ap = blkdiag (Ap1, Ap2, Ap3, Ap4);
+
+Bp = [   0.026
+        -0.251
+         0.033
+        -0.886
+        -4.017
+         0.145
+         3.604
+         0.280   ];
+
+Cp = [  -0.996      -0.105       0.261       0.009      -0.001      -0.043       0.002      -0.026   ];
+
+Dp = [   0.0     ];
+
+P = ss (Ap, Bp, Cp, Dp);
+
+% Controller
+Ac = [  -0.4077      0.9741      0.1073      0.0131      0.0023     -0.0186     -0.0003     -0.0098
+        -0.0977     -0.1750      0.0215     -0.0896     -0.0260      0.0057      0.0109     -0.0105
+         0.0011      0.0218     -0.0148      0.7769      0.0034     -0.0013     -0.0014      0.0011
+        -0.0361     -0.5853     -0.7701     -0.3341     -0.0915      0.0334      0.0378     -0.0290
+        -0.1716     -2.6546     -0.0210     -1.4467     -0.4428      1.5611      0.1715     -0.1318
+        -0.0020      0.0950      0.0029      0.0523     -1.3950     -0.0338     -0.0062      0.0045
+         0.1607      2.3824      0.0170      1.2979      0.3721     -0.1353     -0.1938      1.9685
+        -0.0006      0.1837      0.0048      0.1010      0.0289     -0.0111     -1.8619     -0.0311  ];
+
+Bc = [  -0.4105
+        -0.0868
+        -0.0004
+         0.0036
+         0.0081
+        -0.0085
+        -0.0004
+        -0.0132  ];
+
+Cc = [  -0.0447     -0.6611     -0.0047     -0.3601     -0.1033      0.0375      0.0427     -0.0329  ];
+
+Dc = [   0.0     ];
+
+K = ss (Ac, Bc, Cc, Dc);
+
+% Controller Reduction
+Kr4 = spaconred (P, K, 4, 'feedback', '-')
+Kr2 = spaconred (P, K, 2, 'feedback', '-')
+
+% Open Loop
+L = P * K;
+Lr4 = P * Kr4;
+Lr2 = P * Kr2;
+
+% Closed Loop
+T = feedback (L);
+Tr4 = feedback (Lr4);
+Tr2 = feedback (Lr2);
+
+% Frequency Range
+w = {1e-2, 1e1};
+
+% Bode Plot of Controller
+[mag, pha, w] = bode (K, w);
+[magr4, phar4, wr4] = bode (Kr4, w);
+[magr2, phar2, wr2] = bode (Kr2, w);
+
+mag = 20 * log10 (mag);
+magr4 = 20 * log10 (magr4);
+magr2 = 20 * log10 (magr2);
+
+figure (1)
+subplot (2, 1, 1)
+semilogx (w, mag, wr4, magr4, wr2, magr2)
+axis ('tight')
+ylim (__axis_margin__ (ylim))
+grid ('on')
+title ('Bode Diagrams of K and Kr')
+ylabel ('Magnitude [dB]')
+
+subplot (2, 1, 2)
+semilogx (w, pha, wr4, phar4, wr2, phar2)
+axis ('tight')
+ylim (__axis_margin__ (ylim))
+grid ('on')
+xlabel ('Frequency [rad/s]')
+ylabel ('Phase [deg]')
+legend ('K (8 states)', 'Kr (4 states)', 'Kr (2 states)', 'location', 'southwest')
+    
+% Step Response of Closed Loop
+[y, t] = step (T, 100);
+[yr4, tr4] = step (Tr4, 100);
+[yr2, tr2] = step (Tr2, 100);
+
+figure (2)
+plot (t, y, tr4, yr4, tr2, yr2)
+grid ('on')
+title ('Step Response of Closed Loop')
+xlabel ('Time [s]')
+ylabel ('Output [-]')
+legend ('K (8 states)', 'Kr (4 states)', 'Kr (2 states)', 'Location', 'SouthEast')