X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;ds=sidebyside;f=octave_packages%2Fcontrol-2.3.52%2FMadievski.m;fp=octave_packages%2Fcontrol-2.3.52%2FMadievski.m;h=2bf4fbe547f6b37a54c404e2519f39daa9e30529;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hp=0000000000000000000000000000000000000000;hpb=1705066eceaaea976f010f669ce8e972f3734b05;p=CreaPhase.git diff --git a/octave_packages/control-2.3.52/Madievski.m b/octave_packages/control-2.3.52/Madievski.m new file mode 100644 index 0000000..2bf4fbe --- /dev/null +++ b/octave_packages/control-2.3.52/Madievski.m @@ -0,0 +1,126 @@ +%% -*- 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')