Mercurial > forge
changeset 9550:f905dcc528fb octave-forge
control: work on documentation
| author | paramaniac |
|---|---|
| date | Thu, 01 Mar 2012 17:45:35 +0000 |
| parents | b89d165a0663 |
| children | c2199c8eb019 |
| files | main/control/devel/anderson.m main/control/devel/madievski.m main/control/inst/Anderson.m main/control/inst/Madievski.m main/control/inst/btamodred.m |
| diffstat | 5 files changed, 220 insertions(+), 210 deletions(-) [+] |
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--- a/main/control/devel/anderson.m Thu Mar 01 17:23:50 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,80 +0,0 @@ -%% -*- 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 = lqr (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
--- a/main/control/devel/madievski.m Thu Mar 01 17:23:50 2012 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,126 +0,0 @@ -%% -*- 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')
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/control/inst/Anderson.m Thu Mar 01 17:45:35 2012 +0000 @@ -0,0 +1,80 @@ +%% -*- 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 = lqr (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
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/main/control/inst/Madievski.m Thu Mar 01 17:45:35 2012 +0000 @@ -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')
--- a/main/control/inst/btamodred.m Thu Mar 01 17:23:50 2012 +0000 +++ b/main/control/inst/btamodred.m Thu Mar 01 17:45:35 2012 +0000 @@ -180,14 +180,24 @@ ## @item 'equil', 'scale' ## Boolean indicating whether equilibration (scaling) should be ## performed on system @var{G} prior to order reduction. +## This is done by state transformations. ## Default value is true if @code{G.scaled == false} and ## false if @code{G.scaled == true}. +## Note that for @acronym{MIMO} models,. ## @end table ## -## -## UNSTABLE (from bstmodred) -## -## MIMO (from bstmodred) +## For @acronym{MIMO} models, proper scaling of both inputs and outputs +## is of utmost importance. The input and output scaling can @strong{not} +## be done by the equilibration option or the @command{prescale} command +## because these functions perform state transformations only. +## Signals should not be scaled simply to the range of, say, -1 to +1. +## For all inputs (or outputs), a change from +1 to +2 should be of the +## same importance for the model. +## Think of a chemical reactor, the importance could be the cost to control this +## reactor. Then a change on each input from +1.5 to +2.0 would cost 50$. +## Otherwise, important behaviour of @var{G} could be neglected just because +## the corresponding signals have smaller numbers than those of other, +## less important effects of @var{G}. ## ## Approximation Properties: ## @itemize @bullet