X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2Fltimodels.m;fp=octave_packages%2Fcontrol-2.3.52%2Fltimodels.m;h=369193f492fd278a21d662e27efda0b9f19dffcf;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05
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+## Copyright (C) 2009 Luca Favatella
+## Copyright (C) 2009, 2010, 2011 Lukas Reichlin
+##
+## This file is part of LTI Syncope.
+##
+## LTI Syncope is free software: you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation, either version 3 of the License, or
+## (at your option) any later version.
+##
+## LTI Syncope is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with LTI Syncope. If not, see .
+
+## -*- texinfo -*-
+## @deftypefn {Function File} test ltimodels
+## @deftypefnx {Function File} ltimodels
+## @deftypefnx {Function File} ltimodels (@var{systype})
+## Test suite and help for LTI models.
+## @end deftypefn
+
+## Author: Lukas Reichlin
+## Created: November 2009
+## Version: 0.2
+
+function ltimodels (systype = "general")
+
+ %if (nargin > 1)
+ print_usage ();
+ %endif
+
+ ## TODO: write documentation
+
+ if (! ischar (systype))
+ error ("ltimodels: argument must be a string");
+ endif
+
+ systype = lower (systype);
+
+ switch (systype)
+ case "ss"
+ str = {"State Space (SS) Models"\
+ "-----------------------"\
+ ""};
+
+ case "tf"
+ str = {"Transfer Function (TF) Models"\
+ "-----------------------------"\
+ ""};
+
+ otherwise # general
+ str = {"Linear Time Invariant (LTI) Models"\
+ "----------------------------------"\
+ ""};
+
+ endswitch
+
+ disp ("");
+ disp (char (str));
+
+endfunction
+
+
+
+## ==============================================================================
+## LTI Tests
+## ==============================================================================
+
+## isct, isdt
+%!shared ltisys
+%! ltisys = tf (12);
+%!assert (ltisys.ts, -2);
+%!assert (isct (ltisys));
+%!assert (isdt (ltisys));
+
+%!shared ltisys
+%! ltisys = ss (17);
+%!assert (ltisys.ts, -2);
+%!assert (isct (ltisys));
+%!assert (isdt (ltisys));
+
+%!shared ltisys
+%! ltisys = tf (1, [1 1]);
+%!assert (ltisys.ts, 0);
+%!assert (isct (ltisys));
+%!assert (! isdt (ltisys));
+
+%!shared ltisys, ts
+%! ts = 0.1;
+%! ltisys = ss (-1, 1, 1, 0, ts);
+%!assert (ltisys.ts, ts);
+%!assert (! isct (ltisys));
+%!assert (isdt (ltisys));
+
+
+
+## ==============================================================================
+## TF Tests
+## ==============================================================================
+
+
+
+## ==============================================================================
+## SS Tests
+## ==============================================================================
+
+
+## staircase (SLICOT AB01OD)
+%!shared Ac, Bc, Ace, Bce
+%! A = [ 17.0 24.0 1.0 8.0 15.0
+%! 23.0 5.0 7.0 14.0 16.0
+%! 4.0 6.0 13.0 20.0 22.0
+%! 10.0 12.0 19.0 21.0 3.0
+%! 11.0 18.0 25.0 2.0 9.0 ];
+%!
+%! B = [ -1.0 -4.0
+%! 4.0 9.0
+%! -9.0 -16.0
+%! 16.0 25.0
+%! -25.0 -36.0 ];
+%!
+%! tol = 0;
+%!
+%! A = A.'; # There's a little mistake in the example
+%! # program of routine AB01OD in SLICOT 5.0
+%!
+%! [Ac, Bc, U, ncont] = slab01od (A, B, tol);
+%!
+%! Ace = [ 12.8848 3.2345 11.8211 3.3758 -0.8982
+%! 4.4741 -12.5544 5.3509 5.9403 1.4360
+%! 14.4576 7.6855 23.1452 26.3872 -29.9557
+%! 0.0000 1.4805 27.4668 22.6564 -0.0072
+%! 0.0000 0.0000 -30.4822 0.6745 18.8680 ];
+%!
+%! Bce = [ 31.1199 47.6865
+%! 3.2480 0.0000
+%! 0.0000 0.0000
+%! 0.0000 0.0000
+%! 0.0000 0.0000 ];
+%!
+%!assert (Ac, Ace, 1e-4);
+%!assert (Bc, Bce, 1e-4);
+
+
+## controllability staircase form of descriptor state-space models (SLICOT TG01HD)
+%!shared ac, ec, bc, cc, q, z, ncont, ac_e, ec_e, bc_e, cc_e, q_e, z_e, ncont_e
+%!
+%! a = [ 2 0 2 0 -1 3 1
+%! 0 1 0 0 1 0 0
+%! 0 0 0 1 0 0 1
+%! 0 0 2 0 -1 3 1
+%! 0 0 0 1 0 0 1
+%! 0 1 0 0 1 0 0
+%! 0 0 0 1 0 0 1 ];
+%!
+%! e = [ 0 0 1 0 0 0 0
+%! 0 0 0 0 0 1 0
+%! 0 0 0 0 0 0 1
+%! 0 0 0 0 0 0 1
+%! 0 0 0 1 0 0 0
+%! 0 0 1 0 -1 0 0
+%! 1 3 0 2 0 0 0 ];
+%!
+%! b = [ 2 1 0
+%! 0 0 0
+%! 0 0 0
+%! 0 0 0
+%! 0 0 0
+%! 0 0 0
+%! 1 2 3 ];
+%!
+%! c = [ 1 0 0 1 0 0 1
+%! 0 -1 1 0 -1 1 0 ];
+%!
+%! tol = 0;
+%!
+%! [ac, ec, bc, cc, q, z, ncont] = sltg01hd (a, e, b, c, tol);
+%!
+%! ncont_e = 3;
+%!
+%! ac_e = [ 0.0000 0.0000 0.0000 0.0000 -1.2627 0.4334 0.4666
+%! 0.0000 2.0000 0.0000 -3.7417 -0.8520 0.2924 -0.4342
+%! 0.0000 0.0000 1.7862 0.3780 -0.2651 -0.7723 0.0000
+%! 0.0000 0.0000 0.0000 3.7417 0.8520 -0.2924 0.4342
+%! 0.0000 0.0000 0.0000 0.0000 -1.5540 0.5334 0.5742
+%! 0.0000 0.0000 0.0000 0.0000 -0.6533 0.2242 0.2414
+%! 0.0000 0.0000 0.0000 0.0000 -0.5892 0.2022 0.2177 ];
+%!
+%! ec_e = [ -1.8325 1.0000 2.3752 0.0000 -0.8214 0.2819 1.8016
+%! 0.4887 0.0000 0.3770 -0.5345 0.1874 0.5461 0.0000
+%! -0.1728 0.0000 -0.1333 -1.1339 0.1325 0.3861 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.8520 -0.2924 0.4342
+%! 0.0000 0.0000 0.0000 0.0000 -1.0260 -0.1496 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 1.1937 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 ];
+%!
+%! bc_e = [ 1.0000 2.0000 3.0000
+%! 2.0000 1.0000 0.0000
+%! 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.0000 ];
+%!
+%! cc_e = [ 0.0000 1.0000 0.0000 0.0000 -1.2627 0.4334 0.4666
+%! 0.3665 0.0000 -0.9803 -1.6036 0.1874 0.5461 0.0000 ];
+%!
+%! q_e = [ 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.7071 0.0000 0.2740 -0.6519 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.8304 0.3491 -0.4342
+%! 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.4003 0.1683 0.9008
+%! 0.0000 0.0000 0.7071 0.0000 -0.2740 0.6519 0.0000
+%! 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ];
+%!
+%! z_e = [ 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
+%! -0.6108 0.0000 0.7917 0.0000 0.0000 0.0000 0.0000
+%! 0.4887 0.0000 0.3770 -0.5345 0.1874 0.5461 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 -0.4107 0.1410 0.9008
+%! 0.6108 0.0000 0.4713 0.2673 -0.1874 -0.5461 0.0000
+%! -0.1222 0.0000 -0.0943 -0.8018 -0.1874 -0.5461 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 -0.8520 0.2924 -0.4342 ];
+%!
+%!assert (ac, ac_e, 1e-4);
+%!assert (ec, ec_e, 1e-4);
+%!assert (bc, bc_e, 1e-4);
+%!assert (cc, cc_e, 1e-4);
+%!assert (q, q_e, 1e-4);
+%!assert (z, z_e, 1e-4);
+%!assert (ncont, ncont_e);
+
+
+## observability staircase form of descriptor state-space models (SLICOT TG01ID)
+%!shared ao, eo, bo, co, q, z, nobsv, ao_e, eo_e, bo_e, co_e, q_e, z_e, nobsv_e
+%!
+%! a = [ 2 0 0 0 0 0 0
+%! 0 1 0 0 0 1 0
+%! 2 0 0 2 0 0 0
+%! 0 0 1 0 1 0 1
+%! -1 1 0 -1 0 1 0
+%! 3 0 0 3 0 0 0
+%! 1 0 1 1 1 0 1 ];
+%!
+%! e = [ 0 0 0 0 0 0 1
+%! 0 0 0 0 0 0 3
+%! 1 0 0 0 0 1 0
+%! 0 0 0 0 1 0 2
+%! 0 0 0 0 0 -1 0
+%! 0 1 0 0 0 0 0
+%! 0 0 1 1 0 0 0 ];
+%!
+%! b = [ 1 0
+%! 0 -1
+%! 0 1
+%! 1 0
+%! 0 -1
+%! 0 1
+%! 1 0 ];
+%!
+%! c = [ 2 0 0 0 0 0 1
+%! 1 0 0 0 0 0 2
+%! 0 0 0 0 0 0 3 ];
+%!
+%! tol = 0;
+%!
+%! [ao, eo, bo, co, q, z, nobsv] = sltg01id (a, e, b, c, tol);
+%!
+%! nobsv_e = 3;
+%!
+%! ao_e = [ 0.2177 0.2414 0.5742 0.4342 0.0000 -0.4342 0.4666
+%! 0.2022 0.2242 0.5334 -0.2924 -0.7723 0.2924 0.4334
+%! -0.5892 -0.6533 -1.5540 0.8520 -0.2651 -0.8520 -1.2627
+%! 0.0000 0.0000 0.0000 3.7417 0.3780 -3.7417 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 1.7862 0.0000 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 2.0000 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ];
+%!
+%! eo_e = [ 1.0000 0.0000 0.0000 0.4342 0.0000 0.0000 1.8016
+%! 0.0000 1.1937 -0.1496 -0.2924 0.3861 0.5461 0.2819
+%! 0.0000 0.0000 -1.0260 0.8520 0.1325 0.1874 -0.8214
+%! 0.0000 0.0000 0.0000 0.0000 -1.1339 -0.5345 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 -0.1333 0.3770 2.3752
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
+%! 0.0000 0.0000 0.0000 0.0000 -0.1728 0.4887 -1.8325 ];
+%!
+%! bo_e = [ 0.4666 0.0000
+%! 0.4334 0.5461
+%! -1.2627 0.1874
+%! 0.0000 -1.6036
+%! 0.0000 -0.9803
+%! 1.0000 0.0000
+%! 0.0000 0.3665 ];
+%!
+%! co_e = [ 0.0000 0.0000 0.0000 0.0000 0.0000 2.0000 1.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 2.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3.0000 ];
+%!
+%! q_e = [ 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.7917 0.0000 -0.6108
+%! 0.0000 0.5461 0.1874 -0.5345 0.3770 0.0000 0.4887
+%! 0.9008 0.1410 -0.4107 0.0000 0.0000 0.0000 0.0000
+%! 0.0000 -0.5461 -0.1874 0.2673 0.4713 0.0000 0.6108
+%! 0.0000 -0.5461 -0.1874 -0.8018 -0.0943 0.0000 -0.1222
+%! -0.4342 0.2924 -0.8520 0.0000 0.0000 0.0000 0.0000 ];
+%!
+%! z_e = [ 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000
+%! 0.0000 -0.6519 0.2740 0.0000 0.7071 0.0000 0.0000
+%! -0.4342 0.3491 0.8304 0.0000 0.0000 0.0000 0.0000
+%! 0.0000 0.0000 0.0000 -1.0000 0.0000 0.0000 0.0000
+%! 0.9008 0.1683 0.4003 0.0000 0.0000 0.0000 0.0000
+%! 0.0000 0.6519 -0.2740 0.0000 0.7071 0.0000 0.0000
+%! 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 ];
+%!
+%!assert (ao, ao_e, 1e-4);
+%!assert (eo, eo_e, 1e-4);
+%!assert (bo, bo_e, 1e-4);
+%!assert (co, co_e, 1e-4);
+%!assert (q, q_e, 1e-4);
+%!assert (z, z_e, 1e-4);
+%!assert (nobsv, nobsv_e);
+
+
+## ss2tf conversion by Slicot TB04BD
+## Test provided by Slicot
+%!shared NUM, DEN, NUMe, DENe
+%! A = [ -1.0 0.0 0.0
+%! 0.0 -2.0 0.0
+%! 0.0 0.0 -3.0 ];
+%!
+%! B = [ 0.0 1.0 -1.0
+%! 1.0 1.0 0.0 ].';
+%!
+%! C = [ 0.0 1.0 1.0
+%! 1.0 1.0 1.0 ];
+%!
+%! D = [ 1.0 0.0
+%! 0.0 1.0 ];
+%!
+%! [NUM, DEN] = tfdata (ss (A, B, C, D));
+%!
+%! NUMe = {[1, 5, 7], [1]; [1], [1, 5, 5]};
+%!
+%! DENe = {[1, 5, 6], [1, 2]; [1, 5, 6], [1, 3, 2]};
+%!
+%!assert (NUM, NUMe, 1e-4);
+%!assert (DEN, DENe, 1e-4);
+
+
+## ss2tf conversion by Slicot TB04BD
+## Trivial test
+%!shared NUM, DEN, NUMe, DENe
+%! A = [ 0 ];
+%!
+%! B = [ 1 ];
+%!
+%! C = [ 1 ];
+%!
+%! D = [ 0 ];
+%!
+%! [NUM, DEN] = tfdata (ss (A, B, C, D));
+%!
+%! NUMe = {[1]};
+%!
+%! DENe = {[1, 0]};
+%!
+%!assert (NUM, NUMe, 1e-4);
+%!assert (DEN, DENe, 1e-4);
+
+
+## transfer function to state-space conversion
+## test from SLICOT TD04AD
+%!shared Mo, Me
+%! INDEX = [ 3 3 ];
+%!
+%! DCOEFF = [ 1.0 6.0 11.0 6.0
+%! 1.0 6.0 11.0 6.0 ];
+%!
+%! UCOEFF = zeros (2, 2, 4);
+%!
+%! u11 = [ 1.0 6.0 12.0 7.0 ];
+%! u12 = [ 0.0 1.0 4.0 3.0 ];
+%! u21 = [ 0.0 0.0 1.0 1.0 ];
+%! u22 = [ 1.0 8.0 20.0 15.0 ];
+%!
+%! UCOEFF(1,1,:) = u11;
+%! UCOEFF(1,2,:) = u12;
+%! UCOEFF(2,1,:) = u21;
+%! UCOEFF(2,2,:) = u22;
+%!
+%! [Ao, Bo, Co, Do] = sltd04ad (UCOEFF, DCOEFF, INDEX, 0);
+%!
+%! Ae = [ 0.5000 -0.8028 0.9387
+%! 4.4047 -2.3380 2.5076
+%! -5.5541 1.6872 -4.1620 ];
+%!
+%! Be = [ -0.2000 -1.2500
+%! 0.0000 -0.6097
+%! 0.0000 2.2217 ];
+%!
+%! Ce = [ 0.0000 -0.8679 0.2119
+%! 0.0000 0.0000 0.9002 ];
+%!
+%! De = [ 1.0000 0.0000
+%! 0.0000 1.0000 ];
+%!
+%! Mo = [Ao, Bo; Co, Do];
+%! Me = [Ae, Be; Ce, De];
+%!
+%!assert (Mo, Me, 1e-4);