X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2F%40lti%2Fc2d.m;fp=octave_packages%2Fcontrol-2.3.52%2F%40lti%2Fc2d.m;h=397ce76984507965f3f8ea5a0122a8657d77b72a;hp=0000000000000000000000000000000000000000;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hpb=1705066eceaaea976f010f669ce8e972f3734b05 diff --git a/octave_packages/control-2.3.52/@lti/c2d.m b/octave_packages/control-2.3.52/@lti/c2d.m new file mode 100644 index 0000000..397ce76 --- /dev/null +++ b/octave_packages/control-2.3.52/@lti/c2d.m @@ -0,0 +1,222 @@ +## Copyright (C) 2009, 2011 Lukas F. 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} {@var{sys} =} c2d (@var{sys}, @var{tsam}) +## @deftypefnx {Function File} {@var{sys} =} c2d (@var{sys}, @var{tsam}, @var{method}) +## @deftypefnx {Function File} {@var{sys} =} c2d (@var{sys}, @var{tsam}, @var{"prewarp"}, @var{w0}) +## Convert the continuous lti model into its discrete-time equivalent. +## +## @strong{Inputs} +## @table @var +## @item sys +## Continuous-time LTI model. +## @item tsam +## Sampling time in seconds. +## @item method +## Optional conversion method. If not specified, default method @var{"zoh"} +## is taken. +## @table @var +## @item "zoh" +## Zero-order hold or matrix exponential. +## @item "tustin", "bilin" +## Bilinear transformation or Tustin approximation. +## @item "prewarp" +## Bilinear transformation with pre-warping at frequency @var{w0}. +## @end table +## @end table +## +## @strong{Outputs} +## @table @var +## @item sys +## Discrete-time LTI model. +## @end table +## @end deftypefn + +## Author: Lukas Reichlin +## Created: October 2009 +## Version: 0.3 + +function sys = c2d (sys, tsam, method = "std", w0 = 0) + + if (nargin < 2 || nargin > 4) + print_usage (); + endif + + if (! isa (sys, "lti")) + error ("c2d: first argument is not an lti model"); + endif + + if (isdt (sys)) + error ("c2d: system is already discrete-time"); + endif + + if (! issample (tsam)) + error ("c2d: second argument is not a valid sample time"); + endif + + if (! ischar (method)) + error ("c2d: third argument is not a string"); + endif + + if (! issample (w0, 0)) + error ("c2d: fourth argument is not a valid pre-warping frequency"); + endif + + sys = __c2d__ (sys, tsam, lower (method), w0); + sys.tsam = tsam; + +endfunction + + +## bilinear transformation +## using oct-file directly +%!shared Mo, Me +%! A = [ 1.0 0.5 +%! 0.5 1.0 ].'; +%! +%! B = [ 0.0 -1.0 +%! 1.0 0.0 ].'; +%! +%! C = [ -1.0 0.0 +%! 0.0 1.0 ].'; +%! +%! D = [ 1.0 0.0 +%! 0.0 -1.0 ].'; +%! +%! [Ao, Bo, Co, Do] = slab04md (A, B, C, D, 1.0, 1.0, false); +%! +%! Ae = [ -1.0000 -4.0000 +%! -4.0000 -1.0000 ]; +%! +%! Be = [ 2.8284 0.0000 +%! 0.0000 -2.8284 ]; +%! +%! Ce = [ 0.0000 2.8284 +%! -2.8284 0.0000 ]; +%! +%! De = [ -1.0000 0.0000 +%! 0.0000 -3.0000 ]; +%! +%! Mo = [Ao, Bo; Co, Do]; +%! Me = [Ae, Be; Ce, De]; +%! +%!assert (Mo, Me, 1e-4); + + +## bilinear transformation +## user function +%!shared Mo, Me +%! A = [ 1.0 0.5 +%! 0.5 1.0 ].'; +%! +%! B = [ 0.0 -1.0 +%! 1.0 0.0 ].'; +%! +%! C = [ -1.0 0.0 +%! 0.0 1.0 ].'; +%! +%! D = [ 1.0 0.0 +%! 0.0 -1.0 ].'; +%! +%! [Ao, Bo, Co, Do] = ssdata (c2d (ss (A, B, C, D), 2, "tustin")); +%! +%! Ae = [ -1.0000 -4.0000 +%! -4.0000 -1.0000 ]; +%! +%! Be = [ 2.8284 0.0000 +%! 0.0000 -2.8284 ]; +%! +%! Ce = [ 0.0000 2.8284 +%! -2.8284 0.0000 ]; +%! +%! De = [ -1.0000 0.0000 +%! 0.0000 -3.0000 ]; +%! +%! Mo = [Ao, Bo; Co, Do]; +%! Me = [Ae, Be; Ce, De]; +%! +%!assert (Mo, Me, 1e-4); + + +## bilinear transformation +## both directions +%!shared Mo, Me +%! A = [ 1.0 0.5 +%! 0.5 1.0 ]; +%! +%! B = [ 0.0 -1.0 +%! 1.0 0.0 ]; +%! +%! C = [ -1.0 0.0 +%! 0.0 1.0 ]; +%! +%! D = [ 1.0 0.0 +%! 0.0 -1.0 ]; +%! +%! [Ao, Bo, Co, Do] = ssdata (d2c (c2d (ss (A, B, C, D), 2, "tustin"), "tustin")); +%! +%! Mo = [Ao, Bo; Co, Do]; +%! Me = [A, B; C, D]; +%! +%!assert (Mo, Me, 1e-4); + + +## zero-order hold +## both directions +%!shared Mo, Me +%! A = [ 1.0 0.5 +%! 0.5 1.0 ]; +%! +%! B = [ 0.0 -1.0 +%! 1.0 0.0 ]; +%! +%! C = [ -1.0 0.0 +%! 0.0 1.0 ]; +%! +%! D = [ 1.0 0.0 +%! 0.0 -1.0 ]; +%! +%! [Ao, Bo, Co, Do] = ssdata (d2c (c2d (ss (A, B, C, D), 2, "zoh"), "zoh")); +%! +%! Mo = [Ao, Bo; Co, Do]; +%! Me = [A, B; C, D]; +%! +%!assert (Mo, Me, 1e-4); + + +## bilinear transformation with pre-warping +## both directions +%!shared Mo, Me +%! A = [ 1.0 0.5 +%! 0.5 1.0 ]; +%! +%! B = [ 0.0 -1.0 +%! 1.0 0.0 ]; +%! +%! C = [ -1.0 0.0 +%! 0.0 1.0 ]; +%! +%! D = [ 1.0 0.0 +%! 0.0 -1.0 ]; +%! +%! [Ao, Bo, Co, Do] = ssdata (d2c (c2d (ss (A, B, C, D), 2, "prewarp", 1000), "prewarp", 1000)); +%! +%! Mo = [Ao, Bo; Co, Do]; +%! Me = [A, B; C, D]; +%! +%!assert (Mo, Me, 1e-4);