Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / @lti / c2d.m

diff --git a/octave_packages/control-2.3.52/@lti/c2d.m b/octave_packages/control-2.3.52/@lti/c2d.m
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+## 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 <http://www.gnu.org/licenses/>.
+
+## -*- 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 <lukas.reichlin@gmail.com>
+## 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);