/usr/share/octave/packages/control-2.6.2/@lti/c2d.m is in octave-control 2.6.2-1build1.
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##
## 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 @acronym{LTI} model into its discrete-time equivalent.
##
## @strong{Inputs}
## @table @var
## @item sys
## Continuous-time @acronym{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}.
## @item 'matched'
## Matched pole/zero method.
## @end table
## @end table
##
## @strong{Outputs}
## @table @var
## @item sys
## Discrete-time @acronym{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] = __sl_ab04md__ (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);
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