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%2Fzero.m;fp=octave_packages%2Fcontrol-2.3.52%2F%40lti%2Fzero.m;h=78df1d7d256f13774f3c074a00317f7f32dd0b08;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05
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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 .
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{z} =} zero (@var{sys})
+## @deftypefnx {Function File} {[@var{z}, @var{k}] =} zero (@var{sys})
+## Compute transmission zeros and gain of LTI model.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## LTI model.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item z
+## Transmission zeros of @var{sys}.
+## @item k
+## Gain of @var{sys}.
+## @end table
+## @end deftypefn
+
+## Author: Lukas Reichlin
+## Created: October 2009
+## Version: 0.2
+
+function [zer, gain] = zero (sys)
+
+ if (nargin > 1)
+ print_usage ();
+ endif
+
+ [zer, gain] = __zero__ (sys, nargout);
+
+endfunction
+
+
+## transmission zeros of state-space models
+##
+## Results from the "Dark Side" 7.5 and 7.8
+##
+## -13.2759
+## 12.5774
+## -0.0155
+##
+## Results from Scilab 5.2.0b1 (trzeros)
+##
+## - 13.275931
+## 12.577369
+## - 0.0155265
+##
+%!shared z, z_exp
+%! A = [ -0.7 -0.0458 -12.2 0
+%! 0 -0.014 -0.2904 -0.562
+%! 1 -0.0057 -1.4 0
+%! 1 0 0 0 ];
+%!
+%! B = [ -19.1 -3.1
+%! -0.0119 -0.0096
+%! -0.14 -0.72
+%! 0 0 ];
+%!
+%! C = [ 0 0 -1 1
+%! 0 0 0.733 0 ];
+%!
+%! D = [ 0 0
+%! 0.0768 0.1134 ];
+%!
+%! sys = ss (A, B, C, D, "scaled", true);
+%! z = sort (zero (sys));
+%!
+%! z_exp = sort ([-13.2759; 12.5774; -0.0155]);
+%!
+%!assert (z, z_exp, 1e-4);
+
+
+## transmission zeros of descriptor state-space models
+%!shared z, z_exp
+%! A = [ 1 0 0 0 0 0 0 0 0
+%! 0 1 0 0 0 0 0 0 0
+%! 0 0 1 0 0 0 0 0 0
+%! 0 0 0 1 0 0 0 0 0
+%! 0 0 0 0 1 0 0 0 0
+%! 0 0 0 0 0 1 0 0 0
+%! 0 0 0 0 0 0 1 0 0
+%! 0 0 0 0 0 0 0 1 0
+%! 0 0 0 0 0 0 0 0 1 ];
+%!
+%! E = [ 0 0 0 0 0 0 0 0 0
+%! 1 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 0 0 1 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 0 0 1 0 0
+%! 0 0 0 0 0 0 0 1 0 ];
+%!
+%! B = [ -1 0 0
+%! 0 0 0
+%! 0 0 0
+%! 0 -1 0
+%! 0 0 0
+%! 0 0 0
+%! 0 0 -1
+%! 0 0 0
+%! 0 0 0 ];
+%!
+%! C = [ 0 1 1 0 3 4 0 0 2
+%! 0 1 0 0 4 0 0 2 0
+%! 0 0 1 0 -1 4 0 -2 2 ];
+%!
+%! D = [ 1 2 -2
+%! 0 -1 -2
+%! 0 0 0 ];
+%!
+%! sys = dss (A, B, C, D, E, "scaled", true);
+%! z = zero (sys);
+%!
+%! z_exp = 1;
+%!
+%!assert (z, z_exp, 1e-4);
+
+
+## Gain of descriptor state-space models
+%!shared p, pi, z, zi, k, ki, p_tf, pi_tf, z_tf, zi_tf, k_tf, ki_tf
+%! P = ss (-2, 3, 4, 5);
+%! Pi = inv (P);
+%!
+%! p = pole (P);
+%! [z, k] = zero (P);
+%!
+%! pi = pole (Pi);
+%! [zi, ki] = zero (Pi);
+%!
+%! P_tf = tf (P);
+%! Pi_tf = tf (Pi);
+%!
+%! p_tf = pole (P_tf);
+%! [z_tf, k_tf] = zero (P_tf);
+%!
+%! pi_tf = pole (Pi_tf);
+%! [zi_tf, ki_tf] = zero (Pi_tf);
+%!
+%!assert (p, zi, 1e-4);
+%!assert (z, pi, 1e-4);
+%!assert (k, inv (ki), 1e-4);
+%!assert (p_tf, zi_tf, 1e-4);
+%!assert (z_tf, pi_tf, 1e-4);
+%!assert (k_tf, inv (ki_tf), 1e-4);