Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / @lti / zero.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{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 <lukas.reichlin@gmail.com>
+## 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);