X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2Finitial.m;fp=octave_packages%2Fcontrol-2.3.52%2Finitial.m;h=b7448133441a91520b867d84a7fdd71e781a8548;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05
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+## Copyright (C) 2009 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{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0})
+## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{t})
+## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{tfinal})
+## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{tfinal}, @var{dt})
+## Initial condition response of state-space model.
+## If no output arguments are given, the response is printed on the screen.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## State-space model.
+## @item x0
+## Vector of initial conditions for each state.
+## @item t
+## Optional time vector. Should be evenly spaced. If not specified, it is calculated
+## by the poles of the system to reflect adequately the response transients.
+## @item tfinal
+## Optional simulation horizon. If not specified, it is calculated by
+## the poles of the system to reflect adequately the response transients.
+## @item dt
+## Optional sampling time. Be sure to choose it small enough to capture transient
+## phenomena. If not specified, it is calculated by the poles of the system.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item y
+## Output response array. Has as many rows as time samples (length of t)
+## and as many columns as outputs.
+## @item t
+## Time row vector.
+## @item x
+## State trajectories array. Has @code{length (t)} rows and as many columns as states.
+## @end table
+##
+## @strong{Example}
+## @example
+## @group
+## .
+## Continuous Time: x = A x , y = C x , x(0) = x0
+##
+## Discrete Time: x[k+1] = A x[k] , y[k] = C x[k] , x[0] = x0
+## @end group
+## @end example
+##
+## @seealso{impulse, lsim, step}
+## @end deftypefn
+
+## Author: Lukas Reichlin
+## Created: October 2009
+## Version: 0.1
+
+function [y_r, t_r, x_r] = initial (sys, x0, tfinal = [], dt = [])
+
+ ## TODO: multiplot feature: initial (sys1, "b", sys2, "r", ..., x0, ...)
+
+ if (nargin < 2 || nargin > 4)
+ print_usage ();
+ endif
+
+ [y, t, x] = __time_response__ (sys, "initial", ! nargout, tfinal, dt, x0, inputname (1));
+
+ if (nargout)
+ y_r = y;
+ t_r = t;
+ x_r = x;
+ endif
+
+endfunction
+
+
+%!shared initial_c, initial_c_exp, initial_d, initial_d_exp
+%!
+%! A = [ -2.8 2.0 -1.8
+%! -2.4 -2.0 0.8
+%! 1.1 1.7 -1.0 ];
+%!
+%! B = [ -0.8 0.5 0
+%! 0 0.7 2.3
+%! -0.3 -0.1 0.5 ];
+%!
+%! C = [ -0.1 0 -0.3
+%! 0.9 0.5 1.2
+%! 0.1 -0.1 1.9 ];
+%!
+%! D = [ -0.5 0 0
+%! 0.1 0 0.3
+%! -0.8 0 0 ];
+%!
+%! x_0 = [1, 2, 3];
+%!
+%! sysc = ss (A, B, C, D);
+%!
+%! [yc, tc, xc] = initial (sysc, x_0, 0.2, 0.1);
+%! initial_c = [yc, tc, xc];
+%!
+%! sysd = c2d (sysc, 2);
+%!
+%! [yd, td, xd] = initial (sysd, x_0, 4);
+%! initial_d = [yd, td, xd];
+%!
+%! ## expected values computed by the "dark side"
+%!
+%! yc_exp = [ -1.0000 5.5000 5.6000
+%! -0.9872 5.0898 5.7671
+%! -0.9536 4.6931 5.7598 ];
+%!
+%! tc_exp = [ 0.0000
+%! 0.1000
+%! 0.2000 ];
+%!
+%! xc_exp = [ 1.0000 2.0000 3.0000
+%! 0.5937 1.6879 3.0929
+%! 0.2390 1.5187 3.0988 ];
+%!
+%! initial_c_exp = [yc_exp, tc_exp, xc_exp];
+%!
+%! yd_exp = [ -1.0000 5.5000 5.6000
+%! -0.6550 3.1673 4.2228
+%! -0.5421 2.6186 3.4968 ];
+%!
+%! td_exp = [ 0
+%! 2
+%! 4 ];
+%!
+%! xd_exp = [ 1.0000 2.0000 3.0000
+%! -0.4247 1.5194 2.3249
+%! -0.3538 1.2540 1.9250 ];
+%!
+%! initial_d_exp = [yd_exp, td_exp, xd_exp];
+%!
+%!assert (initial_c, initial_c_exp, 1e-4)
+%!assert (initial_d, initial_d_exp, 1e-4)