/usr/share/octave/packages/control-2.6.2/lsim.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} {} lsim (@var{sys}, @var{u})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @var{sys2}, @dots{}, @var{sysN}, @var{u})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @var{'style1'}, @dots{}, @var{sysN}, @var{'styleN'}, @var{u})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @dots{}, @var{u}, @var{t})
## @deftypefnx{Function File} {} lsim (@var{sys1}, @dots{}, @var{u}, @var{t}, @var{x0})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t})
## @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})
## Simulate @acronym{LTI} model response to arbitrary inputs. If no output arguments are given,
## the system response is plotted on the screen.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model. System must be proper, i.e. it must not have more zeros than poles.
## @item u
## Vector or array of input signal. Needs @code{length(t)} rows and as many columns
## as there are inputs. If @var{sys} is a single-input system, row vectors @var{u}
## of length @code{length(t)} are accepted as well.
## @item t
## Time vector. Should be evenly spaced. If @var{sys} is a continuous-time system
## and @var{t} is a real scalar, @var{sys} is discretized with sampling time
## @code{tsam = t/(rows(u)-1)}. If @var{sys} is a discrete-time system and @var{t}
## is not specified, vector @var{t} is assumed to be @code{0 : tsam : tsam*(rows(u)-1)}.
## @item x0
## Vector of initial conditions for each state. If not specified, a zero vector is assumed.
## @item 'style'
## Line style and color, e.g. 'r' for a solid red line or '-.k' for a dash-dotted
## black line. See @command{help plot} for details.
## @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. It is always evenly spaced.
## @item x
## State trajectories array. Has @code{length (t)} rows and as many columns as states.
## @end table
##
## @seealso{impulse, initial, step}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: October 2009
## Version: 0.4
function [y_r, t_r, x_r] = lsim (varargin)
## TODO: individual initial state vectors 'x0' for each system
## there would be conflicts with other arguments,
## maybe a cell {x0_1, x0_2, ..., x0_N} would be a solution?
if (nargin < 2)
print_usage ();
endif
sys_idx = find (cellfun (@isa, varargin, {"lti"})); # look for LTI models, 'find' needed for plot styles
sys_cell = cellfun (@ss, varargin(sys_idx), "uniformoutput", false); # convert to state-space
if (! size_equal (sys_cell{:}))
error ("lsim: models must have equal sizes");
endif
mat_idx = find (cellfun (@is_real_matrix, varargin)); # indices of matrix arguments
n_mat = length (mat_idx); # number of vector arguments
n_sys = length (sys_cell); # number of LTI systems
t = [];
x0 = [];
if (n_mat < 1)
error ("lsim: require input signal 'u'");
else
arg = varargin{mat_idx(1)};
if (is_real_vector (arg))
u = reshape (arg, [], 1); # allow row vectors for single-input systems
elseif (is_real_matrix (arg));
u = arg;
else
error ("lsim: input signal 'u' must be an array of real numbers");
endif
if (n_mat > 1) # time vector t
arg = varargin{mat_idx(2)};
if (is_real_vector (arg) || isempty (arg))
t = arg;
else
error ("lsim: time vector 't' must be real-valued or empty");
endif
if (n_mat > 2) # initial state vector x0
arg = varargin{mat_idx(3)};
if (is_real_vector (arg))
x0 = arg;
else
error ("lsim: initial state vector 'x0' must be a real-valued vector");
endif
if (n_mat > 3)
warning ("lsim: ignored");
endif
endif
endif
endif
## function [y, t, x_arr] = __linear_simulation__ (sys, u, t, x0)
[y, t, x] = cellfun (@__linear_simulation__, sys_cell, {u}, {t}, {x0}, "uniformoutput", false);
if (nargout == 0) # plot information
[p, m] = size (sys_cell{1});
style_idx = find (cellfun (@ischar, varargin));
ct_idx = cellfun (@isct, sys_cell);
str = "Linear Simulation Results";
outname = get (sys_cell{end}, "outname");
outname = __labels__ (outname, "y");
colororder = get (gca, "colororder");
rc = rows (colororder);
sysname = cell (n_sys, 1);
for k = 1 : n_sys # for every system
if (k == n_sys)
lim = nargin;
else
lim = sys_idx(k+1);
endif
style = varargin(style_idx(style_idx > sys_idx(k) & style_idx <= lim));
if (isempty (style))
color = colororder(1+rem (k-1, rc), :);
style = {"color", color};
endif
try
sysname{k} = inputname(sys_idx(k));
catch
sysname{k} = "";
end_try_catch
if (ct_idx(k)) # continuous-time system
for i = 1 : p # for every output
if (p != 1)
subplot (p, 1, i);
endif
plot (t{k}, y{k}(:, i), style{:});
hold on;
grid on;
if (k == n_sys)
axis tight
ylim (__axis_margin__ (ylim))
ylabel (outname{i});
if (i == 1)
title (str);
endif
endif
endfor
else # discrete-time system
for i = 1 : p # for every output
if (p != 1)
subplot (p, 1, i);
endif
stairs (t{k}, y{k}(:, i), style{:});
hold on;
grid on;
if (k == n_sys)
axis tight;
ylim (__axis_margin__ (ylim))
ylabel (outname{i});
if (i == 1)
title (str);
endif
endif
endfor
endif
endfor
xlabel ("Time [s]");
if (p == 1 && m == 1)
legend (sysname)
endif
hold off;
else # return values
y_r = y{1};
t_r = t{1};
x_r = x{1};
endif
endfunction
function [y, t, x_arr] = __linear_simulation__ (sys, u, t, x0)
method = "zoh";
[urows, ucols] = size (u);
if (isct (sys)) # continuous-time system
if (isempty (t)) # lsim (sys, u, [], ...)
error ("lsim: invalid time vector");
elseif (length (t) == 1) # lsim (sys, u, tfinal, ...)
dt = t / (urows - 1);
tinitial = 0;
tfinal = t;
else # lsim (sys, u, t, ...)
dt = t(2) - t(1); # assume that t is regularly spaced
tinitial = t(1);
tfinal = t(end);
endif
sys = c2d (sys, dt, method); # convert to discrete-time model
else # discrete-time system
dt = abs (get (sys, "tsam")); # use 1 second as default if tsam is unspecified (-1)
if (isempty (t)) # lsim (sys, u)
tinitial = 0;
tfinal = dt * (urows - 1);
elseif (length (t) == 1) # lsim (sys, u, tfinal)
tinitial = 0;
tfinal = t;
else # lsim (sys, u, t, ...)
warning ("lsim: spacing of time vector has no effect on sampling time of discrete-time system");
tinitial = t(1);
tfinal = t(end);
endif
endif
[A, B, C, D] = ssdata (sys);
[p, m] = size (D); # number of outputs and inputs
n = rows (A); # number of states
## time vector
t = reshape (tinitial : dt : tfinal, [], 1);
len_t = length (t);
if (urows != len_t)
error ("lsim: input vector u must have %d rows", len_t);
endif
if (ucols != m)
error ("lsim: input vector u must have %d columns", m);
endif
## preallocate memory
y = zeros (len_t, p);
x_arr = zeros (len_t, n);
## initial conditions
if (isempty (x0))
x0 = zeros (n, 1);
elseif (n != length (x0) || ! is_real_vector (x0))
error ("lsim: x0 must be a vector with %d elements", n);
endif
x = reshape (x0, [], 1); # make sure that x is a column vector
## simulation
for k = 1 : len_t
y(k, :) = C * x + D * u(k, :).';
x_arr(k, :) = x;
x = A * x + B * u(k, :).';
endfor
endfunction
## TODO: add test cases
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