/usr/share/octave/packages/control-3.0.0/lsim.m is in octave-control 3.0.0-1.
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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: 0.5
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
idx = cellfun (@islogical, varargin);
tmp = cellfun (@double, varargin(idx), "uniformoutput", false);
varargin(idx) = tmp;
sys_idx = cellfun (@isa, varargin, {"lti"}); # LTI models
mat_idx = cellfun (@is_real_matrix, varargin); # matrices
sty_idx = cellfun (@ischar, varargin); # string (style arguments)
inv_idx = ! (sys_idx | mat_idx | sty_idx); # invalid arguments
if (any (inv_idx))
warning ("lsim: arguments number %s are invalid and are being ignored", ...
mat2str (find (inv_idx)(:).'));
endif
if (nnz (sys_idx) == 0)
error ("lsim: require at least one LTI model");
endif
if (nargout > 0 && (nnz (sys_idx) > 1 || any (sty_idx)))
print_usage ();
endif
if (! size_equal (varargin{sys_idx}))
error ("lsim: all LTI models must have equal size");
endif
if (any (find (sty_idx) < find (sys_idx)(1)))
warning ("lsim: strings in front of first LTI model are being ignored");
endif
t = []; x0 = []; # default arguments
switch (nnz (mat_idx))
case 0
error ("lsim: require input signal 'u'");
case 1
u = varargin{mat_idx};
case 2
[u, t] = varargin{mat_idx};
case 3
[u, t, x0] = varargin{mat_idx};
otherwise
print_usage ();
endswitch
if (is_real_vector (u)) # allow row vectors for single-input systems
u = vec (u);
elseif (isempty (u)) # ! is_real_matrix (u) already tested
error ("lsim: input signal 'u' must be a real-valued matrix");
endif
if (! is_real_vector (t) && ! isempty (t))
error ("lsim: time vector 't' must be real-valued or empty");
endif
if (! isequal (t, unique (t)))
error ("lsim: time vector 't' must be sorted");
endif
if (! is_real_vector (x0) && ! isempty (x0))
error ("lsim: initial state vector 'x0' must be empty or a real-valued vector");
endif
## function [y, t, x_arr] = __linear_simulation__ (sys, u, t, x0)
[y, t, x] = cellfun (@__linear_simulation__, varargin(sys_idx), {u}, {t}, {x0}, "uniformoutput", false);
if (nargout == 0) # plot information
## extract plotting styles
tmp = cumsum (sys_idx);
tmp(sys_idx | ! sty_idx) = 0;
n_sys = nnz (sys_idx);
sty = arrayfun (@(x) varargin(tmp == x), 1:n_sys, "uniformoutput", false);
## default plotting styles if empty
colororder = get (gca, "colororder");
rc = rows (colororder);
def = arrayfun (@(k) {"color", colororder(1+rem (k-1, rc), :)}, 1:n_sys, "uniformoutput", false);
idx = cellfun (@isempty, sty);
sty(idx) = def(idx);
## get system names for legend
## leg = cellfun (@inputname, find (sys_idx), "uniformoutput", false);
leg = cell (1, n_sys);
idx = find (sys_idx);
for k = 1 : n_sys
try
leg{k} = inputname (idx(k));
catch
leg{k} = ""; # catch case lsim (lticell{:}, ...)
end_try_catch
endfor
[p, m] = size (varargin(sys_idx){1});
ct_idx = cellfun (@isct, varargin(sys_idx));
str = "Linear Simulation Results";
outname = get (varargin(sys_idx){end}, "outname");
outname = __labels__ (outname, "y");
for k = 1 : n_sys # for every system
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), sty{k}{:});
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), sty{k}{:});
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 (leg)
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);
len_t = length (t);
if (isct (sys)) # continuous-time system
if (isempty (t)) # lsim (sys, u, [], ...)
error ("lsim: time vector 't' must not be empty");
elseif (len_t == 1) # lsim (sys, u, tfinal, ...)
dt = t / (urows - 1);
t = vec (linspace (0, t, urows));
elseif (len_t != urows)
error ("lsim: length of time vector (%d) doesn't match input signal (%dx%d)", ...
len_t, urows, ucols);
else # lsim (sys, u, t, ...)
dt = abs (t(end) - t(1)) / (urows - 1); # assume that t is regularly spaced
t = vec (linspace (t(1), t(end), urows));
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)
t = vec (linspace (0, dt*(urows-1), urows));
elseif (len_t == 1) # lsim (sys, u, tfinal)
## TODO: maybe raise warning if abs (tfinal - dt*(urows-1)) > dt
t = vec (linspace (0, dt*(urows-1), urows));
elseif (len_t != urows)
error ("lsim: length of time vector (%d) doesn't match input signal (%dx%d)", ...
len_t, urows, ucols);
else # lsim (sys, u, t, ...)
t = vec (linspace (t(1), t(end), len_t));
endif
endif
[A, B, C, D] = ssdata (sys);
[p, m] = size (D); # number of outputs and inputs
n = rows (A); # number of states
if (ucols != m)
error ("lsim: input vector 'u' must have %d columns", m);
endif
## preallocate memory
y = zeros (urows, p);
x_arr = zeros (urows, 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 = vec (x0); # make sure that x is a column vector
## simulation
for k = 1 : urows
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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