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## Copyright (C) 1996, 1998, 2000, 2003, 2004, 2005, 2006, 2007
## Auburn University. All rights reserved.
##
##
## This program 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.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## Undocumented internal function.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{y}, @var{t}] =} __stepimp__ (@var{sitype}, @var{sys} [, @var{inp}, @var{tstop}, @var{n}])
## Impulse or step response for a linear system.
## The system can be discrete or multivariable (or both).
## This m-file contains the ``common code'' of step and impulse.
##
## Produces a plot or the response data for system @var{sys}.
##
## Limited argument checking; ``do not attempt to do this at home''.
## Used internally in @command{impulse}, @command{step}. Use @command{step}
## or @command{impulse} instead.
## @seealso{step, impulse}
## @end deftypefn
## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
## Created: October 2, 1997
## based on lsim.m of Scottedward Hodel
function [y, t] = __stepimp__ (sitype, sys, inp, tstop, n)
if (sitype == 1)
IMPULSE = 0;
elseif (sitype == 2)
IMPULSE = 1;
else
error ("__stepimp__: invalid sitype argument");
endif
sys = sysupdate (sys, "ss");
USE_DEF = 0; # default tstop and n if we have to give up
N_MIN = 50; # minimum number of points
N_MAX = 2000; # maximum number of points
T_DEF = 10.0; # default simulation time
## collect useful information about the system
[ncstates, ndstates, NIN, NOUT] = sysdimensions (sys);
TSAMPLE = sysgettsam (sys);
if (nargin < 3)
inp = 1;
elseif (inp < 1 || inp > NIN)
error ("__stepimp__: argument inp out of range");
endif
DIGITAL = is_digital (sys);
if (DIGITAL)
NSTATES = ndstates;
if (isa (TSAMPLE, "single") && TSAMPLE < eps ("single") ||
!isa (TSAMPLE, "single") && TSAMPLE < eps)
error ("__stepimp__: sampling time of discrete system too small")
endif
else
NSTATES = ncstates;
endif
if (NSTATES < 1)
error ("__stepimp__: pure gain block (n_states < 1), step response is trivial");
endif
if (nargin < 5)
## we have to compute the time when the system reaches steady state
## and the step size
ev = eig (sys2ss (sys));
if (DIGITAL)
## perform bilinear transformation on poles in z
for i = 1:NSTATES
pole = ev(i);
if (abs(pole + 1) < 1.0e-10)
ev(i) = 0;
else
ev(i) = 2 / TSAMPLE * (pole - 1) / (pole + 1);
endif
endfor
endif
## remove poles near zero from eigenvalue array ev
nk = NSTATES;
for i = 1:NSTATES
if (abs (real (ev(i))) < 1.0e-10)
ev(i) = 0;
nk = nk - 1;
endif
endfor
if (nk == 0)
USE_DEF = 1;
## printf("##STEPIMP-DEBUG: using defaults.\n");
else
ev = ev(find (ev));
x = max (abs (ev));
t_step = 0.2 * pi / x;
x = min (abs (real (ev)));
t_sim = 5.0 / x;
## round up
yy = 10^(ceil (log10 (t_sim)) - 1);
t_sim = yy * ceil (t_sim / yy);
## printf("##STEPIMP-DEBUG: nk=%d t_step=%f t_sim=%f\n",
## nk, t_step, t_sim);
endif
endif
if (DIGITAL)
## ---- sampled system
if (nargin == 5)
n = round (n);
if (n < 2)
error ("__stepimp__: n must not be less than 2.")
endif
else
if (nargin == 4)
## n is unknown
elseif (nargin >= 1)
## tstop and n are unknown
if (USE_DEF)
tstop = (N_MIN - 1) * TSAMPLE;
else
tstop = t_sim;
endif
endif
n = floor (tstop / TSAMPLE) + 1;
if (n < 2)
n = 2;
endif
if (n > N_MAX)
n = N_MAX;
printf ("Hint: number of samples limited to %d by default.\n", \
N_MAX);
printf (" ==> increase \"n\" parameter for longer simulations.\n");
endif
endif
tstop = (n - 1) * TSAMPLE;
t_step = TSAMPLE;
else
## ---- continuous system
if (nargin == 5)
n = round (n);
if (n < 2)
error("step: n must not be less than 2.")
endif
t_step = tstop / (n - 1);
else
if (nargin == 4)
## only n in unknown
if (USE_DEF)
n = N_MIN;
t_step = tstop / (n - 1);
else
n = floor (tstop / t_step) + 1;
endif
else
## tstop and n are unknown
if (USE_DEF)
tstop = T_DEF;
n = N_MIN;
t_step = tstop / (n - 1);
else
tstop = t_sim;
n = floor (tstop / t_step) + 1;
endif
endif
if (n < N_MIN)
n = N_MIN;
t_step = tstop / (n - 1);
endif
if (n > N_MAX)
tstop = (n - 1) * t_step;
t_step = tstop / (N_MAX - 1);
n = N_MAX;
endif
endif
tstop = (n - 1) * t_step;
[jnk,B] = sys2ss (sys);
B = B(:,inp);
sys = c2d (sys, t_step);
endif
## printf("##STEPIMP-DEBUG: t_step=%f n=%d tstop=%f\n", t_step, n, tstop);
F = sys.a;
G = sys.b(:,inp);
C = sys.c;
D = sys.d(:,inp);
y = zeros (NOUT, n);
t = linspace (0, tstop, n);
if (IMPULSE)
if (! DIGITAL && D'*D > 0)
error ("impulse: D matrix is nonzero, impulse response infinite.")
endif
if (DIGITAL)
y(:,1) = D / t_step;
x = G / t_step;
else
x = B;
y(:,1) = C * x;
x = F * x;
endif
for i = 2:n
y(:,i) = C * x;
x = F * x;
endfor
if (DIGITAL)
y *= t_step;
endif
else
x = zeros (NSTATES, 1);
for i = 1:n
y(:,i) = C * x + D;
x = F * x + G;
endfor
endif
if (nargout == 0)
if (IMPULSE)
gm = zeros (NOUT, 1);
tt = "impulse";
else
ssys = ss (F, G, C, D, t_step);
gm = dcgain (ssys);
tt = "step";
endif
ncols = floor (sqrt (NOUT));
nrows = ceil (NOUT / ncols);
for i = 1:NOUT
if (nrows > 1 || ncols > 1)
subplot (nrows, ncols, i);
endif
if (DIGITAL)
[ts, ys] = stairs (t, y(i,:));
ts = ts(1:2*n-2)';
ys = ys(1:2*n-2)';
if (length (gm) > 0)
yy = [ys; gm(i)*ones(size(ts))];
else
yy = ys;
endif
plot (ts, yy);
grid ("on");
xlabel ("time [s]");
ylabel ("y(t)");
else
if (length (gm) > 0)
yy = [y(i,:); gm(i)*ones(size(t))];
else
yy = y(i,:);
endif
plot (t, yy);
grid ("on");
xlabel ("time [s]");
ylabel ("y(t)");
endif
title (sprintf ("%s: | %s -> %s", tt,
sysgetsignals (sys, "in", inp, 1),
sysgetsignals (sys, "out", i, 1)));
endfor
y = [];
t = [];
endif
endfunction
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