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[Octave-cvsupdate] SF.net SVN: octave:[6337] trunk/octave-forge/extra/control-oo
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From: <par...@us...> - 2009-10-19 03:26:56
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Revision: 6337
http://octave.svn.sourceforge.net/octave/?rev=6337&view=rev
Author: paramaniac
Date: 2009-10-19 03:26:50 +0000 (Mon, 19 Oct 2009)
Log Message:
-----------
control-oo: add gensig and gram
Modified Paths:
--------------
trunk/octave-forge/extra/control-oo/INDEX
Added Paths:
-----------
trunk/octave-forge/extra/control-oo/inst/control/gensig.m
trunk/octave-forge/extra/control-oo/inst/control/gram.m
Modified: trunk/octave-forge/extra/control-oo/INDEX
===================================================================
--- trunk/octave-forge/extra/control-oo/INDEX 2009-10-19 02:38:00 UTC (rev 6336)
+++ trunk/octave-forge/extra/control-oo/INDEX 2009-10-19 03:26:50 UTC (rev 6337)
@@ -23,6 +23,7 @@
pole
zero
Time Domain Analysis
+ gensig
Frequency Domain Analysis
Model Simplification
Compensator Design
@@ -31,6 +32,7 @@
lqr
State-Space Models
ctrb
+ gram
obsv
Model Dimensions and Characteristics
isct
Added: trunk/octave-forge/extra/control-oo/inst/control/gensig.m
===================================================================
--- trunk/octave-forge/extra/control-oo/inst/control/gensig.m (rev 0)
+++ trunk/octave-forge/extra/control-oo/inst/control/gensig.m 2009-10-19 03:26:50 UTC (rev 6337)
@@ -0,0 +1,95 @@
+## 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 this program. If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {[@var{u}, @var{t}] =} gensig (@var{sigtype}, @var{tau})
+## @deftypefnx{Function File} {[@var{u}, @var{t}] =} gensig (@var{sigtype}, @var{tau}, @var{tfinal})
+## @deftypefnx{Function File} {[@var{u}, @var{t}] =} gensig (@var{sigtype}, @var{tau}, @var{tfinal}, @var{tsam})
+## Generate periodic signal. Useful in combination with lsim.
+##
+## @strong{Inputs}
+## @table @var
+## @item sigtype = "sin"
+## Sine wave.
+## @item sigtype = "cos"
+## Cosine wave.
+## @item sigtype = "square"
+## Square wave.
+## @item sigtype = "pulse"
+## Periodic pulse.
+## @item tau
+## Duration of one period in seconds.
+## @item tfinal
+## Optional duration of the signal in seconds. Default duration is 5 periods
+## @item tsam
+## Optional sampling time in seconds. Default spacing is tau/64.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item u
+## Vector of signal values.
+## @item t
+## Time vector of the signal.
+## @end table
+##
+## @seealso{lsim}
+## @end deftypefn
+
+## Author: Lukas Reichlin <luk...@gm...>
+## Created: August 2009
+## Version: 0.1
+
+function [u, t] = gensig (sigtype, tau, tfinal, tsam)
+
+ if (nargin < 2 || nargin > 4)
+ print_usage ();
+ endif
+
+ if (! ischar (sigtype))
+ error ("gensig: first argument must be a string");
+ endif
+
+ if (nargin < 3)
+ tfinal = 5 * tau;
+ endif
+
+ if (nargin < 4)
+ tsam = tau / 64;
+ endif
+
+ t = (0 : tsam : tfinal)';
+
+ sigtype = lower (sigtype);
+
+ switch (sigtype(1:2))
+ case "si"
+ u = sin (2*pi/tau * t);
+ case "co"
+ u = cos (2*pi/tau * t);
+ case "sq"
+ u = +(rem (t, tau) >= tau/2);
+ case "pu"
+ u = +(rem (t, tau) < (1 - 1000*eps) * tsam);
+ otherwise
+ error ("gensig: invalid signal type");
+ endswitch
+
+endfunction
+
+
+## TODO: Add a test
Added: trunk/octave-forge/extra/control-oo/inst/control/gram.m
===================================================================
--- trunk/octave-forge/extra/control-oo/inst/control/gram.m (rev 0)
+++ trunk/octave-forge/extra/control-oo/inst/control/gram.m 2009-10-19 03:26:50 UTC (rev 6337)
@@ -0,0 +1,130 @@
+## Copyright (C) 1996, 2000, 2003, 2004, 2005, 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/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{W} =} gram (@var{sys}, @var{mode})
+## @deftypefnx {Function File} {@var{Wc} =} gram (@var{a}, @var{b})
+## @code{gram (@var{sys}, 'c')} returns the controllability gramian of
+## the (continuous- or discrete-time) system @var{sys}.
+## @code{gram (@var{sys}, 'o')} returns the observability gramian of the
+## (continuous- or discrete-time) system @var{sys}.
+## @code{gram (@var{a}, @var{b})} returns the controllability gramian
+## @var{Wc} of the continuous-time system @math{dx/dt = a x + b u};
+## i.e., @var{Wc} satisfies @math{a Wc + m Wc' + b b' = 0}.
+##
+## @end deftypefn
+
+## Author: A. S. Hodel <a.s...@en...>
+
+function W = gram (argin1, argin2)
+
+ if (nargin != 2)
+ print_usage ();
+ endif
+
+ if (! ischar (argin2)) # the function was called as "gram (a, b)"
+ a = argin1;
+ b = argin2;
+
+ ## b, c and d matrices are irrelevant for stability
+ ## assume that a and b are matrices of continous-time system
+
+ sys = ss (a, b, zeros (1, columns (a)), zeros (1, columns (b)));
+
+ if (! isstable (sys))
+ error ("gram: the continuous-time system must have a stable 'a' matrix");
+ else
+
+ ## let lyap do the error checking about dimensions
+ W = lyap (a', b*b');
+ endif
+
+ else # the function was called as "gram (sys, mode)"
+ argin2 = lower (argin2);
+
+ if (! (strcmp (argin2, "c") || strcmp (argin2, "o")))
+ print_usage ();
+ else
+ if (strcmp (argin2, "c"))
+ [a, b] = ssdata (argin1);
+ elseif (strcmp (argin2, "o"))
+ [a, b, c] = ssdata (argin1);
+ a = a';
+ b = c';
+ endif
+
+ if (isct (argin1))
+ if (! isstable (argin1))
+ error ("gram: the continuous-time system must be stable");
+ else
+ ## let lyap do the error checking about dimensions
+ W = lyap (a', b*b');
+ endif
+
+ else # if (isdt (argin1))
+ if (! isstable (argin1))
+ error ("gram: the discrete-time system must be stable");
+ else
+ ## let dlyap do the error checking about dimensions
+ W = dlyap (a, b*b');
+ endif
+ endif
+
+ endif
+ endif
+
+endfunction
+
+
+%!test
+%! a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
+%! b = [1 0; 0 -1; 0 1];
+%! c = [0 0 1; 1 1 0]; ## it doesn't matter what the value of c is
+%! Wc = gram (ss (a, b, c), 'c');
+%! assert (a * Wc + Wc * a' + b * b', zeros (size (a)))
+
+%!test
+%! a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
+%! b = [1 0; 0 -1; 0 1]; ## it doesn't matter what the value of b is
+%! c = [0 0 1; 1 1 0];
+%! Wo = gram (ss (a, b, c), 'o');
+%! assert (a' * Wo + Wo * a + c' * c, zeros (size (a)))
+
+%!test
+%! a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
+%! b = [1 0; 0 -1; 0 1];
+%! Wc = gram (a, b);
+%! assert (a * Wc + Wc * a' + b * b', zeros (size (a)))
+
+%!test
+%! a = [-1 0 0; 1/2 1 0; 1/2 0 -1] / 2;
+%! b = [1 0; 0 -1; 0 1];
+%! c = [0 0 1; 1 1 0]; ## it doesn't matter what the value of c is
+%! d = zeros (rows (c), columns (b)); ## it doesn't matter what the value of d is
+%! Ts = 0.1; ## Ts != 0
+%! Wc = gram (ss (a, b, c, d, Ts), 'c');
+%! assert (a * Wc * a' - Wc + b * b', zeros (size (a)), 1e-12)
+
+%!test
+%! a = [-1 0 0; 1/2 1 0; 1/2 0 -1] / 2;
+%! b = [1 0; 0 -1; 0 1]; ## it doesn't matter what the value of b is
+%! c = [0 0 1; 1 1 0];
+%! d = zeros (rows (c), columns (b)); ## it doesn't matter what the value of d is
+%! Ts = 0.1; ## Ts != 0
+%! Wo = gram (ss (a, b, c, d, Ts), 'o');
+%! assert (a' * Wo * a - Wo + c' * c, zeros (size (a)), 1e-12)
\ No newline at end of file
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