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## Copyright (C) 1996, 1998, 2000, 2002, 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{a}, @var{b}, @var{c}, @var{d}] =} tf2ss (@var{num}, @var{den})
## Conversion from transfer function to state-space.
## The state space system:
## @iftex
## @tex
## $$ \dot x = Ax + Bu $$
## $$ y = Cx + Du $$
## @end tex
## @end iftex
## @ifinfo
## @example
## .
## x = Ax + Bu
## y = Cx + Du
## @end example
## @end ifinfo
## is obtained from a transfer function:
## @iftex
## @tex
## $$ G(s) = { { \rm num }(s) \over { \rm den }(s) } $$
## @end tex
## @end iftex
## @ifinfo
## @example
## num(s)
## G(s)=-------
## den(s)
## @end example
## @end ifinfo
##
## The vector @var{den} must contain only one row, whereas the vector
## @var{num} may contain as many rows as there are outputs @var{y} of
## the system. The state space system matrices obtained from this function
## will be in controllable canonical form as described in @cite{Modern Control
## Theory}, (Brogan, 1991).
## @end deftypefn
## Author: R. Bruce Tenison <btenison@eng.auburn.edu>
## Created: June 22, 1994
## mod A S Hodel July, Aug 1995
function [a, b, c, d] = tf2ss (num, den)
if (nargin != 2)
print_usage ();
elseif (isempty (num))
error ("tf2ss: empty numerator");
elseif (isempty (den))
error ("tf2ss: empy denominator");
elseif (! isvector (num))
error ("num(%dx%d) must be a vector", rows (num), columns (num));
elseif (! isvector (den))
error ("den(%dx%d) must be a vector", rows (den), columns (den));
endif
## strip leading zeros from num, den
nz = find (num != 0);
if (isempty (nz))
num = 0;
else
num = num(nz(1):length(num));
endif
nz = find (den != 0);
if (isempty (nz))
error ("denominator is 0.");
else
den = den(nz(1):length(den));
endif
## force num, den to be row vectors
num = vec (num)';
den = vec (den)';
nn = length (num);
nd = length (den);
if (nn > nd)
error ("deg(num)=%d > deg(den)= %d", nn, nd);
endif
## Check sizes
if (nd == 1)
a = b = c = [];
d = num(:,1) / den(1);
else
## Pad num so that length(num) = length(den)
if (nd-nn > 0)
num = [zeros(1,nd-nn), num];
endif
## Normalize the numerator and denominator vector w.r.t. the leading
## coefficient
d1 = den(1);
num = num / d1;
den = den(2:nd)/d1;
sw = nd-1:-1:1;
## Form the A matrix
if (nd > 2)
a = [zeros(nd-2,1), eye(nd-2,nd-2); -den(sw)];
else
a = -den(sw);
endif
## Form the B matrix
b = zeros (nd-1, 1);
b(nd-1,1) = 1;
## Form the C matrix
c = num(:,2:nd)-num(:,1)*den;
c = c(:,sw);
## Form the D matrix
d = num(:,1);
endif
endfunction
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