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## Copyright (C) 1996, 2000, 2002, 2003, 2004, 2005, 2007
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## Auburn University. All rights reserved.
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## This file is part of Octave.
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## Octave is free software; you can redistribute it and/or modify it
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## under the terms of the GNU General Public License as published by
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## the Free Software Foundation; either version 3 of the License, or (at
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## your option) any later version.
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## Octave is distributed in the hope that it will be useful, but
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## WITHOUT ANY WARRANTY; without even the implied warranty of
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## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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## General Public License for more details.
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## You should have received a copy of the GNU General Public License
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## along with Octave; see the file COPYING. If not, see
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## <http://www.gnu.org/licenses/>.
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## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} zp2ss (@var{zer}, @var{pol}, @var{k})
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## Conversion from zero / pole to state space.
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## Vectors of (possibly) complex poles and zeros of a transfer
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## function. Complex values must come in conjugate pairs
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## (i.e., @math{x+jy} in @var{zer} means that @math{x-jy} is also in @var{zer}).
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## The number of zeros must not exceed the number of poles.
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## Real scalar (leading coefficient).
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## The state space system, in the form:
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## $$ \dot x = Ax + Bu $$
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## Created: August 15, 1994
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function [a, b, c, d] = zp2ss (zer, pol, k)
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if (! (isvector (zer) || isempty (zer)))
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error ("zer(%d,%d) should be a vector", rows (zer), columns (zer));
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elseif (! (isvector (pol) || isempty (pol)))
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error ("pol(%d,%d) should be a vector", rows (pol), columns (pol));
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elseif (! isscalar(k))
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error ("k(%d,%d) should be a scalar", rows (k), columns (k));
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elseif (k != real (k))
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warning ("zp2ss: k is complex")
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zpsys = ss (zeros (0, 0), zeros (0, 1), zeros (1, 0), k);
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## Find the number of zeros and the number of poles
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error ("%d zeros, exceeds number of poles=%d", nzer, npol);
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## Sort to place complex conjugate pairs together
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## construct the system as a series connection of poles and zeros
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## problem: poles and zeros may come in conjugate pairs, and not
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## approach: remove poles/zeros from the list as they are included in
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## search for complex poles, zeros
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cpol = find (imag (pol) != 0);
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czer = find (imag (zer) != 0);
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if (isempty (cpol) && isempty (czer))
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num = 1; # assume no zeros left.
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## real pole/zero combination
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zer = zer(2:length(zer));
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pol = pol(2:length(pol));
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## got a complex pole or zero, need two roots (if available)
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if (length (zer) > 1)
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[num, zer] = __zp2ssg2__ (zer); # get two zeros
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elseif (length (zer) == 1)
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num = [1, -zer]; # use last zero (better be real!)
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[den, pol] = __zp2ssg2__ (pol); # get two poles
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error ("pcnt = %d", pcnt);
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## pack tf into system form and put in series with earlier realization
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zpsys1 = tf (num, den, 0, "u", "yy");
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## change names to avoid warning messages from sysgroup
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zpsys = syssetsignals (zpsys, "in", "u1", 1);
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zpsys1 = sysupdate (zpsys1, "ss");
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nn = sysdimensions (zpsys); # working with continuous system
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zpsys = syssetsignals (zpsys, "st", __sysdefioname__ (nn, "x"));
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nn1 = sysdimensions (zpsys1);
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zpsys1 = syssetsignals (zpsys1, "st", __sysdefioname__ (nn1, "xx"));
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zpsys = sysmult (zpsys, zpsys1);
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[a, b, c, d] = sys2ss (zpsys);
added
removed
scripts/control/system/zp2ss.m
