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zp2ss.m
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1999-04-29
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# Copyright (C) 1996 A. Scottedward Hodel
#
# This file is part of Octave.
#
# Octave 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 2, or (at your option) any
# later version.
#
# Octave 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 Octave; see the file COPYING. If not, write to the Free
# Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
function [a,b,c,d] = zp2ss(zer,pol,k)
# [A,B,C,D] = zp2ss(zer,pol,k)
# Conversion from zero / pole to state space.
# Inputs:
# zer, pol: vectors of (possibly) complex poles and zeros of a transfer
# function. Complex values must come in conjugate pairs
# (i.e., x+jy in zer means that x-jy is also in zer)
# k: real scalar (leading coefficient)
# Outputs:
# A, B, C, D:
# The state space system
# .
# x = Ax + Bu
# y = Cx + Du
#
# is obtained from a vector of zeros and a vector of poles via the
# function call [a,b,c,d] = zp2ss(zer,pol,k). The vectors 'zer' and
# 'pol' may either be row or column vectors. Each zero and pole that
# has an imaginary part must have a conjugate in the list.
# The number of poles must at least equal the number of zeros.
# k is a gain that is associated with the zero vector.
# Written by David Clem August 15, 1994
sav_val = empty_list_elements_ok;
empty_list_elements_ok = 1;
if(nargin != 3)
error("Incorrect number of input arguments");
endif
if(! (is_vec(zer) | isempty(zer)) )
error(["zer(",num2str(rows(zer)),",",num2str(columns(zer)), ...
") should be a vector"]);
elseif(! (is_vec(pol) | isempty(pol) ) )
error(["pol(",num2str(rows(pol)),",",num2str(columns(pol)), ...
") should be a vector"]);
elseif(! is_scal(k))
error(["k(",num2str(rows(k)),",",num2str(columns(k)), ...
") should be a scalar"]);
elseif( k != real(k))
warning("zp2ss: k is complex")
endif
zpsys = ss2sys([],[],[],k);
# Find the number of zeros and the number of poles
nzer=length(zer);
npol =length(pol);
if(nzer > npol)
error([num2str(nzer)," zeros, exceeds number of poles=",num2str(npol)]);
endif
# Sort to place complex conjugate pairs together
zer=sortcom(zer);
pol=sortcom(pol);
# construct the system as a series connection of poles and zeros
# problem: poles and zeros may come in conjugate pairs, and not
# matched up!
# approach: remove poles/zeros from the list as they are included in
# the ss system
while(length(pol))
# search for complex poles, zeros
cpol=[]; czer = [];
if(!isempty(pol))
cpol = find(imag(pol) != 0);
endif
if(!isempty(zer))
czer = find(imag(zer) != 0);
endif
if(isempty(cpol) & isempty(czer))
pcnt = 1;
else
pcnt = 2;
endif
num=1; # assume no zeros left.
switch(pcnt)
case(1)
# real pole/zero combination
if(length(zer))
num = [1 -zer(1)];
zer = zer(2:length(zer));
endif
den = [1 -pol(1)];
pol = pol(2:length(pol));
case(2)
# got a complex pole or zero, need two roots (if available)
if(length(zer) > 1)
[num,zer] = zp2ssg2(zer); # get two zeros
elseif(length(zer) == 1)
num = [1 -zer]; # use last zero (better be real!)
zer = [];
endif
[den,pol] = zp2ssg2(pol); # get two poles
otherwise
error(["pcnt = ",num2str(pcnt)])
endswitch
# pack tf into system form and put in series with earlier realization
zpsys1 = tf2sys(num,den,0,"u","yy");
# change names to avoid warning messages from sysgroup
zpsys = syssetsg(zpsys,"in","u1",1);
zpsys1 = sysupdat(zpsys1,"ss");
nn = sysdimen(zpsys); # working with continuous system
zpsys = syssetsg(zpsys,"st", sysdefio(nn,"x"));
nn1 = sysdimen(zpsys1);
zpsys1 = syssetsg(zpsys1,"st",sysdefio(nn1,"xx"));
zpsys = sysmult(zpsys,zpsys1);
endwhile
[a,b,c,d] = sys2ss(zpsys);
empty_list_elements_ok = sav_val;
endfunction