Mercurial > octave-nkf
view scripts/control/zp2ss.m @ 3425:8625164a0a39
[project @ 2000-01-13 08:31:37 by jwe]
author | jwe |
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date | Thu, 13 Jan 2000 08:32:16 +0000 |
parents | 9610d364e444 |
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## Copyright (C) 1996 Auburn University. All rights reserved. ## ## 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, 59 Temple Place, Suite 330, Boston, MA 02111 USA. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{A}, @var{B}, @var{C}, @var{D}] =} zp2ss (@var{zer}, @var{pol}, @var{k}) ## Conversion from zero / pole to state space. ## @strong{Inputs} ## @table @var ## @item zer ## @itemx 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) ## @item k ## real scalar (leading coefficient) ## @end table ## @strong{Outputs} ## @var{A}, @var{B}, @var{C}, @var{D} ## The state space system ## @example ## . ## x = Ax + Bu ## y = Cx + Du ## @end example ## is obtained from a vector of zeros and a vector of poles via the ## function call @code{[a,b,c,d] = zp2ss(zer,pol,k)}. ## The vectors @samp{zer} and ## @samp{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 zeros must not exceed the number of poles. ## @samp{k} is @code{zp}-form leading coefficient. ## @end deftypefn ## Author: David Clem ## Created: August 15, 1994 function [a, b, c, d] = zp2ss (zer, pol, k) sav_val = empty_list_elements_ok; empty_list_elements_ok = 1; if(nargin != 3) error("Incorrect number of input arguments"); endif if(! (is_vector(zer) | isempty(zer)) ) error(["zer(",num2str(rows(zer)),",",num2str(columns(zer)), ... ") should be a vector"]); elseif(! (is_vector(pol) | isempty(pol) ) ) error(["pol(",num2str(rows(pol)),",",num2str(columns(pol)), ... ") should be a vector"]); elseif(! is_scalar(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 = syssetsignals(zpsys,"in","u1",1); zpsys1 = sysupdate(zpsys1,"ss"); nn = sysdimensions(zpsys); # working with continuous system zpsys = syssetsignals(zpsys,"st", sysdefioname(nn,"x")); nn1 = sysdimensions(zpsys1); zpsys1 = syssetsignals(zpsys1,"st",sysdefioname(nn1,"xx")); zpsys = sysmult(zpsys,zpsys1); endwhile [a,b,c,d] = sys2ss(zpsys); empty_list_elements_ok = sav_val; endfunction