Mercurial > hg > octave-nkf
view scripts/control/system/ss2sys.m @ 11651:74de76325d12 release-3-0-x
more xGELSD workspace fixes
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 15 Feb 2008 18:55:45 -0500 |
parents | 8aa770b6c5bf |
children |
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## Copyright (C) 1996, 1998, 2000, 2002, 2004, 2005, 2007 ## 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 3 of the License, 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, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} ss2sys (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist}) ## Create system structure from state-space data. May be continuous, ## discrete, or mixed (sampled data) ## ## @strong{Inputs} ## @table @var ## @item a ## @itemx b ## @itemx c ## @itemx d ## usual state space matrices. ## ## default: @var{d} = zero matrix ## ## @item tsam ## sampling rate. Default: @math{tsam = 0} (continuous system) ## ## @item n ## @itemx nz ## number of continuous, discrete states in the system ## ## If @var{tsam} is 0, @math{n = @code{rows}(@var{a})}, @math{nz = 0}. ## ## If @var{tsam} is greater than zero, @math{n = 0}, ## @math{nz = @code{rows}(@var{a})} ## ## see below for system partitioning ## ## @item stname ## cell array of strings of state signal names ## ## default (@var{stname}=[] on input): @code{x_n} for continuous states, ## @code{xd_n} for discrete states ## ## @item inname ## cell array of strings of input signal names ## ## default (@var{inname} = [] on input): @code{u_n} ## ## @item outname ## cell array of strings of input signal names ## ## default (@var{outname} = [] on input): @code{y_n} ## ## @item outlist ## ## list of indices of outputs y that are sampled ## ## If @var{tsam} is 0, @math{outlist = []}. ## ## If @var{tsam} is greater than 0, @math{outlist = 1:@code{rows}(@var{c})}. ## @end table ## ## Unlike states, discrete/continuous outputs may appear in any order. ## ## @code{sys2ss} returns a vector @var{yd} where ## @var{yd}(@var{outlist}) = 1; all other entries of @var{yd} are 0. ## ## @strong{Outputs} ## @var{outsys} = system data structure ## ## @strong{System partitioning} ## ## Suppose for simplicity that outlist specified ## that the first several outputs were continuous and the remaining outputs ## were discrete. Then the system is partitioned as ## @example ## @group ## x = [ xc ] (n x 1) ## [ xd ] (nz x 1 discrete states) ## a = [ acc acd ] b = [ bc ] ## [ adc add ] [ bd ] ## c = [ ccc ccd ] d = [ dc ] ## [ cdc cdd ] [ dd ] ## ## (cdc = c(outlist,1:n), etc.) ## @end group ## @end example ## with dynamic equations: ## @ifinfo ## @math{d/dt xc(t) = acc*xc(t) + acd*xd(k*tsam) + bc*u(t)} ## ## @math{xd((k+1)*tsam) = adc*xc(k*tsam) + add*xd(k*tsam) + bd*u(k*tsam)} ## ## @math{yc(t) = ccc*xc(t) + ccd*xd(k*tsam) + dc*u(t)} ## ## @math{yd(k*tsam) = cdc*xc(k*tsam) + cdd*xd(k*tsam) + dd*u(k*tsam)} ## @end ifinfo ## @iftex ## @tex ## $$\eqalign{ ## {d \over dt} x_c(t) ## & = a_{cc} x_c(t) + a_{cd} x_d(k*t_{sam}) + bc*u(t) \cr ## x_d((k+1)*t_{sam}) ## & = a_{dc} x_c(k t_{sam}) + a_{dd} x_d(k t_{sam}) + b_d u(k t_{sam}) \cr ## y_c(t) ## & = c_{cc} x_c(t) + c_{cd} x_d(k t_{sam}) + d_c u(t) \cr ## y_d(k t_{sam}) ## & = c_{dc} x_c(k t_{sam}) + c_{dd} x_d(k t_{sam}) + d_d u(k t_{sam}) ## }$$ ## @end tex ## @end iftex ## ## @strong{Signal partitions} ## @example ## @group ## | continuous | discrete | ## ---------------------------------------------------- ## states | stname(1:n,:) | stname((n+1):(n+nz),:) | ## ---------------------------------------------------- ## outputs | outname(cout,:) | outname(outlist,:) | ## ---------------------------------------------------- ## @end group ## @end example ## where @math{cout} is the list of in 1:@code{rows}(@var{p}) ## that are not contained in outlist. (Discrete/continuous outputs ## may be entered in any order desired by the user.) ## ## @strong{Example} ## @example ## octave:1> a = [1 2 3; 4 5 6; 7 8 10]; ## octave:2> b = [0 0 ; 0 1 ; 1 0]; ## octave:3> c = eye (3); ## octave:4> sys = ss (a, b, c, [], 0, 3, 0, ## > @{"volts", "amps", "joules"@}); ## octave:5> sysout(sys); ## Input(s) ## 1: u_1 ## 2: u_2 ## ## Output(s): ## 1: y_1 ## 2: y_2 ## 3: y_3 ## ## state-space form: ## 3 continuous states, 0 discrete states ## State(s): ## 1: volts ## 2: amps ## 3: joules ## ## A matrix: 3 x 3 ## 1 2 3 ## 4 5 6 ## 7 8 10 ## B matrix: 3 x 2 ## 0 0 ## 0 1 ## 1 0 ## C matrix: 3 x 3 ## 1 0 0 ## 0 1 0 ## 0 0 1 ## D matrix: 3 x 3 ## 0 0 ## 0 0 ## 0 0 ## @end example ## Notice that the @math{D} matrix is constructed by default to the ## correct dimensions. Default input and output signals names were assigned ## since none were given. ## @end deftypefn ## Author: John Ingram <ingraje@eng.auburn.edu> ## Created: July 20, 1996 function retsys = ss2sys (varargin ) warning ("ss2sys is deprecated. Use ss instead."); retsys = ss (varargin{:}); endfunction