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view main/control/inst/sigma.m @ 9413:36c5d50f3ff7 octave-forge
control: document new feature of frequency response commands
author | paramaniac |
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date | Thu, 09 Feb 2012 13:42:44 +0000 |
parents | d647ee27e561 |
children | d5e100fe4b22 |
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## Copyright (C) 2009, 2010, 2011, 2012 Lukas F. Reichlin ## ## This file is part of LTI Syncope. ## ## LTI Syncope 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. ## ## LTI Syncope 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 LTI Syncope. If not, see <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}) ## @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{w}) ## @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{[]}, @var{ptype}) ## @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{w}, @var{ptype}) ## Singular values of frequency response. If no output arguments are given, ## the singular value plot is printed on the screen; ## ## @strong{Inputs} ## @table @var ## @item sys ## LTI system. Multiple inputs and/or outputs (MIMO systems) make practical sense. ## @item w ## Optional vector of frequency values. If @var{w} is not specified, ## it is calculated by the zeros and poles of the system. ## Alternatively, the cell @code{@{wmin, wmax@}} specifies a frequency range, ## where @var{wmin} and @var{wmax} denote minimum and maximum frequencies ## in rad/s. ## @item ptype = 0 ## Singular values of the frequency response @var{H} of system @var{sys}. Default Value. ## @item ptype = 1 ## Singular values of the frequency response @code{inv(H)}; i.e. inversed system. ## @item ptype = 2 ## Singular values of the frequency response @code{I + H}; i.e. inversed sensitivity ## (or return difference) if @code{H = P * C}. ## @item ptype = 3 ## Singular values of the frequency response @code{I + inv(H)}; i.e. inversed complementary ## sensitivity if @code{H = P * C}. ## @end table ## ## @strong{Outputs} ## @table @var ## @item sv ## Array of singular values. For a system with m inputs and p outputs, the array sv ## has @code{min (m, p)} rows and as many columns as frequency points @code{length (w)}. ## The singular values at the frequency @code{w(k)} are given by @code{sv(:,k)}. ## @item w ## Vector of frequency values used. ## @end table ## ## @seealso{bodemag, svd} ## @end deftypefn ## Author: Lukas Reichlin <lukas.reichlin@gmail.com> ## Created: May 2009 ## Version: 0.5 function [sv_r, w_r] = sigma (sys, w = [], resptype = 0) ## TODO: multiplot feature: sigma (sys1, "b", sys2, "r", ...) if (nargin == 0 || nargin > 3) print_usage (); endif [H, w] = __frequency_response__ (sys, w, true, resptype, "std", true); sv = cellfun (@svd, H, "uniformoutput", false); sv = horzcat (sv{:}); if (! nargout) # plot the information ## convert to dB for plotting sv_db = 20 * log10 (sv); ## determine axes ax_vec = __axis_limits__ ([reshape(w, [], 1), reshape(min(sv_db, [], 1), [], 1); reshape(w, [], 1), reshape(max(sv_db, [], 1), [], 1)]); ax_vec(1:2) = [min(w), max(w)]; ## determine xlabel if (isct (sys)) xl_str = "Frequency [rad/s]"; else xl_str = sprintf ("Frequency [rad/s] w_N = %g", pi / get (sys, "tsam")); endif ## plot results semilogx (w, sv_db, "b") ax = axis; if (any (isinf (ax_vec))) # catch case purely imaginary poles or zeros ax_vec(3:4) = ax(3:4); endif axis (ax_vec) title (["Singular Values of ", inputname(1)]) xlabel (xl_str) ylabel ("Singular Values [dB]") grid ("on") else # return values sv_r = sv; w_r = reshape (w, [], 1); endif endfunction %!shared sv_exp, w_exp, sv_obs, w_obs %! A = [1, 2; 3, 4]; %! B = [5, 6; 7, 8]; %! C = [4, 3; 2, 1]; %! D = [8, 7; 6, 5]; %! w = [2, 3, 4]; %! sv_exp = [7.9176, 8.6275, 9.4393; %! 0.6985, 0.6086, 0.5195]; %! w_exp = [2; 3; 4]; %! [sv_obs, w_obs] = sigma (ss (A, B, C, D), w); %!assert (sv_obs, sv_exp, 1e-4); %!assert (w_obs, w_exp, 1e-4);