X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2Flqr.m;fp=octave_packages%2Fcontrol-2.3.52%2Flqr.m;h=b69274717a9b821b251eb93a312f099518e5022e;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05 diff --git a/octave_packages/control-2.3.52/lqr.m b/octave_packages/control-2.3.52/lqr.m new file mode 100644 index 0000000..b692747 --- /dev/null +++ b/octave_packages/control-2.3.52/lqr.m @@ -0,0 +1,98 @@ +## Copyright (C) 2009, 2010 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 . + +## -*- texinfo -*- +## @deftypefn {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{sys}, @var{q}, @var{r}) +## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{sys}, @var{q}, @var{r}, @var{s}) +## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}) +## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}) +## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e}) +## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e}) +## Linear-quadratic regulator. +## +## @strong{Inputs} +## @table @var +## @item sys +## Continuous or discrete-time LTI model (p-by-m, n states). +## @item a +## State transition matrix of continuous-time system (n-by-n). +## @item b +## Input matrix of continuous-time system (n-by-m). +## @item q +## State weighting matrix (n-by-n). +## @item r +## Input weighting matrix (m-by-m). +## @item s +## Optional cross term matrix (n-by-m). If @var{s} is not specified, a zero matrix is assumed. +## @item e +## Optional descriptor matrix (n-by-n). If @var{e} is not specified, an identity matrix is assumed. +## @end table +## +## @strong{Outputs} +## @table @var +## @item g +## State feedback matrix (m-by-n). +## @item x +## Unique stabilizing solution of the continuous-time Riccati equation (n-by-n). +## @item l +## Closed-loop poles (n-by-1). +## @end table +## +## @strong{Equations} +## @example +## @group +## . +## x = A x + B u, x(0) = x0 +## +## inf +## J(x0) = INT (x' Q x + u' R u + 2 x' S u) dt +## 0 +## +## L = eig (A - B*G) +## @end group +## @end example +## @seealso{care, dare, dlqr} +## @end deftypefn + +## Author: Lukas Reichlin +## Created: November 2009 +## Version: 0.2 + +function [g, x, l] = lqr (a, b, q, r = [], s = [], e = []) + + if (nargin < 3 || nargin > 6) + print_usage (); + endif + + if (isa (a, "lti")) + s = r; + r = q; + q = b; + [a, b, c, d, e, tsam] = dssdata (a, []); + elseif (nargin < 4) + print_usage (); + else + tsam = 0; + endif + + if (issample (tsam, -1)) + [x, l, g] = dare (a, b, q, r, s, e); + else + [x, l, g] = care (a, b, q, r, s, e); + endif + +endfunction \ No newline at end of file