Mercurial > octave-libtiff
view scripts/control/dlqr.m @ 2311:2b5788792cad
[project @ 1996-07-11 20:18:38 by jwe]
author | jwe |
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date | Thu, 11 Jul 1996 20:18:38 +0000 |
parents | 5cffc4b8de57 |
children | 204cc7db6f4a |
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### Copyright (C) 1996 John W. Eaton ### ### 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 ### 02111-1307, USA. ## Usage: [k, p, e] = dlqr (A, B, Q, R {,Z}) ## ## Linear quadratic regulator design for the discrete time system ## ## x[k+1] = A x[k] + B u[k] ## ## to minimize the cost functional ## ## J = Sum { x' Q x + u' R u } Z omitted ## ## or ## ## J = Sum { x' Q x + u' R u +2 x' Z u} Z included ## ## Returns: ## ## k = state feedback gain, (A - B K) is stable ## p = solution of algebraic Riccati equation ## e = closed loop poles of (A - B K) function [k, p, e] = dlqr (a, b, q, r, zz) ## Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. ## Converted to discrete time by R. B. Tenison ## (btenison@eng.auburn.edu) October 1993 if (nargin != 4 && nargin != 5) error ("dlqr: invalid number of arguments"); endif ## Check a. if ((n = is_square (a)) == 0) error ("dlqr: requires 1st parameter(a) to be square"); endif ## Check b. [n1, m] = size (b); if (n1 != n) error ("dlqr: a,b not conformal"); endif ## Check q. if ((n1 = is_square (q)) == 0 || n1 != n) error ("dlqr: q must be square and conformal with a"); endif ## Check r. if((m1 = is_square(r)) == 0 || m1 != m) error ("dlqr: r must be square and conformal with column dimension of b"); endif ## Check if n is there. if (nargin == 5) [n1, m1] = size (zz); if (n1 != n || m1 != m) error ("dlqr: z must be identically dimensioned with b"); endif ## Incorporate cross term into a and q. ao = a - (b/r)*zz'; qo = q - (zz/r)*zz'; else zz = zeros (n, m); ao = a; qo = q; endif ## Check that q, (r) are symmetric, positive (semi)definite if (is_symmetric (q) && is_symmetric (r) ... && all (eig (q) >= 0) && all (eig (r) > 0)) p = dare (ao, b, qo, r); k = (r+b'*p*b)\b'*p*a + r\zz'; e = eig (a - b*k); else error ("dlqr: q (r) must be symmetric positive (semi) definite"); endif endfunction