Mercurial > octave-nkf
view scripts/control/lqr.m @ 76:c69be6819009
[project @ 1993-08-30 15:29:38 by jwe]
Initial revision
author | jwe |
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date | Mon, 30 Aug 1993 15:29:38 +0000 |
parents | |
children | 16a24e76d6e0 |
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function [k, p, e] = lqr (a, b, q, r, zz) # Usage: [k, p, e] = lqr (A, B, Q, R {,Z}) # # Linear quadratic regulator design for the continuous time system # # dx/dt = A x + B u # # to minimize the cost functional # # J = int_0^\infty{ x' Q x + u' R u } Z omitted # # or # # J = int_0^\infty{ 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) # Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. if (nargin != 4 && nargin != 5) error ("lqr: illegal number of arguments"); endif # Check a. if ((n = is_square (a)) == 0) error ("lqr: requires 1st parameter(a) to be square"); endif # Check b. [n1, m] = size (b); if (n1 != n) error ("lqr: a,b not conformal"); endif # Check q. if ((n1 = is_square (q)) == 0 || n1 != n) error ("lqr: q must be square and conformal with a"); endif # Check r. if((m1 = is_square(r)) == 0 || m1 != m) error ("lqr: 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 ("lqr: 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 = are (ao, (b/r)*b', qo); k = r\(b'*p + zz'); e = eig (a - b*k); else error ("lqr: q (r) must be symmetric positive (semi) definite"); endif endfunction