--- /dev/null
+## Copyright (C) 2009 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{K}, @var{N}, @var{gamma}, @var{rcond}] =} hinfsyn (@var{P}, @var{nmeas}, @var{ncon})
+## @deftypefnx{Function File} {[@var{K}, @var{N}, @var{gamma}, @var{rcond}] =} hinfsyn (@var{P}, @var{nmeas}, @var{ncon}, @var{gmax})
+## H-infinity control synthesis for LTI plant.
+##
+## @strong{Inputs}
+## @table @var
+## @item P
+## Generalized plant. Must be a proper/realizable LTI model.
+## @item nmeas
+## Number of measured outputs v. The last @var{nmeas} outputs of @var{P} are connected to the
+## inputs of controller @var{K}. The remaining outputs z (indices 1 to p-nmeas) are used
+## to calculate the H-infinity norm.
+## @item ncon
+## Number of controlled inputs u. The last @var{ncon} inputs of @var{P} are connected to the
+## outputs of controller @var{K}. The remaining inputs w (indices 1 to m-ncon) are excited
+## by a harmonic test signal.
+## @item gmax
+## The maximum value of the H-infinity norm of @var{N}. It is assumed that @var{gmax} is
+## sufficiently large so that the controller is admissible.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item K
+## State-space model of the H-infinity (sub-)optimal controller.
+## @item N
+## State-space model of the lower LFT of @var{P} and @var{K}.
+## @item gamma
+## L-infinity norm of @var{N}.
+## @item rcond
+## Vector @var{rcond} contains estimates of the reciprocal condition
+## numbers of the matrices which are to be inverted and
+## estimates of the reciprocal condition numbers of the
+## Riccati equations which have to be solved during the
+## computation of the controller @var{K}. For details,
+## see the description of the corresponding SLICOT algorithm.
+## @end table
+##
+## @strong{Block Diagram}
+## @example
+## @group
+##
+## gamma = min||N(K)|| N = lft (P, K)
+## K inf
+##
+## +--------+
+## w ----->| |-----> z
+## | P(s) |
+## u +---->| |-----+ v
+## | +--------+ |
+## | |
+## | +--------+ |
+## +-----| K(s) |<----+
+## +--------+
+##
+## +--------+
+## w ----->| N(s) |-----> z
+## +--------+
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB10FD and SB10DD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{augw, mixsyn}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: December 2009
+## Version: 0.1
+
+## TODO: improve compatibility for nargin >= 4
+
+function [K, varargout] = hinfsyn (P, nmeas, ncon, gmax = 1e15)
+
+ ## check input arguments
+ if (nargin < 3 || nargin > 4)
+ print_usage ();
+ endif
+
+ if (! isa (P, "lti"))
+ error ("hinfsyn: first argument must be an LTI system");
+ endif
+
+ if (! is_real_scalar (nmeas))
+ error ("hinfsyn: second argument invalid");
+ endif
+
+ if (! is_real_scalar (ncon))
+ error ("hinfsyn: third argument invalid");
+ endif
+
+ if (! is_real_scalar (gmax) || gmax < 0)
+ error ("hinfsyn: fourth argument invalid");
+ endif
+
+ [a, b, c, d, tsam] = ssdata (P);
+
+ ## check assumption A1
+ m = columns (b);
+ p = rows (c);
+
+ m1 = m - ncon;
+ p1 = p - nmeas;
+
+ if (! isstabilizable (P(:, m1+1:m)))
+ error ("hinfsyn: (A, B2) must be stabilizable");
+ endif
+
+ if (! isdetectable (P(p1+1:p, :)))
+ error ("hinfsyn: (C2, A) must be detectable");
+ endif
+
+ ## H-infinity synthesis
+ if (isct (P)) # continuous plant
+ [ak, bk, ck, dk, rcond] = slsb10fd (a, b, c, d, ncon, nmeas, gmax);
+ else # discrete plant
+ [ak, bk, ck, dk, rcond] = slsb10dd (a, b, c, d, ncon, nmeas, gmax);
+ endif
+
+ ## controller
+ K = ss (ak, bk, ck, dk, tsam);
+
+ if (nargout > 1)
+ N = lft (P, K);
+ varargout{1} = N;
+ if (nargout > 2)
+ varargout{2} = norm (N, inf);
+ if (nargout > 3)
+ varargout{3} = rcond;
+ endif
+ endif
+ endif
+
+endfunction
+
+
+## continuous-time case
+%!shared M, M_exp
+%! A = [-1.0 0.0 4.0 5.0 -3.0 -2.0
+%! -2.0 4.0 -7.0 -2.0 0.0 3.0
+%! -6.0 9.0 -5.0 0.0 2.0 -1.0
+%! -8.0 4.0 7.0 -1.0 -3.0 0.0
+%! 2.0 5.0 8.0 -9.0 1.0 -4.0
+%! 3.0 -5.0 8.0 0.0 2.0 -6.0];
+%!
+%! B = [-3.0 -4.0 -2.0 1.0 0.0
+%! 2.0 0.0 1.0 -5.0 2.0
+%! -5.0 -7.0 0.0 7.0 -2.0
+%! 4.0 -6.0 1.0 1.0 -2.0
+%! -3.0 9.0 -8.0 0.0 5.0
+%! 1.0 -2.0 3.0 -6.0 -2.0];
+%!
+%! C = [ 1.0 -1.0 2.0 -4.0 0.0 -3.0
+%! -3.0 0.0 5.0 -1.0 1.0 1.0
+%! -7.0 5.0 0.0 -8.0 2.0 -2.0
+%! 9.0 -3.0 4.0 0.0 3.0 7.0
+%! 0.0 1.0 -2.0 1.0 -6.0 -2.0];
+%!
+%! D = [ 1.0 -2.0 -3.0 0.0 0.0
+%! 0.0 4.0 0.0 1.0 0.0
+%! 5.0 -3.0 -4.0 0.0 1.0
+%! 0.0 1.0 0.0 1.0 -3.0
+%! 0.0 0.0 1.0 7.0 1.0];
+%!
+%! P = ss (A, B, C, D);
+%! K = hinfsyn (P, 2, 2, 15);
+%! M = [K.A, K.B; K.C, K.D];
+%!
+%! KA = [ -2.8043 14.7367 4.6658 8.1596 0.0848 2.5290
+%! 4.6609 3.2756 -3.5754 -2.8941 0.2393 8.2920
+%! -15.3127 23.5592 -7.1229 2.7599 5.9775 -2.0285
+%! -22.0691 16.4758 12.5523 -16.3602 4.4300 -3.3168
+%! 30.6789 -3.9026 -1.3868 26.2357 -8.8267 10.4860
+%! -5.7429 0.0577 10.8216 -11.2275 1.5074 -10.7244];
+%!
+%! KB = [ -0.1581 -0.0793
+%! -0.9237 -0.5718
+%! 0.7984 0.6627
+%! 0.1145 0.1496
+%! -0.6743 -0.2376
+%! 0.0196 -0.7598];
+%!
+%! KC = [ -0.2480 -0.1713 -0.0880 0.1534 0.5016 -0.0730
+%! 2.8810 -0.3658 1.3007 0.3945 1.2244 2.5690];
+%!
+%! KD = [ 0.0554 0.1334
+%! -0.3195 0.0333];
+%!
+%! M_exp = [KA, KB; KC, KD];
+%!
+%!assert (M, M_exp, 1e-4);
+
+
+## discrete-time case
+%!shared M, M_exp
+%! A = [-0.7 0.0 0.3 0.0 -0.5 -0.1
+%! -0.6 0.2 -0.4 -0.3 0.0 0.0
+%! -0.5 0.7 -0.1 0.0 0.0 -0.8
+%! -0.7 0.0 0.0 -0.5 -1.0 0.0
+%! 0.0 0.3 0.6 -0.9 0.1 -0.4
+%! 0.5 -0.8 0.0 0.0 0.2 -0.9];
+%!
+%! B = [-1.0 -2.0 -2.0 1.0 0.0
+%! 1.0 0.0 1.0 -2.0 1.0
+%! -3.0 -4.0 0.0 2.0 -2.0
+%! 1.0 -2.0 1.0 0.0 -1.0
+%! 0.0 1.0 -2.0 0.0 3.0
+%! 1.0 0.0 3.0 -1.0 -2.0];
+%!
+%! C = [ 1.0 -1.0 2.0 -2.0 0.0 -3.0
+%! -3.0 0.0 1.0 -1.0 1.0 0.0
+%! 0.0 2.0 0.0 -4.0 0.0 -2.0
+%! 1.0 -3.0 0.0 0.0 3.0 1.0
+%! 0.0 1.0 -2.0 1.0 0.0 -2.0];
+%!
+%! D = [ 1.0 -1.0 -2.0 0.0 0.0
+%! 0.0 1.0 0.0 1.0 0.0
+%! 2.0 -1.0 -3.0 0.0 1.0
+%! 0.0 1.0 0.0 1.0 -1.0
+%! 0.0 0.0 1.0 2.0 1.0];
+%!
+%! P = ss (A, B, C, D, 1); # value of sampling time doesn't matter
+%! K = hinfsyn (P, 2, 2, 111.294);
+%! M = [K.A, K.B; K.C, K.D];
+%!
+%! KA = [-18.0030 52.0376 26.0831 -0.4271 -40.9022 18.0857
+%! 18.8203 -57.6244 -29.0938 0.5870 45.3309 -19.8644
+%! -26.5994 77.9693 39.0368 -1.4020 -60.1129 26.6910
+%! -21.4163 62.1719 30.7507 -0.9201 -48.6221 21.8351
+%! -0.8911 4.2787 2.3286 -0.2424 -3.0376 1.2169
+%! -5.3286 16.1955 8.4824 -0.2489 -12.2348 5.1590];
+%!
+%! KB = [ 16.9788 14.1648
+%! -18.9215 -15.6726
+%! 25.2046 21.2848
+%! 20.1122 16.8322
+%! 1.4104 1.2040
+%! 5.3181 4.5149];
+%!
+%! KC = [ -9.1941 27.5165 13.7364 -0.3639 -21.5983 9.6025
+%! 3.6490 -10.6194 -5.2772 0.2432 8.1108 -3.6293];
+%!
+%! KD = [ 9.0317 7.5348
+%! -3.4006 -2.8219];
+%!
+%! M_exp = [KA, KB; KC, KD];
+%!
+%!assert (M, M_exp, 1e-4);
\ No newline at end of file
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff