--- /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}] =} mixsyn (@var{G}, @var{W1}, @var{W2}, @var{W3}, @dots{})
+## Solve stacked S/KS/T H-infinity problem. Bound the largest singular values
+## of @var{S} (for performance), @var{K S} (to penalize large inputs) and
+## @var{T} (for robustness and to avoid sensitivity to noise).
+## In other words, the inputs r are excited by a harmonic test signal.
+## Then the algorithm tries to find a controller @var{K} which minimizes
+## the H-infinity norm calculated from the outputs z.
+##
+## @strong{Inputs}
+## @table @var
+## @item G
+## LTI model of plant.
+## @item W1
+## LTI model of performance weight. Bounds the largest singular values of sensitivity @var{S}.
+## Model must be empty @code{[]}, SISO or of appropriate size.
+## @item W2
+## LTI model to penalize large control inputs. Bounds the largest singular values of @var{KS}.
+## Model must be empty @code{[]}, SISO or of appropriate size.
+## @item W3
+## LTI model of robustness and noise sensitivity weight. Bounds the largest singular values of
+## complementary sensitivity @var{T}. Model must be empty @code{[]}, SISO or of appropriate size.
+## @item @dots{}
+## Optional arguments of @command{hinfsyn}. Type @command{help hinfsyn} for more information.
+## @end table
+##
+## All inputs must be proper/realizable.
+## Scalars, vectors and matrices are possible instead of LTI models.
+##
+## @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
+##
+## | W1 S |
+## gamma = min||N(K)|| N = | W2 K S | = lft (P, K)
+## K inf | W3 T |
+## @end group
+## @end example
+## @example
+## @group
+## +------+ z1
+## +---------------------------------------->| W1 |----->
+## | +------+
+## | +------+ z2
+## | +---------------------->| W2 |----->
+## | | +------+
+## r + e | +--------+ u | +--------+ y +------+ z3
+## ----->(+)---+-->| K(s) |----+-->| G(s) |----+---->| W3 |----->
+## ^ - +--------+ +--------+ | +------+
+## | |
+## +----------------------------------------+
+## @end group
+## @end example
+## @example
+## @group
+## +--------+
+## | |-----> z1 (p1x1) z1 = W1 e
+## r (px1) ----->| P(s) |-----> z2 (p2x1) z2 = W2 u
+## | |-----> z3 (p3x1) z3 = W3 y
+## u (mx1) ----->| |-----> e (px1) e = r - y
+## +--------+
+## @end group
+## @end example
+## @example
+## @group
+## +--------+
+## r ----->| |-----> z
+## | P(s) |
+## u +---->| |-----+ e
+## | +--------+ |
+## | |
+## | +--------+ |
+## +-----| K(s) |<----+
+## +--------+
+## @end group
+## @end example
+## @example
+## @group
+## +--------+
+## r ----->| N(s) |-----> z
+## +--------+
+## @end group
+## @end example
+## @example
+## @group
+## Extended Plant: P = augw (G, W1, W2, W3)
+## Controller: K = mixsyn (G, W1, W2, W3)
+## Entire System: N = lft (P, K)
+## Open Loop: L = G * K
+## Closed Loop: T = feedback (L)
+## @end group
+## @end example
+## @example
+## @group
+## Reference:
+## Skogestad, S. and Postlethwaite I.
+## Multivariable Feedback Control: Analysis and Design
+## Second Edition
+## Wiley 2005
+## Chapter 3.8: General Control Problem Formulation
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Relies on commands @command{augw} and @command{hinfsyn},
+## which use SLICOT SB10FD and SB10DD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{hinfsyn, augw}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: December 2009
+## Version: 0.1
+
+function [K, N, gamma, rcond] = mixsyn (G, W1 = [], W2 = [], W3 = [], varargin)
+
+ if (nargin == 0)
+ print_usage ();
+ endif
+
+ [p, m] = size (G);
+
+ P = augw (G, W1, W2, W3);
+
+ [K, N, gamma, rcond] = hinfsyn (P, p, m, varargin{:});
+
+endfunction
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff