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## 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
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