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## Copyright (C) 2009-2014 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{P} =} augw (@var{G}, @var{W1}, @var{W2}, @var{W3})
## Extend plant for stacked S/KS/T problem. Subsequently, the robust control problem
## can be solved by h2syn or hinfsyn.
##
## @strong{Inputs}
## @table @var
## @item G
## @acronym{LTI} model of plant.
## @item W1
## @acronym{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
## @acronym{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
## @acronym{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.
## @end table
##
## All inputs must be proper/realizable.
## Scalars, vectors and matrices are possible instead of @acronym{LTI} models.
##
## @strong{Outputs}
## @table @var
## @item P
## State-space model of augmented plant.
## @end table
##
## @strong{Block Diagram}
## @example
## @group
##
## | W1 | -W1*G | z1 = W1 r - W1 G u
## | 0 | W2 | z2 = W2 u
## P = | 0 | W3*G | z3 = W3 G u
## |----+-------|
## | I | -G | e = r - G u
## @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
##
## @strong{References}@*
## [1] Skogestad, S. and Postlethwaite I. (2005)
## @cite{Multivariable Feedback Control: Analysis and Design:
## Second Edition}. Wiley.
##
## @seealso{h2syn, hinfsyn, mixsyn}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: December 2009
## Version: 0.3
function P = augw (G, W1 = [], W2 = [], W3 = [])
if (nargin == 0 || nargin > 4)
print_usage ();
endif
G = ss (G);
[p, m] = size (G);
[W1, p1, m1] = __adjust_weighting__ (W1, p);
[W2, p2, m2] = __adjust_weighting__ (W2, m);
[W3, p3, m3] = __adjust_weighting__ (W3, p);
## Pr = [1; 0; 0; 1];
## Pu = [-1; 0; 1; -1]*G + [0; 1; 0; 0];
Pr = ss ([eye(m1,p) ;
zeros(m2,p);
zeros(m3,p);
eye(p,p) ]);
Pu1 = ss ([-eye(m1,p) ;
zeros(m2,p);
eye(m3,p) ;
-eye(p,p) ]);
Pu2 = ss ([zeros(m1,m);
eye(m2,m) ;
zeros(m3,m);
zeros(p,m) ]);
Pu = Pu1 * G + Pu2;
P = append (W1, W2, W3, eye (p, p)) * [Pr, Pu];
P = mktito (P, p, m);
endfunction
function [W, p, m] = __adjust_weighting__ (W, s)
W = ss (W);
[p, m] = size (W);
if (m == 0 || m == s) # model is empty or has s inputs
return;
elseif (m == 1) # model is SISO or SIMO
tmp = W;
for k = 2 : s
W = append (W, tmp); # stack single-input model s times
endfor
[p, m] = size (W); # weighting function now of correct size
else # model is MIMO or MISO
error ("augw: %s must have 1 or %d inputs", inputname (1), s);
endif
endfunction