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## Copyright (C) 2009-2016 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} =} mktito (@var{P}, @var{nmeas}, @var{ncon})
## Partition @acronym{LTI} plant @var{P} for robust controller synthesis.
## If a plant is partitioned this way, one can omit the inputs @var{nmeas}
## and @var{ncon} when calling the functions @command{hinfsyn} and @command{h2syn}.
##
## @strong{Inputs}
## @table @var
## @item P
## Generalized plant.
## @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-2/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.
## @end table
##
## @strong{Outputs}
## @table @var
## @item P
## Partitioned plant. The input/output groups and names are overwritten with designations
## according to [1].
## @end table
##
## @strong{Block Diagram}
## @example
## @group
##
## min||N(K)|| N = lft (P, K)
## K norm
##
## +--------+
## w = u1 ----->| |-----> z = y1
## | P(s) |
## u = u2 +---->| |-----+ y = y2
## | +--------+ |
## | |
## | +--------+ |
## +-----| K(s) |<----+
## +--------+
##
## +--------+
## w = u1 ----->| N(s) |-----> z = y1
## +--------+
## @end group
## @end example
##
## @strong{Reference}@*
## [1] Skogestad, S. and Postlethwaite, I. (2005)
## @cite{Multivariable Feedback Control: Analysis and Design:
## Second Edition}. Wiley, Chichester, England.
##
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: October 2013
## Version: 0.1
function P = mktito (P, nmeas, ncon)
if (nargin != 3)
print_usage ();
endif
if (! isa (P, "lti"))
error ("mktito: first argument must be an LTI model");
endif
[p, m] = size (P);
if (! is_index (nmeas, p))
error ("mktito: second argument 'nmeas' invalid");
endif
if (! is_index (ncon, m))
error ("mktito: third argument 'ncon' invalid");
endif
outgroup = struct ("Y1", 1:p-nmeas, "Y2", p-nmeas+1:p);
outname = vertcat (strseq ("y", 1:p));
ingroup = struct ("U1", 1:m-ncon, "U2", m-ncon+1:m);
inname = vertcat (strseq ("u", 1:m));
P = set (P, "outgroup", outgroup, "ingroup", ingroup, ...
"outname", outname, "inname", inname);
endfunction
function bool = is_index (idx, s)
## (idx < s) and not (idx <= s) because we need at least one Z or W
bool = is_real_scalar (idx) && fix (idx) == idx && idx > 0 && idx < s;
endfunction
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