Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / @ss / __sys_connect__.m

diff --git a/octave_packages/control-2.3.52/@ss/__sys_connect__.m b/octave_packages/control-2.3.52/@ss/__sys_connect__.m
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+## Copyright (C) 2009, 2010   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{retsys} =} __sys_connect__ (@var{sys}, @var{M})
+## This function is part of the Model Abstraction Layer.  No argument checking.
+## For internal use only.
+## @example
+## @group
+## Problem: Solve the system equations of
+##   .
+## E x(t) = A x(t) + B e(t)
+##
+##   y(t) = C x(t) + D e(t)
+##
+##   e(t) = u(t) + M y(t)
+##
+## in order to build
+##   .
+## K x(t) = F x(t) + G u(t)
+##
+##   y(t) = H x(t) + J u(t)
+##
+## Solution: Laplace Transformation
+## E s X(s) = A X(s) + B U(s) + B M Y(s)                     [1]
+##
+##     Y(s) = C X(s) + D U(s) + D M Y(s)                     [2]
+##
+## solve [2] for Y(s)
+## Y(s) = [I - D M]^(-1) C X(s)  +  [I - D M]^(-1) D U(s)
+##
+## substitute Z = [I - D M]^(-1)
+## Y(s) = Z C X(s) + Z D U(s)                                [3]
+##
+## insert [3] in [1], solve for X(s)
+## X(s) = [s E - (A + B M Z C)]^(-1) (B + B M Z D) U(s)      [4]
+##
+## inserting [4] in [3] finally yields
+## Y(s) = Z C [s E - (A + B M Z C)]^(-1) (B + B M Z D) U(s)  +  Z D U(s)
+##        \ /    |   \_____ _____/       \_____ _____/          \ /
+##         H     K         F                   G                 J
+## @end group
+## @end example
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: September 2009
+## Version: 0.2
+
+function sys = __sys_connect__ (sys, m)
+
+  a = sys.a;
+  b = sys.b;
+  c = sys.c;
+  d = sys.d;
+
+  z = eye (rows (d)) - d*m;
+
+  if (rcond (z) < eps)  # check for singularity
+    error ("ss: sys_connect: (I - D*M) singular");
+  endif
+
+  z = inv (z);
+
+  sys.a = a + b*m*z*c;  # F
+  sys.b = b + b*m*z*d;  # G
+  sys.c = z*c;          # H
+  sys.d = z*d;          # J
+
+  ## sys.e remains constant: [] for ss models, e for dss models
+
+endfunction
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