place.m

similer program for matlab

## Copyright (C) 1997, 2000, 2002, 2003, 2004, 2005, 2007
##               Jose Daniel Munoz Frias
##
## This file is part of Octave.
##
## Octave 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.
##
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## 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 Octave; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{K} =} place (@var{sys}, @var{p})
## Computes the matrix @var{K} such that if the state
## is feedback with gain @var{K}, then the eigenvalues  of the closed loop
## system (i.e. @math{A-BK}) are those specified in the vector @var{p}.
##
## Version: Beta (May-1997): If you have any comments, please let me know.
## (see the file place.m for my address)
## @end deftypefn

## Author: Jose Daniel Munoz Frias

## Universidad Pontificia Comillas
## ICAIdea
## Alberto Aguilera, 23
## 28015 Madrid, Spain
##
## E-Mail: [e-mail]
##
## Phone: [phone]   Fax: [phone]
##
## Algorithm taken from "The Control Handbook", IEEE press pp. 209-212
##
## code adaped by A.S.Hodel ([e-mail]) for use in controls
## toolbox

function K = place (sys, P)

  if (nargin != 2)
    print_usage ();
  endif

  ## check arguments

  if (! isstruct (sys))
    error ("sys must be in system data structure format (see ss)");
  endif
  sys = sysupdate (sys, "ss");    # make sure it has state space form up to date
  if (! is_controllable (sys))
    error ("sys is not controllable");
  elseif (min (size (P)) != 1)
    error ("P must be a vector")
  else
    P = P(:); # make P a column vector
  endif
  ## system must be purely continuous or discrete
  is_digital (sys);
  [n, nz, m, p] = sysdimensions (sys);
  nx = n+nz;    # already checked that it's not a mixed system.
  if (m != 1)
    error ("sys has %d inputs; need only 1", m);
  endif

  ## takes the A and B matrix from the system representation
  [A, B] = sys2ss (sys);
  sp = length (P);
  if (nx == 0)
    error ("place: A matrix is empty (0x0)");
  elseif (nx != length (P))
    error ("A=(%dx%d), P has %d entries", nx, nx, length (P))
  endif

  ## arguments appear to be compatible; let's give it a try!
  ## The second step is the calculation of the characteristic polynomial ofA
  PC = poly (A);

  ## Third step: Calculate the transformation matrix T that transforms the state
  ## equation in the controllable canonical form.

  ## first we must calculate the controllability matrix M:
  M = B;
  AA = A;
  for n = 2:nx
    M(:,n) = AA*B;
    AA = AA*A;
  endfor

  ## second, construct the matrix W
  PCO = PC(nx:-1:1);
  PC1 = PCO;      # Matrix to shift and create W row by row

  for n = 1:nx
    W(n,:) = PC1;
    PC1 = [PCO(n+1:nx), zeros(1,n)];
  endfor

  T = M*W;

  ## finaly the matrix K is calculated
  PD = poly (P); # The desired characteristic polynomial
  PD = PD(nx+1:-1:2);
  PC = PC(nx+1:-1:2);

  K = (PD-PC)/T;

  ## Check if the eigenvalues of (A-BK) are the same specified in P
  Pcalc = eig (A-B*K);

  Pcalc = sortcom (Pcalc);
  P = sortcom (P);

  if (max ((abs(Pcalc)-abs(P))./abs(P) ) > 0.1)
    warning ("place: Pole placed at more than 10% relative error from specified");
  endif

endfunction