__bodquist__.m

similer program for matlab

## Copyright (C) 1996, 1998, 2000, 2002, 2003, 2004, 2005, 2006, 2007
##               Auburn University.  All rights reserved.
##
## This file is part of Octave.
##
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## 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/>.

## Undocumented internal function.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{f}, @var{w}, @var{rsys}] =} __bodquist__ (@var{sys}, @var{w}, @var{out_idx}, @var{in_idx})
## Used internally by @command{bode}, @command{nyquist}; compute system frequency response.
##
## @strong{Inputs}
## @table @var
## @item sys
## input system structure
## @item w
## range of frequencies; empty if user wants default
## @item out_idx
## @itemx in_idx
## names or indices of output/input signal names; empty if user wants all
## @item rname
## name of routine that called __bodquist__ ("bode", "nyquist", or "nichols")
## @end table
## @strong{Outputs}
## @table @var
## @item w
## list of frequencies
## @item f
## frequency response of sys; @math{f(ii) = f(omega(ii))}
## @item rsys
## system with selected inputs and outputs
## @end table
##
## @code{bode}, @code{nichols}, and @code{nyquist} share the same 
## introduction, so the common parts are
## in __bodquist__.  It contains the part that finds the number of arguments,
## determines whether or not the system is @acronym{SISO}, and computes the frequency
## response.  Only the way the response is plotted is different between the
## these functions.
## @end deftypefn

function [f, w, rsys] = __bodquist__ (sys, w, outputs, inputs, rname)

  ## check number of input arguments given
  if (nargin != 5)
    print_usage ();
  endif

  ## check each argument to see if it's in the correct form
  if (! isstruct (sys))
    error ("sys must be a system data structure");
  endif

  ## let __freqresp__ determine w if it's not already given
  USEW = freqchkw (w);

  ## get initial dimensions (revised below if sysprune is called)
  [nn, nz, mm, pp] = sysdimensions (sys);

  ## check for an output vector and to see whether it`s correct
  if (! isempty (outputs))
    if (isempty (inputs))
      inputs = 1:mm;                    # use all inputs
      warning ("%s: outputs specified but not inputs", rname);
    elseif (is_signal_list (inputs) || ischar (inputs))
      inputs = sysidx (sys, "in", inputs);
    endif
    if (is_signal_list (outputs) || ischar (outputs))
      outputs = sysidx (sys, "out", outputs);
    endif
    sys = sysprune (sys, outputs, inputs);
    [nn, nz, mm, pp] = sysdimensions (sys);
  endif

  ## for speed in computation, convert local copy of
  ## SISO state space systems to zero-pole  form
  if (is_siso (sys) && strcmp (sysgettype (sys), "ss"))
    [zer, pol, k, tsam, inname, outname] = sys2zp (sys);
    sys = zp (zer, pol, k, tsam, inname, outname);
  endif

  ## get system frequency response
  [f, w] = __freqresp__ (sys, USEW, w);

  phase = arg(f)*180.0/pi;

  if (! USEW)
    ## smooth plots
    pcnt = 5;           # max number of refinement steps
    dphase = 5;         # desired max change in phase
    dmag = 0.2;         # desired max change in magnitude
    while (pcnt)
      pd = abs (diff (phase));                    # phase variation
      pdbig = find (pd > dphase);

      ## relative variation
      lp = length (f);
      lp1 = lp-1;

      fd = abs (diff (f));
      fm = max (abs ([f(1:lp1); f(2:lp)]));
      fdbig = find (fd > fm/10);

      bigpts = union (fdbig, pdbig);

      if (isempty (bigpts))
        pcnt = 0;
      else
        pcnt = pcnt - 1;
        wnew = [];
        crossover_points = find (phase(1:lp1).*phase(2:lp) < 0);
        pd(crossover_points) = abs (359.99+dphase - pd(crossover_points));
        np_pts = max (3, ceil(pd/dphase)+2);              # phase points
        nm_pts = max (3, ceil(log(fd./fm)/log(dmag))+2);  # magnitude points
        npts = min (5, max(np_pts, nm_pts));

        w1 = log10 (w(1:lp1));
        w2 = log10 (w(2:lp));
        for ii = bigpts
          if (npts(ii))
            wtmp = logspace (w1(ii), w2(ii), npts(ii));
            wseg(ii,1:(npts(ii)-2)) = wtmp(2:(npts(ii)-1));
          endif
        endfor
        wnew = vec(wseg)'; # make a row vector
        wnew = wnew(find (wnew != 0));
        wnew = sort (wnew);
        wnew = create_set (wnew);
        if (isempty (wnew))   # all small crossovers
          pcnt = 0;
        else
	  ## get new freq resp points, combine with old, and sort.
          [fnew, wnew] = __freqresp__ (sys, 1, wnew);
          w = [w, wnew];
          f = [f, fnew];
          [w, idx] = sort (w);
          f = f (idx);
          phase = arg(f)*180.0/pi;
        endif
      endif
    endwhile
  endif

  ## ensure unique frequency values
  [w, idx] = sort (w);
  f = f(idx);

  w_diff = diff (w);
  w_dup = find (w_diff == 0);
  w_idx = complement (w_dup, 1:length(w));
  w = w(w_idx);
  f = f(w_idx);

  ## set rsys to pruned system
  rsys = sys;

endfunction