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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} {} bode (@var{sys})
## @deftypefnx {Function File} {} bode (@var{sys1}, @var{sys2}, @dots{}, @var{sysN})
## @deftypefnx {Function File} {} bode (@var{sys1}, @var{sys2}, @dots{}, @var{sysN}, @var{w})
## @deftypefnx {Function File} {} bode (@var{sys1}, @var{'style1'}, @dots{}, @var{sysN}, @var{'styleN'})
## @deftypefnx {Function File} {[@var{mag}, @var{pha}, @var{w}] =} bode (@var{sys})
## @deftypefnx {Function File} {[@var{mag}, @var{pha}, @var{w}] =} bode (@var{sys}, @var{w})
## Bode diagram of frequency response. If no output arguments are given,
## the response is printed on the screen. In the latter case, the chidlren
## of the figure handle are the handles for (1) the phase plot, (2) the
## legend, and (3) the magnitude plot. The magnitude plot is the active
## handle after the bode plot is finished.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} system. Must be a single-input and single-output (SISO) system.
## @item w
## Optional vector of frequency values. If @var{w} is not specified,
## it is calculated by the zeros and poles of the system.
## Alternatively, the cell @code{@{wmin, wmax@}} specifies a frequency range,
## where @var{wmin} and @var{wmax} denote minimum and maximum frequencies
## in rad/s.
## @item 'style'
## Line style and color, e.g. 'r' for a solid red line or '-.k' for a dash-dotted
## black line. See @command{help plot} for details.
## @end table
##
## @strong{Outputs}
## @table @var
## @item mag
## Vector of magnitude. Has length of frequency vector @var{w}.
## @item pha
## Vector of phase. Has length of frequency vector @var{w}.
## @item w
## Vector of frequency values used.
## @end table
##
## @seealso{nichols, nyquist, sigma}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: November 2009
## Version: 1.0
function [mag_r, pha_r, w_r] = bode (varargin)
if (nargin == 0)
print_usage ();
endif
[H, w, sty, sys_idx, H_auto, w_auto] = __frequency_response__ ("bode", varargin, nargout);
H = cellfun (@reshape, H, {[]}, {1}, "uniformoutput", false);
H_auto = cellfun (@reshape, H_auto, {[]}, {1}, "uniformoutput", false);
mag = cellfun (@abs, H, "uniformoutput", false);
pha = cellfun (@(H) unwrap (arg (H)) * 180 / pi, H, "uniformoutput", false);
pha_auto = cellfun (@(H_auto) unwrap (arg (H_auto)) * 180 / pi, H_auto, "uniformoutput", false);
numsys = length (sys_idx);
## check for poles and zeroes at the origin for each of the numsys systems
## and compare this asymptotic value to initial phase for the full auto
## w-range, which is supposed to start at sufficiently small values fo w
initial_phase_auto = cellfun(@(x) x(1), pha_auto);
initial_phase = cellfun(@(x) x(1), pha);
all_poles = cell(1,numsys);
all_zeros = cell(1,numsys);
for h = 1:numsys
sys1 = varargin{sys_idx(h)};
[num,den] = tfdata (sys1,'v');
all_poles{h} = roots (den);
all_zeros{h} = roots (num);
n_poles_at_origin = sum (all_poles{h} == 0);
n_zeros_at_origin = sum (all_zeros{h} == 0);
asymptotic_low_freq_phase = (n_zeros_at_origin - n_poles_at_origin)*90;
pha_auto(h)={cell2mat(pha_auto(h)) + round((asymptotic_low_freq_phase - initial_phase_auto(h))/90)*90};
pha(h)={cell2mat(pha(h)) + round((asymptotic_low_freq_phase - initial_phase(h))/90)*90};
endfor
## check if possibly given w-range is at higher frequencies and provide
## missing "history" for the the phase
initial_phase = cellfun(@(x) x(1), pha);
for h = 1:numsys
if (length (w{h}) != length (w_auto{h})) || any (w{h} - w_auto{h})
## the w-range to use is not the auto (full) range, thus, make sure
## the inforamtion on the phase form beginning at small frequencies
## is used to determine the correct pahse at the beginning of the desired
## w range
if w{h}(1) > w_auto{h}(1)
## w range starts at higher frequencies; get the nearest w in the auto
## range and add +/-360 degrees minimizing the differenze betwenn the
## phases
pha_idx = length (find (w_auto{h} < w{h}(1)));
pha_cmp = pha_auto{h}(pha_idx);
pha(h)={cell2mat(pha(h)) + round((pha_cmp - initial_phase(h))/90)*90};
endif
else
## w range is identical to auto range, just use the phase for the
## auto range
pha(h) = pha_auto(h);
endif
endfor
## now fix the phase in case of a conjugate complex pair of poles on the
## imag. axis
tol = sqrt (eps);
max_idx = length (pha{1});
w0_poles = cellfun (@(p) imag (p(abs(real(p))<tol & imag(p)>0)), all_poles,...
'uniformoutput', false);
w0_zeros = cellfun (@(p) imag (p(abs(real(p))<tol & imag(p)>0)), all_zeros,...
'uniformoutput', false);
dpha = cellfun (@diff, pha, 'uniformoutput', false);
w0_inc = cellfun (@(dp) find (dp > 90), dpha, 'uniformoutput', false);
w0_dec = cellfun (@(dp) find (dp < -90), dpha, 'uniformoutput', false);
for h = 1:numsys
for j = 1:length(w0_inc{h})
if (w0_inc{h}(j)-2 > 0 && w0_inc{h}(j)+2 <= max_idx)
lb = w{h}(w0_inc{h}(j)-2) < w0_poles{h};
ub = w{h}(w0_inc{h}(j)+2) > w0_poles{h};
if sum (lb & ub) == 1
## phase is increasing although poles
pha{h}(w0_inc{h}(j)+1:end) -= 360;
endif
endif
endfor
for j = 1:length(w0_dec{h})
if (w0_dec{h}(j)-2 > 0 && w0_dec{h}(j)+2 <= max_idx)
lb = w{h}(w0_dec{h}(j)-2) < w0_zeros{h};
ub = w{h}(w0_dec{h}(j)+2) > w0_zeros{h};
if sum (lb & ub) == 1
## phase is decreasing although zeros
pha{h}(w0_dec{h}(j)+1:end) += 360;
endif
endif
endfor
endfor
## do the plotting
if (! nargout)
## get system names and create the legend
leg = cell (1, numsys);
for k = 1:numsys
leg{k} = inputname (sys_idx(k));
if (isempty (leg{k}))
leg{k} = sprintf("Sys %d", k);
endif
endfor
## plot
mag_db = cellfun (@mag2db, mag, "uniformoutput", false);
mag_args = horzcat (cellfun (@horzcat, w, mag_db, sty, "uniformoutput", false){:});
pha_args = horzcat (cellfun (@horzcat, w, pha, sty, "uniformoutput", false){:});
hax1 = subplot (2, 1, 1);
semilogx (mag_args{:})
axis ("tight")
ylim (__axis_margin__ (ylim))
grid ("on")
title ("Bode Diagram")
ylabel ("Magnitude [dB]")
legend (leg)
subplot (2, 1, 2)
semilogx (pha_args{:})
axis ("tight")
ylim (__axis_margin__ (ylim))
grid ("on")
xlabel ("Frequency [rad/s]")
ylabel ("Phase [deg]")
## Make top axes current for ML compatibility
set (gcf, "currentaxes", hax1);
else
## no plotting, assign values to the output parameters
mag_r = mag{1};
pha_r = pha{1};
w_r = w{1};
endif
endfunction
%!demo
%! G = tf ([10 1],[1 0.1 1 0]);
%! bode(G);
%!test
%! s = tf('s');
%! K = 1;
%! T = 2;
%! G = K/(1+T*s);
%! [mag phas w] = bode(G);
%! mag_dB = 20*log10(mag);
%! index = find(mag_dB < -3,1);
%! w_cutoff = w(index);
%! assert (1/T, w_cutoff, eps);
%!test
%! G = tf ([100 0 1],conv([1 0.00001 1],[1/100 0 1]));
%! [mag pha w] = bode(G);
%! pha_final = pha(end);
%! assert (-180, pha_final, 1e-4);
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