1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
|
## Copyright (C) 1998, 2000, 2003, 2004, 2005, 2006, 2007
## Auburn University. All rights reserved.
##
##
## This program 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.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} nichols (@var{sys}, @var{w}, @var{outputs}, @var{inputs})
## Produce Nichols plot of a system.
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure (must be either purely continuous or discrete;
## see @command{is_digital}).
## @item w
## Frequency values for evaluation.
## @itemize
## @item if sys is continuous, then nichols evaluates @math{G(jw)}.
## @item if sys is discrete, then nichols evaluates @math{G(exp(jwT))},
## where @var{T}=@var{sys}. @var{tsam} is the system sampling time.
## @item the default frequency range is selected as follows (These
## steps are @strong{not} performed if @var{w} is specified):
## @enumerate
## @item via routine @command{__bodquist__}, isolate all poles and zeros away from
## @var{w}=0 (@math{jw=0} or @math{exp(jwT)=1}) and select the frequency range
## based on the breakpoint locations of the frequencies.
## @item if sys is discrete time, the frequency range is limited to jwT in
## @iftex
## @tex
## $ [0, 2p\pi] $.
## @end tex
## @end iftex
## @ifinfo
## [0,2p*pi].
## @end ifinfo
## @item A ``smoothing'' routine is used to ensure that the plot phase does
## not change excessively from point to point and that singular points
## (e.g., crossovers from +/- 180) are accurately shown.
## @end enumerate
## @end itemize
## @item outputs
## @itemx inputs
## the names or indices of the output(s) and input(s) to be used in the
## frequency response; see @command{sysprune}.
## @end table
## @strong{Outputs}
## @table @var
## @item mag
## @itemx phase
## The magnitude and phase of the frequency response @math{G(jw)} or
## @math{G(exp(jwT))} at the selected frequency values.
## @item w
## The vector of frequency values used.
## @end table
## If no output arguments are given, @command{nichols} plots the results to the screen.
## Descriptive labels are automatically placed. See @command{xlabel},
## @command{ylabel}, and @command{title}.
##
## Note: if the requested plot is for an @acronym{MIMO} system, @var{mag} is set to
## @iftex
## @tex
## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $
## @end tex
## @end iftex
## @ifinfo
## ||G(jw)|| or ||G(exp(jwT))||
## @end ifinfo
## and phase information is not computed.
## @end deftypefn
function [mag2, phase2, w2] = nichols (sys, w, outputs, inputs)
## check number of input arguments given
if (nargin < 1 || nargin > 4)
print_usage ();
endif
if (nargin < 2)
w = [];
endif
if (nargin < 3)
outputs = [];
endif
if (nargin < 4)
inputs = [];
endif
[f, w, sys] = __bodquist__ (sys, w, outputs, inputs, "nichols");
[stname, inname, outname] = sysgetsignals (sys);
systsam = sysgettsam (sys);
## Get the magnitude and phase of f.
mag = abs (f);
phase = arg (f)*180.0/pi;
if (nargout < 1),
## Plot the information
if (max (mag) > 0)
md = 20 * log10 (mag);
plot (phase, md);
ylabel ("Gain in dB");
else
md = mag;
plot (phase, md);
ylabel ("Gain |Y/U|")
endif
grid ("on");
if (is_digital (sys))
tistr = "(exp(jwT)) ";
else
tistr = "(jw)";
endif
xlabel ("Phase (deg)");
if (is_siso (sys))
title (sprintf ("Nichols plot of |[Y/U]%s|, u=%s, y=%s", tistr,
sysgetsignals (sys, "in", 1, 1),
sysgetsignals (sys, "out", 1, 1)));
else
title ([ "||Y(", tistr, ")/U(", tistr, ")||"]);
printf ("MIMO plot from\n%s\nto\n%s\n", __outlist__ (inname, " "),
__outlist__ (outname, " "));
endif
axis (axis2dlim ([phase(:), md(:)]));
else
mag2 = mag;
phase2 = phase;
w2 = w;
endif
endfunction
|
