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1 ## Copyright (C) 1998 Auburn University. All rights reserved. |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by the |
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7 ## Free Software Foundation; either version 2, or (at your option) any |
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8 ## later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 ## for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301 USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} nichols (@var{sys}, @var{w}, @var{outputs}, @var{inputs}) |
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22 ## Produce Nichols plot of a system. |
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23 ## |
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24 ## @strong{Inputs} |
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25 ## @table @var |
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26 ## @item sys |
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27 ## System data structure (must be either purely continuous or discrete; |
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28 ## see @command{is_digital}). |
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29 ## @item w |
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30 ## Frequency values for evaluation. |
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31 ## @itemize |
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32 ## @item if sys is continuous, then nichols evaluates @math{G(jw)}. |
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33 ## @item if sys is discrete, then nichols evaluates @math{G(exp(jwT))}, |
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34 ## where @var{T}=@var{sys}. @var{tsam} is the system sampling time. |
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35 ## @item the default frequency range is selected as follows (These |
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36 ## steps are @strong{not} performed if @var{w} is specified): |
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37 ## @enumerate |
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38 ## @item via routine @command{__bodquist__}, isolate all poles and zeros away from |
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39 ## @var{w}=0 (@math{jw=0} or @math{exp(jwT)=1}) and select the frequency range |
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40 ## based on the breakpoint locations of the frequencies. |
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41 ## @item if sys is discrete time, the frequency range is limited to jwT in |
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42 ## @iftex |
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43 ## @tex |
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44 ## $ [0, 2p\pi] $. |
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45 ## @end tex |
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46 ## @end iftex |
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47 ## @ifinfo |
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48 ## [0,2p*pi]. |
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49 ## @end ifinfo |
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50 ## @item A ``smoothing'' routine is used to ensure that the plot phase does |
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51 ## not change excessively from point to point and that singular points |
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52 ## (e.g., crossovers from +/- 180) are accurately shown. |
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53 ## @end enumerate |
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54 ## @end itemize |
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55 ## @item outputs |
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56 ## @itemx inputs |
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57 ## the names or indices of the output(s) and input(s) to be used in the |
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58 ## frequency response; see @command{sysprune}. |
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59 ## @end table |
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60 ## @strong{Outputs} |
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61 ## @table @var |
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62 ## @item mag |
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63 ## @itemx phase |
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64 ## The magnitude and phase of the frequency response @math{G(jw)} or |
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65 ## @math{G(exp(jwT))} at the selected frequency values. |
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66 ## @item w |
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67 ## The vector of frequency values used. |
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68 ## @end table |
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69 ## If no output arguments are given, @command{nichols} plots the results to the screen. |
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70 ## Descriptive labels are automatically placed. See @command{xlabel}, |
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71 ## @command{ylabel}, and @command{title}. |
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72 ## |
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73 ## Note: if the requested plot is for an @acronym{MIMO} system, @var{mag} is set to |
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74 ## @iftex |
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75 ## @tex |
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76 ## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $ |
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77 ## @end tex |
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78 ## @end iftex |
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79 ## @ifinfo |
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80 ## ||G(jw)|| or ||G(exp(jwT))|| |
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81 ## @end ifinfo |
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82 ## and phase information is not computed. |
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83 ## @end deftypefn |
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84 |
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85 function [mag, phase, w] = nichols (sys, w, outputs, inputs) |
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86 |
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87 ## check number of input arguments given |
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88 if (nargin < 1 || nargin > 4) |
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89 print_usage (); |
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90 endif |
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91 if (nargin < 2) |
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92 w = []; |
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93 endif |
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94 if (nargin < 3) |
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95 outputs = []; |
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96 endif |
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97 if (nargin < 4) |
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98 inputs = []; |
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99 endif |
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100 |
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101 [f, w, sys] = __bodquist__ (sys, w, outputs, inputs, "nichols"); |
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102 |
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103 [stname,inname,outname] = sysgetsignals (sys); |
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104 systsam = sysgettsam (sys); |
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105 |
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106 ## Get the magnitude and phase of f. |
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107 mag = abs (f); |
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108 phase = arg (f)*180.0/pi; |
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109 |
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110 if (nargout < 1), |
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111 ## Plot the information |
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112 |
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113 if (max (mag) > 0) |
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114 plot (phase, 20 * log10 (mag)); |
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115 ylabel ("Gain in dB"); |
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116 else |
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117 plot (phase, mag); |
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118 ylabel ("Gain |Y/U|") |
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119 endif |
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120 |
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121 grid ("on"); |
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122 |
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123 if (is_digital (sys)) |
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124 tistr = "(exp(jwT)) "; |
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125 else |
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126 tistr = "(jw)"; |
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127 endif |
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128 |
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129 xlabel ("Phase (deg)"); |
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130 |
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131 if (is_siso (sys)) |
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132 title (sprintf ("Nichols plot of |[Y/U]%s|, u=%s, y=%s", tistr, |
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133 sysgetsignals (sys, "in", 1, 1), |
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134 sysgetsignals (sys, "out", 1, 1)); |
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135 else |
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136 title ([ "||Y(", tistr, ")/U(", tistr, ")||"]); |
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137 printf ("MIMO plot from\n%s\nto\n%s\n", __outlist__ (inname, " "), |
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138 __outlist__ (outname, " ")); |
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139 endif |
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140 |
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141 axis (axis2dlim ([phase(:), md(:)])); |
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142 |
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143 mag = phase = w = []; |
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144 endif |
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145 |
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146 endfunction |
