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1 ## Copyright (C) 1998, 2000, 2002, 2004, 2005, 2006, 2007 Kai P. Mueller |
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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 |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} buildssic (@var{clst}, @var{ulst}, @var{olst}, @var{ilst}, @var{s1}, @var{s2}, @var{s3}, @var{s4}, @var{s5}, @var{s6}, @var{s7}, @var{s8}) |
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21 ## |
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22 ## Form an arbitrary complex (open or closed loop) system in |
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23 ## state-space form from several systems. @command{buildssic} can |
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24 ## easily (despite its cryptic syntax) integrate transfer functions |
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25 ## from a complex block diagram into a single system with one call. |
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26 ## This function is especially useful for building open loop |
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27 ## interconnections for |
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28 ## @iftex |
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29 ## @tex |
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30 ## $ { \cal H }_\infty $ and $ { \cal H }_2 $ |
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31 ## @end tex |
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32 ## @end iftex |
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33 ## @ifinfo |
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34 ## H-infinity and H-2 |
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35 ## @end ifinfo |
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36 ## designs or for closing loops with these controllers. |
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37 ## |
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38 ## Although this function is general purpose, the use of @command{sysgroup} |
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39 ## @command{sysmult}, @command{sysconnect} and the like is recommended for |
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40 ## standard operations since they can handle mixed discrete and continuous |
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41 ## systems and also the names of inputs, outputs, and states. |
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42 ## |
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43 ## The parameters consist of 4 lists that describe the connections |
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44 ## outputs and inputs and up to 8 systems @var{s1}--@var{s8}. |
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45 ## Format of the lists: |
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46 ## @table @var |
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47 ## @item clst |
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48 ## connection list, describes the input signal of |
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49 ## each system. The maximum number of rows of Clst is |
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50 ## equal to the sum of all inputs of s1-s8. |
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51 ## |
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52 ## Example: |
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53 ## @code{[1 2 -1; 2 1 0]} means that: new input 1 is old input 1 |
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54 ## + output 2 - output 1, and new input 2 is old input 2 |
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55 ## + output 1. The order of rows is arbitrary. |
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56 ## |
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57 ## @item ulst |
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58 ## if not empty the old inputs in vector @var{ulst} will |
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59 ## be appended to the outputs. You need this if you |
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60 ## want to ``pull out'' the input of a system. Elements |
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61 ## are input numbers of @var{s1}--@var{s8}. |
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62 ## |
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63 ## @item olst |
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64 ## output list, specifies the outputs of the resulting |
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65 ## systems. Elements are output numbers of @var{s1}--@var{s8}. |
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66 ## The numbers are allowed to be negative and may |
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67 ## appear in any order. An empty matrix means |
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68 ## all outputs. |
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69 ## |
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70 ## @item ilst |
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71 ## input list, specifies the inputs of the resulting |
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72 ## systems. Elements are input numbers of @var{s1}--@var{s8}. |
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73 ## The numbers are allowed to be negative and may |
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74 ## appear in any order. An empty matrix means |
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75 ## all inputs. |
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76 ## @end table |
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77 ## |
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78 ## Example: Very simple closed loop system. |
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79 ## @example |
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80 ## @group |
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81 ## w e +-----+ u +-----+ |
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82 ## --->o--*-->| K |--*-->| G |--*---> y |
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83 ## ^ | +-----+ | +-----+ | |
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84 ## - | | | | |
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85 ## | | +----------------> u |
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86 ## | | | |
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87 ## | +-------------------------|---> e |
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88 ## | | |
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89 ## +----------------------------+ |
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90 ## @end group |
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91 ## @end example |
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92 ## |
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93 ## The closed loop system @var{GW} can be obtained by |
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94 ## @example |
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95 ## GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K); |
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96 ## @end example |
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97 ## @table @var |
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98 ## @item clst |
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99 ## 1st row: connect input 1 (@var{G}) with output 2 (@var{K}). |
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100 ## |
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101 ## 2nd row: connect input 2 (@var{K}) with negative output 1 (@var{G}). |
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102 ## @item ulst |
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103 ## Append input of 2 (@var{K}) to the number of outputs. |
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104 ## @item olst |
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105 ## Outputs are output of 1 (@var{G}), 2 (@var{K}) and |
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106 ## appended output 3 (from @var{ulst}). |
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107 ## @item ilst |
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108 ## The only input is 2 (@var{K}). |
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109 ## @end table |
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110 ## |
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111 ## Here is a real example: |
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112 ## @example |
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113 ## @group |
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114 ## +----+ |
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115 ## -------------------->| W1 |---> v1 |
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116 ## z | +----+ |
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117 ## ----|-------------+ |
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118 ## | | |
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119 ## | +---+ v +----+ |
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120 ## *--->| G |--->O--*-->| W2 |---> v2 |
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121 ## | +---+ | +----+ |
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122 ## | | |
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123 ## | v |
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124 ## u y |
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125 ## @end group |
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126 ## @end example |
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127 ## @iftex |
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128 ## @tex |
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129 ## $$ { \rm min } \Vert GW_{vz} \Vert _\infty $$ |
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130 ## @end tex |
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131 ## @end iftex |
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132 ## @ifinfo |
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133 ## @example |
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134 ## min || GW || |
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135 ## vz infty |
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136 ## @end example |
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137 ## @end ifinfo |
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138 ## |
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139 ## The closed loop system @var{GW} |
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140 ## @iftex |
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141 ## @tex |
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142 ## from $ [z, u]^T $ to $ [v_1, v_2, y]^T $ |
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143 ## @end tex |
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144 ## @end iftex |
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145 ## @ifinfo |
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146 ## from [z, u]' to [v1, v2, y]' |
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147 ## @end ifinfo |
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148 ## can be obtained by (all @acronym{SISO} systems): |
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149 ## @example |
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150 ## GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5], |
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151 ## [3, 4], G, W1, W2, One); |
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152 ## @end example |
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153 ## where ``One'' is a unity gain (auxiliary) function with order 0. |
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154 ## (e.g. @code{One = ugain(1);}) |
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155 ## @end deftypefn |
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156 |
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157 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de> |
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158 ## Created: April 1998 |
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159 |
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160 function sys = buildssic (Clst, Ulst, Olst, Ilst, s1, s2, s3, s4, s5, s6, s7, s8) |
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161 |
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162 if (nargin < 5 || nargin > 12) |
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163 print_usage (); |
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164 endif |
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165 if (nargin >= 5) |
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166 if (! isstruct (s1)) |
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167 error ("---> s1 must be a structed system."); |
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168 endif |
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169 s1 = sysupdate (s1, "ss"); |
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170 [n, nz, m, p] = sysdimensions (s1); |
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171 if (! n && ! nz) |
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172 error ("---> pure static system must not be the first in list."); |
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173 endif |
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174 if (n && nz) |
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175 error ("---> cannot handle mixed continuous and discrete systems."); |
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176 endif |
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177 D_SYS = (nz > 0); |
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178 [A, B, C, D, tsam] = sys2ss (s1); |
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179 nt = n + nz; |
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180 endif |
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181 for ii = 6:nargin |
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182 eval (["mysys = s", num2str(ii-4), ";"]); |
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183 if (! isstruct (mysys)) |
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184 error ("---> Parameter must be a structed system."); |
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185 endif |
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186 mysys = sysupdate (mysys, "ss"); |
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187 [n1, nz1, m1, p1] = sysdimensions (mysys); |
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188 if (n1 && nz1) |
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189 error ("---> cannot handle mixed continuous and discrete systems."); |
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190 endif |
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191 if (D_SYS) |
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192 if (n1) |
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193 error ("---> cannot handle mixed cont. and discr. systems."); |
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194 endif |
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195 if (tsam != sysgettsam (mysys)) |
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196 error ("---> sampling time of all systems must match."); |
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197 endif |
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198 endif |
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199 [as, bs, cs, ds] = sys2ss (mysys); |
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200 nt1 = n1 + nz1; |
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201 if (! nt1) |
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202 ## pure gain (pad B, C with zeros) |
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203 B = [B, zeros(nt,m1)]; |
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204 C = [C; zeros(p1,nt)]; |
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205 else |
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206 A = [A, zeros(nt,nt1); zeros(nt1,nt), as]; |
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207 B = [B, zeros(nt,m1); zeros(nt1,m), bs]; |
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208 C = [C, zeros(p,nt1); zeros(p1,nt), cs]; |
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209 endif |
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210 D = [D, zeros(p,m1); zeros(p1,m), ds]; |
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211 n = n + n1; |
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212 nz = nz + nz1; |
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213 nt = nt + nt1; |
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214 m = m + m1; |
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215 p = p + p1; |
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216 endfor |
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217 |
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218 ## check maximum dimensions |
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219 [nx, mx] = size (Clst); |
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220 if (nx > m) |
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221 error ("---> more rows in Clst than total number of inputs."); |
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222 endif |
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223 if (mx > p+1) |
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224 error ("---> more cols in Clst than total number of outputs."); |
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225 endif |
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226 ## empty vector Ulst is OK |
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227 lul = length (Ulst); |
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228 if (lul) |
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229 if (! isvector (Ulst)) |
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230 error ("---> Input u list Ulst must be a vector."); |
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231 endif |
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232 if (lul > m) |
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233 error ("---> more values in Ulst than number of inputs."); |
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234 endif |
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235 endif |
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236 if (! length (Olst)) |
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237 Olst = 1:(p+lul); |
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238 endif |
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239 if (! length (Ilst)) |
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240 Ilst = 1:m; |
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241 endif |
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242 if (! isvector(Olst)) |
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243 error ("---> Output list Olst must be a vector."); |
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244 endif |
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245 if (! isvector (Ilst)) |
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246 error ("---> Input list Ilst must be a vector."); |
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247 endif |
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248 |
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249 ## build the feedback "K" from the interconnection data Clst |
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250 K = zeros (m, p); |
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251 inp_used = zeros (m, 1); |
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252 for ii = 1:nx |
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253 xx = Clst(ii,:); |
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254 iu = xx(1); |
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255 if (iu < 1 || iu > m) |
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256 error ("---> invalid value in first col of Clst."); |
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257 endif |
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258 if (inp_used(iu)) |
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259 error ("---> Input specified more than once."); |
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260 endif |
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261 inp_used(iu) = 1; |
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262 for kk = 2:mx |
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263 it = xx(kk); |
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264 if (abs (it) > p) |
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265 error ("---> invalid row value in Clst."); |
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266 elseif (it) |
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267 K(iu,abs(it)) = sign (it); |
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268 endif |
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269 endfor |
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270 endfor |
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271 |
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272 ## form the "closed loop", i.e replace u in |
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273 ## . |
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274 ## x = Ax + Bu |
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275 ## ~ |
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276 ## y = Cx + Du by u = K*y+u |
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277 ## |
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278 ## -1 |
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279 ## R = (I-D*K) must exist. |
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280 |
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281 R = eye (p) - D*K; |
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282 if (rank (R) < p) |
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283 error ("---> singularity in algebraic loop."); |
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284 else |
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285 R = inv (R); |
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286 endif |
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287 A = A + B*K*R*C; |
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288 B = B + B*K*R*D; |
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289 C = R*C; |
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290 D = R*D; |
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291 |
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292 ## append old inputs u to the outputs (if lul > 0) |
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293 kc = K*C; |
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294 kdi = eye (m) + K*D; |
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295 for ii = 1:lul |
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296 it = Ulst(ii); |
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297 if (it < 1 || it > m) |
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298 error ("---> invalid value in Ulst."); |
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299 endif |
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300 C = [C; kc(it,:)]; |
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301 D = [D; kdi(it,:)]; |
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302 endfor |
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303 |
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304 ## select and rearrange outputs |
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305 nn = length (A); |
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306 lol = length (Olst); |
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307 Cnew = zeros (lol, nn); |
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308 Dnew = zeros (lol, m); |
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309 for ii = 1:lol |
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310 iu = Olst(ii); |
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311 if (! iu || abs(iu) > p+lul) |
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312 error ("---> invalid value in Olst."); |
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313 endif |
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314 Cnew(ii,:) = sign(iu)*C(abs(iu),:); |
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315 Dnew(ii,:) = sign(iu)*D(abs(iu),:); |
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316 endfor |
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317 C = Cnew; |
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318 D = Dnew; |
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319 lil = length (Ilst); |
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320 Bnew = zeros (nn, lil); |
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321 Dnew = zeros (lol, lil); |
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322 for ii = 1:lil |
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323 iu = Ilst(ii); |
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324 if (! iu || abs(iu) > m) |
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325 error ("---> invalid value in Ilst."); |
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326 endif |
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327 Bnew(:,ii) = sign (iu) * B(:,abs(iu)); |
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328 Dnew(:,ii) = sign (iu) * D(:,abs(iu)); |
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329 endfor |
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330 |
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331 sys = ss (A, Bnew, C, Dnew, tsam, n, nz); |
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332 |
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333 endfunction |
