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1 # Copyright (C) 1998 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 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, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
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18 |
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19 function [sys] = buildssic(Clst,Ulst,Olst,Ilst,s1,s2,s3,s4,s5,s6,s7,s8) |
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20 # |
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21 # [sys] = buildssic(Clst,Ulst,Olst,Ilst,s1,s2,s3,s4,s5,s6,s7,s8) |
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22 # |
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23 # Form an arbitrary complex (open or closed loop) system in |
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24 # state-space form from several systems. "buildssic" can |
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25 # easily (despite it's cryptic syntax) integrate transfer functions |
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26 # from a complex block diagram into a single system with one call. |
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27 # This function is especially useful for building open loop |
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28 # interconnections for H_infinity and H2 designs or for closing |
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29 # loops with these controllers. |
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30 # |
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31 # Although this function is general purpose, the use of "sysgroup" |
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32 # "sysmult", "sysconnect" and the like ist recommended for standard |
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33 # operations since they can handle mixed discrete and continuous |
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34 # systems and also the names of inputs, outputs, and states. |
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35 # |
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36 # The parameters consist of 4 lists which describe the connections |
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37 # outputs and inputs and up to 8 systems s1-s8. |
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38 # Format of the lists: |
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39 # |
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40 # Clst: connection list, describes the input signal of |
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41 # each system. The maximum number of rows of Clst is |
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42 # equal to the sum of all inputs of s1-s8. |
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43 # Example: |
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44 # [1 2 -1; 2 1 0] ==> new input 1 is old inpout 1 |
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45 # + output 2 - output 1, new input 2 is old input 2 |
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46 # + output 1. The order of rows is arbitrary. |
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47 # |
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48 # Ulst: if not empty the old inputs in vector Ulst will |
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49 # be appended to the outputs. You need this if you |
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50 # want to "pull out" the input of a system. Elements |
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51 # are input numbers of s1-s8. |
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52 # |
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53 # Olst: output list, specifiy the outputs of the resulting |
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54 # systems. Elements are output numbers of s1-s8. |
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55 # The numbers are alowed to be negative and may |
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56 # appear in any order. An empty matrix means |
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57 # all outputs. |
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58 # |
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59 # Ilst: input list, specifiy the inputs of the resulting |
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60 # systems. Elements are input numbers of s1-s8. |
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61 # The numbers are alowed to be negative and may |
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62 # appear in any order. An empty matrix means |
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63 # all inputs. |
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64 # |
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65 # Example: Very simple closed loop system. |
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66 # |
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67 # w e +-----+ u +-----+ |
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68 # --->o--*-->| K |--*-->| G |--*---> y |
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69 # ^ | +-----+ | +-----+ | |
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70 # - | | | | |
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71 # | | +----------------> u |
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72 # | | | |
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73 # | +-------------------------|---> e |
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74 # | | |
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75 # +----------------------------+ |
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76 # |
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77 # The closed loop system GW can be optained by |
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78 # |
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79 # GW = buildssic([1 2; 2 -1], [2], [1 2 3], [2], G, K); |
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80 # |
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81 # Clst: (1. row) connect input 1 (G) with output 2 (K). |
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82 # (2. row) connect input 2 (K) with neg. output 1 (G). |
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83 # Ulst: append input of (2) K to the number of outputs. |
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84 # Olst: Outputs are output of 1 (G), 2 (K) and appended |
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85 # output 3 (from Ulst). |
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86 # Ilst: the only input is 2 (K). |
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87 # |
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88 # Here is a real example: |
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89 # +----+ |
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90 # -------------------->| W1 |---> v1 |
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91 # z | +----+ |
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92 # ----|-------------+ || GW || => min. |
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93 # | | vz infty |
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94 # | +---+ v +----+ |
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95 # *--->| G |--->O--*-->| W2 |---> v2 |
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96 # | +---+ | +----+ |
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97 # | | |
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98 # | v |
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99 # u y |
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100 # |
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101 # The closed loop system GW from [z; u]' to [v1; v2; y]' can be |
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102 # obtained by (all SISO systems): |
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103 # |
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104 # GW = buildssic([1 4;2 4;3 1],[3],[2 3 5],[3 4],G,W1,W2,One); |
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105 # |
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106 # where "One" is a unity gain (auxillary) function with order 0. |
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107 # (e.g. One = ugain(1);) |
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108 # |
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109 |
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110 # Written by Kai Mueller April 1998 |
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111 |
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112 if((nargin < 5) || (nargin > 12)) |
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113 usage("[sys] = buildssic(Clst,Ulst,Olst,Ilst,s1,s2,s3,s4,s5,s6,s7,s8)"); |
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114 endif |
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115 if (nargin >= 5) |
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116 if (!is_struct(s1)) |
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117 error("---> s1 must be a structed system."); |
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118 endif |
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119 s1 = sysupdate(s1, "ss"); |
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120 [n, nz, m, p] = sysdimensions(s1); |
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121 if (!n && !nz) |
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122 error("---> pure static system must not be the first in list."); |
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123 endif |
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124 if (n && nz) |
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125 error("---> cannot handle mixed continuous and discrete systems."); |
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126 endif |
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127 D_SYS = (nz > 0); |
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128 [A,B,C,D,tsam] = sys2ss(s1); |
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129 nt = n + nz; |
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130 endif |
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131 for ii = 6:nargin |
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132 eval(["ss = s", num2str(ii-4), ";"]); |
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133 if (!is_struct(ss)) |
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134 error("---> Parameter must be a structed system."); |
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135 endif |
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136 ss = sysupdate(ss, "ss"); |
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137 [n1, nz1, m1, p1] = sysdimensions(ss); |
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138 if (n1 && nz1) |
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139 error("---> cannot handle mixed continuous and discrete systems."); |
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140 endif |
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141 if (D_SYS) |
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142 if (n1) |
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143 error("---> cannot handle mixed cont. and discr. systems."); |
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144 endif |
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145 if (tsam != sysgettsam(ss)) |
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146 error("---> sampling time of all systems must match."); |
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147 endif |
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148 endif |
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149 [as,bs,cs,ds] = sys2ss(ss); |
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150 nt1 = n1 + nz1; |
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151 if (!nt1) |
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152 # pure gain (pad B, C with zeros) |
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153 B = [B, zeros(nt,m1)]; |
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154 C = [C; zeros(p1,nt)]; |
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155 else |
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156 A = [A, zeros(nt,nt1); zeros(nt1,nt), as]; |
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157 B = [B, zeros(nt,m1); zeros(nt1,m), bs]; |
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158 C = [C, zeros(p,nt1); zeros(p1,nt), cs]; |
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159 endif |
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160 D = [D, zeros(p,m1); zeros(p1,m), ds]; |
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161 n = n + n1; |
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162 nz = nz + nz1; |
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163 nt = nt + nt1; |
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164 m = m + m1; |
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165 p = p + p1; |
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166 endfor |
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167 |
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168 # check maximum dimensions |
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169 [nx, mx] = size(Clst); |
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170 if (nx > m) |
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171 error("---> more rows in Clst than total number of inputs."); |
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172 endif |
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173 if (mx > p+1) |
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174 error("---> more cols in Clst than total number of outputs."); |
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175 endif |
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176 # empty vector Ulst is OK |
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177 lul = length(Ulst); |
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178 if (lul) |
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179 if (!is_vector(Ulst)) |
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180 error("---> Input u list Ulst must be a vector."); |
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181 endif |
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182 if (lul > m) |
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183 error("---> more values in Ulst than number of inputs."); |
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184 endif |
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185 endif |
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186 if (!length(Olst)) Olst = [1:(p+lul)]; endif |
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187 if (!length(Ilst)) Ilst = [1:m]; endif |
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188 if (!is_vector(Olst)) |
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189 error("---> Output list Olst must be a vector."); |
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190 endif |
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191 if (!is_vector(Ilst)) |
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192 error("---> Input list Ilst must be a vector."); |
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193 endif |
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194 |
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195 # build the feedback "K" from the interconnection data Clst |
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196 K = zeros(m, p); |
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197 inp_used = zeros(m,1); |
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198 for ii = 1:nx |
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199 xx = Clst(ii,:); |
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200 iu = xx(1); |
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201 if ((iu < 1) || (iu > m)) |
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202 error("---> Illegal value in first col of Clst."); |
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203 endif |
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204 if (inp_used(iu)) |
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205 error("---> Input specified more than once."); |
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206 endif |
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207 inp_used(iu) = 1; |
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208 for kk = 2:mx |
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209 it = xx(kk); |
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210 if (abs(it) > p) |
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211 error("---> Illegal row value in Clst."); |
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212 elseif (it) |
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213 K(iu,abs(it)) = sign(it); |
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214 endif |
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215 endfor |
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216 endfor |
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217 |
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218 # form the "closed loop", i.e replace u in |
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219 # . |
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220 # x = Ax + Bu |
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221 # ~ |
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222 # y = Cx + Du by u = K*y+u |
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223 # |
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224 # -1 |
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225 # R = (I-D*K) must exist. |
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226 # |
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227 R = eye(p) - D*K; |
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228 if (rank(R) < p) |
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229 error("---> singularity in algebraic loop."); |
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230 else |
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231 R = inv(R); |
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232 endif |
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233 A = A + B*K*R*C; |
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234 B = B + B*K*R*D; |
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235 C = R*C; |
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236 D = R*D; |
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237 |
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238 # append old inputs u to the outputs (if lul > 0) |
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239 kc = K*C; |
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240 kdi = eye(m) + K*D; |
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241 for ii = 1:lul |
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242 it = Ulst(ii); |
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243 if ((it < 1) || (it > m)) |
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244 error("---> Illegal value in Ulst."); |
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245 endif |
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246 C = [C; kc(it,:)]; |
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247 D = [D; kdi(it,:)]; |
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248 endfor |
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249 |
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250 # select and rearrange outputs |
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251 nn = length(A); |
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252 lol = length(Olst); |
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253 Cnew = zeros(lol,nn); |
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254 Dnew = zeros(lol,m); |
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255 for ii = 1:lol |
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256 iu = Olst(ii); |
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257 if (!iu || (abs(iu) > p+lul)) |
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258 error("---> Illegal value in Olst."); |
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259 endif |
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260 Cnew(ii,:) = sign(iu)*C(abs(iu),:); |
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261 Dnew(ii,:) = sign(iu)*D(abs(iu),:); |
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262 endfor |
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263 C = Cnew; |
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264 D = Dnew; |
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265 lil = length(Ilst); |
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266 Bnew = zeros(nn,lil); |
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267 Dnew = zeros(lol,lil); |
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268 for ii = 1:lil |
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269 iu = Ilst(ii); |
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270 if (!iu || (abs(iu) > m)) |
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271 error("---> Illegal value in Ilst."); |
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272 endif |
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273 Bnew(:,ii) = sign(iu)*B(:,abs(iu)); |
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274 Dnew(:,ii) = sign(iu)*D(:,abs(iu)); |
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275 endfor |
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276 |
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277 sys = ss2sys(A, Bnew, C, Dnew, tsam, n, nz); |
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278 |
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279 endfunction |
