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1 ## Copyright (C) 1996, 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, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} ss2sys (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist}) |
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21 ## Create system structure from state-space data. May be continous, |
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22 ## discrete, or mixed (sampeled-data) |
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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 a |
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27 ## @itemx b |
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28 ## @itemx c |
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29 ## @itemx d |
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30 ## usual state space matrices. |
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31 ## |
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32 ## default: @var{d} = zero matrix |
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33 ## |
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34 ## @item tsam |
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35 ## sampling rate. Default: @math{tsam = 0} (continuous system) |
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36 ## |
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37 ## @item n |
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38 ## @itemx nz |
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39 ## number of continuous, discrete states in the system |
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40 ## |
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41 ## If @var{tsam} is 0, @math{n = @code{rows}(@var{a})}, @math{nz = 0}. |
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42 ## |
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43 ## If @var{tsam} is greater than zero, @math{n = 0}, |
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44 ## @math{nz = @code{rows}(@var{a})} |
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45 ## |
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46 ## see below for system partitioning |
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47 ## |
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48 ## @item stname |
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49 ## list of strings of state signal names |
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50 ## |
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51 ## default (@var{stname}=[] on input): @code{x_n} for continuous states, |
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52 ## @code{xd_n} for discrete states |
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53 ## |
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54 ## @item inname |
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55 ## list of strings of input signal names |
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56 ## |
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57 ## default (@var{inname} = [] on input): @code{u_n} |
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58 ## |
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59 ## @item outname |
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60 ## list of strings of input signal names |
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61 ## |
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62 ## default (@var{outname} = [] on input): @code{y_n} |
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63 ## |
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64 ## @item outlist |
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65 ## |
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66 ## list of indices of outputs y that are sampled |
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67 ## |
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68 ## If @var{tsam} is 0, @math{outlist = []}. |
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69 ## |
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70 ## If @var{tsam} is greater than 0, @math{outlist = 1:@code{rows}(@var{c})}. |
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71 ## @end table |
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72 ## |
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73 ## Unlike states, discrete/continous outputs may appear in any order. |
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74 ## |
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75 ## @strong{Note} @code{sys2ss} returns a vector @var{yd} where |
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76 ## @var{yd}(@var{outlist}) = 1; all other entries of @var{yd} are 0. |
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77 ## |
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78 ## @strong{Outputs} |
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79 ## @var{outsys} = system data structure |
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80 ## |
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81 ## @strong{System partitioning} |
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82 ## |
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83 ## Suppose for simplicity that outlist specified |
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84 ## that the first several outputs were continuous and the remaining outputs |
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85 ## were discrete. Then the system is partitioned as |
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86 ## @example |
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87 ## @group |
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88 ## x = [ xc ] (n x 1) |
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89 ## [ xd ] (nz x 1 discrete states) |
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90 ## a = [ acc acd ] b = [ bc ] |
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91 ## [ adc add ] [ bd ] |
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92 ## c = [ ccc ccd ] d = [ dc ] |
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93 ## [ cdc cdd ] [ dd ] |
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94 ## |
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95 ## (cdc = c(outlist,1:n), etc.) |
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96 ## @end group |
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97 ## @end example |
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98 ## with dynamic equations: |
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99 ## @ifinfo |
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100 ## @math{d/dt xc(t) = acc*xc(t) + acd*xd(k*tsam) + bc*u(t)} |
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101 ## |
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102 ## @math{xd((k+1)*tsam) = adc*xc(k*tsam) + add*xd(k*tsam) + bd*u(k*tsam)} |
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103 ## |
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104 ## @math{yc(t) = ccc*xc(t) + ccd*xd(k*tsam) + dc*u(t)} |
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105 ## |
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106 ## @math{yd(k*tsam) = cdc*xc(k*tsam) + cdd*xd(k*tsam) + dd*u(k*tsam)} |
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107 ## @end ifinfo |
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108 ## @iftex |
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109 ## @tex |
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110 ## $$\eqalign{ |
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111 ## {d \over dt} x_c(t) |
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112 ## & = a_{cc} x_c(t) + a_{cd} x_d(k*t_{sam}) + bc*u(t) \cr |
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113 ## x_d((k+1)*t_{sam}) |
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114 ## & = a_{dc} x_c(k t_{sam}) + a_{dd} x_d(k t_{sam}) + b_d u(k t_{sam}) \cr |
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115 ## y_c(t) |
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116 ## & = c_{cc} x_c(t) + c_{cd} x_d(k t_{sam}) + d_c u(t) \cr |
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117 ## y_d(k t_{sam}) |
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118 ## & = c_{dc} x_c(k t_{sam}) + c_{dd} x_d(k t_{sam}) + d_d u(k t_{sam}) |
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119 ## }$$ |
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120 ## @end tex |
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121 ## @end iftex |
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122 ## |
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123 ## @strong{Signal partitions} |
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124 ## @example |
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125 ## @group |
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126 ## | continuous | discrete | |
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127 ## ---------------------------------------------------- |
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128 ## states | stname(1:n,:) | stname((n+1):(n+nz),:) | |
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129 ## ---------------------------------------------------- |
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130 ## outputs | outname(cout,:) | outname(outlist,:) | |
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131 ## ---------------------------------------------------- |
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132 ## @end group |
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133 ## @end example |
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134 ## where @math{cout} is the list of in 1:@code{rows}(@var{p}) |
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135 ## that are not contained in outlist. (Discrete/continuous outputs |
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136 ## may be entered in any order desired by the user.) |
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137 ## |
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138 ## @strong{Example} |
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139 ## @example |
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140 ## octave:1> a = [1 2 3; 4 5 6; 7 8 10]; |
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141 ## octave:2> b = [0 0 ; 0 1 ; 1 0]; |
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142 ## octave:3> c = eye(3); |
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143 ## octave:4> sys = ss2sys(a,b,c,[],0,3,0,list("volts","amps","joules")); |
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144 ## octave:5> sysout(sys); |
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145 ## Input(s) |
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146 ## 1: u_1 |
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147 ## 2: u_2 |
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148 ## |
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149 ## Output(s): |
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150 ## 1: y_1 |
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151 ## 2: y_2 |
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152 ## 3: y_3 |
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153 ## |
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154 ## state-space form: |
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155 ## 3 continuous states, 0 discrete states |
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156 ## State(s): |
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157 ## 1: volts |
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158 ## 2: amps |
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159 ## 3: joules |
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160 ## |
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161 ## A matrix: 3 x 3 |
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162 ## 1 2 3 |
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163 ## 4 5 6 |
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164 ## 7 8 10 |
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165 ## B matrix: 3 x 2 |
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166 ## 0 0 |
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167 ## 0 1 |
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168 ## 1 0 |
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169 ## C matrix: 3 x 3 |
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170 ## 1 0 0 |
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171 ## 0 1 0 |
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172 ## 0 0 1 |
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173 ## D matrix: 3 x 3 |
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174 ## 0 0 |
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175 ## 0 0 |
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176 ## 0 0 |
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177 ## @end example |
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178 ## Notice that the @math{D} matrix is constructed by default to the |
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179 ## correct dimensions. Default input and output signals names were assigned |
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180 ## since none were given. |
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181 ## @end deftypefn |
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182 |
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183 ## Author: John Ingram <ingraje@eng.auburn.edu> |
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184 ## Created: July 20, 1996 |
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185 |
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186 function retsys = ss2sys (a, b, c, d, tsam, n, nz, stname, inname, outname, outlist) |
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187 |
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188 ## Test for correct number of inputs |
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189 if ((nargin < 3) | (nargin > 11)) |
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190 usage("retsys = ss2sys (a,b,c{,d,tsam,n,nz,stname,inname,outname,outlist})"); |
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191 endif |
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192 |
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193 ## verify A, B, C, D arguments |
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194 ## If D is not specified, set it to a zero matrix of appriate dimension. |
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195 if (nargin == 3) d = zeros(rows(c) , columns(b)); |
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196 elseif (isempty(d)) d = zeros(rows(c) , columns(b)); endif |
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197 |
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198 ## Check the dimensions |
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199 [na,m,p] = abcddim(a,b,c,d); |
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200 |
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201 ## If dimensions are wrong, exit function |
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202 if (m == -1) |
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203 error("a(%dx%d), b(%dx%d), c(%dx%d), d(%dx%d); incompatible", ... |
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204 rows(a), columns(a), rows(b), columns(b), rows(c), columns(c), ... |
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205 rows(d), columns(d)); |
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206 endif |
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207 |
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208 ## check for tsam input |
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209 if(nargin < 5) tsam = 0; |
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210 elseif( !( is_sample(tsam) | (tsam == 0) ) ) |
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211 error("tsam must be a nonnegative real scalar"); |
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212 endif |
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213 |
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214 ## check for continuous states |
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215 if( (nargin < 6) & (tsam == 0) ) n = na; |
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216 elseif(nargin < 6) n = 0; |
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217 elseif((!ismatrix(n)) | isstr(n)) |
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218 error("Parameter n is not a numerical value."); |
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219 elseif( (!isscalar(n)) | (n < 0 ) | (n != round(n)) ) |
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220 if(isscalar(n)) error("invalid value of n=%d,%e",n,n); |
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221 else error("invalid value of n=(%dx%d)", ... |
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222 rows(n), columns(n)); endif |
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223 endif |
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224 |
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225 ## check for num discrete states |
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226 if( (nargin < 7) & (tsam == 0)) nz = 0; |
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227 elseif(nargin < 7) nz = na - n; |
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228 elseif((!ismatrix(nz)) | isstr(nz)) |
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229 error("Parameter nz is not a numerical value."); |
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230 elseif( (!isscalar(nz)) | (nz < 0 ) | (nz != round(nz)) ) |
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231 if(isscalar(nz)) |
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232 error(["invalid value of nz=",num2str(nz)]); |
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233 else |
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234 error(["invalid value of nz=(",num2str(rows(nz)),"x", ... |
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235 num2str(columns(nz)),")"]); |
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236 endif |
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237 endif |
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238 |
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239 ## check for total number of states |
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240 if( (n + nz) != na ) |
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241 error(["invalid: a is ",num2str(na),"x",num2str(na),", n=", ... |
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242 num2str(n),", nz=",num2str(nz)]); |
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243 endif |
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244 |
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245 ## construct system with default names |
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246 retsys.a = a; |
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247 retsys.b = b; |
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248 retsys.c = c; |
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249 retsys.d = d; |
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250 |
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251 retsys.n = n; |
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252 retsys.nz = nz; |
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253 retsys.tsam = tsam; |
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254 retsys.yd = zeros(1,p); # default value entered below |
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255 |
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256 ## Set the system vector: active = 2(ss), updated = [0 0 1]; |
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257 retsys.sys = [2, 0, 0, 1]; |
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258 |
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259 retsys.stname = __sysdefstname__ (n, nz); |
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260 retsys.inname = __sysdefioname__ (m, "u"); |
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261 retsys.outname = __sysdefioname__ (p, "y"); |
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262 |
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263 ## check for state names |
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264 if(nargin >= 8) |
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265 if(!isempty(stname)) retsys = syssetsignals(retsys,"st",stname); endif |
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266 endif |
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267 |
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268 ## check for input names |
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269 if(nargin >= 9) |
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270 if(!isempty(inname)) retsys = syssetsignals(retsys,"in",inname); endif |
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271 endif |
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272 |
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273 ## check for output names |
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274 if(nargin >= 10) |
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275 if(!isempty(outname)) retsys = syssetsignals(retsys,"out",outname); endif |
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276 endif |
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277 |
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278 ## set up yd |
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279 if(nargin < 11) |
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280 retsys = syssetsignals(retsys,"yd",ones(1,p)*(tsam > 0)); |
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281 else |
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282 if(!isempty(outlist)) |
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283 retsys = syssetsignals(retsys,"yd",ones(size(outlist)),outlist); |
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284 endif |
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285 endif |
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286 |
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287 endfunction |
