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1 ## Copyright (C) 1993, 1994, 1995 John W. Eaton |
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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} {} c2d (@var{sys}, @var{opt}, @var{T}) |
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21 ## @deftypefnx {Function File} {} c2d (@var{sys}, @var{T}) |
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22 ## |
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23 ## @strong{Inputs} |
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24 ## @table @var |
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25 ## @item sys |
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26 ## system data structure (may have both continuous time and discrete |
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27 ## time subsystems) |
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28 ## @item opt |
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29 ## string argument; conversion option (optional argument; |
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30 ## may be omitted as shown above) |
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31 ## @table @code |
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32 ## @item "ex" |
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33 ## use the matrix exponential (default) |
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34 ## @item "bi" |
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35 ## use the bilinear transformation |
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36 ## @end table |
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37 ## @example |
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38 ## 2(z-1) |
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39 ## s = ----- |
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40 ## T(z+1) |
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41 ## @end example |
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42 ## FIXME: This option exits with an error if @var{sys} is not purely |
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43 ## continuous. (The @code{ex} option can handle mixed systems.) |
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44 ## @item @var{T} |
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45 ## sampling time; required if sys is purely continuous. |
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46 ## |
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47 ## @strong{Note} If the 2nd argument is not a string, @code{c2d} assumes that |
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48 ## the 2nd argument is @var{T} and performs appropriate argument checks. |
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49 ## @end table |
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50 ## |
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51 ## @strong{Outputs} |
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52 ## @var{dsys} discrete time equivalent via zero-order hold, |
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53 ## sample each @var{T} sec. |
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54 ## |
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55 ## converts the system data structure describing |
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56 ## @example |
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57 ## . |
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58 ## x = Ac x + Bc u |
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59 ## @end example |
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60 ## into a discrete time equivalent model |
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61 ## @example |
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62 ## x[n+1] = Ad x[n] + Bd u[n] |
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63 ## @end example |
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64 ## via the matrix exponential or bilinear transform |
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65 ## |
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66 ## @strong{Note} This function adds the suffix @code{_d} |
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67 ## to the names of the new discrete states. |
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68 ## @end deftypefn |
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69 |
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70 ## Author: R. Bruce Tenison <btenison@eng.auburn.edu> |
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71 ## Created: October 1993 |
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72 ## Updated by John Ingram for system data structure August 1996 |
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73 |
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74 function dsys = c2d (sys, opt, T) |
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75 ## parse input arguments |
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76 if(nargin < 1 | nargin > 3) |
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77 usage("dsys=c2d(sys[,T])"); |
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78 elseif (!is_struct(sys)) |
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79 error("sys must be a system data structure"); |
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80 elseif (nargin == 1) |
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81 opt = "ex"; |
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82 elseif (nargin == 2 & !isstr(opt) ) |
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83 T = opt; |
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84 opt = "ex"; |
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85 endif |
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86 |
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87 ## check if sampling period T was passed. |
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88 Ts = sysgettsam(sys); |
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89 if(!exist("T")) |
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90 T = Ts; |
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91 if(T == 0) |
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92 error("sys is purely continuous; no sampling period T provided"); |
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93 endif |
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94 elseif (T != Ts & Ts > 0) |
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95 warning(["c2d: T=",num2str(T),", system tsam==",num2str(Ts), ... |
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96 ": using T=", num2str(min(T,Ts))]); |
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97 T = min(T,Ts); |
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98 endif |
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99 |
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100 if (!is_sample(T)) |
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101 error("sampling period T must be a postive, real scalar"); |
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102 elseif( ! (strcmp(opt,"ex") | strcmp(opt,"bi") ) ) |
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103 error(["invalid option passed: ",opt]) |
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104 endif |
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105 |
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106 sys = sysupdate(sys,"ss"); |
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107 [n,nz,m,p] = sysdimensions(sys); |
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108 if(n == 0) |
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109 dsys = syssetsignals(sys,"yd",ones(1:p)); |
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110 elseif(strcmp(opt,"ex")); |
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111 [aa,bb,cc,dd] = sys2ss(sys); |
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112 crng= 1:n; |
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113 drng = n+(1:nz); |
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114 |
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115 ## partition state equations into continuous, imaginary subsystems |
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116 Ac = aa(crng,crng); |
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117 Bc = bb(crng,:); |
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118 if(nz == 0) |
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119 Acd = Adc = Add = Bd = 0; |
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120 else |
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121 Acd = aa(crng,drng); |
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122 Adc = aa(drng,crng); |
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123 Add = aa(drng,drng); |
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124 Bd = bb(drng,:); |
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125 Bc = [Bc, Acd]; ## append discrete states as inputs to cont system |
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126 endif |
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127 |
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128 ## convert state equations |
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129 mat = [Ac, Bc; zeros(m+nz,n+nz+m)]; |
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130 matexp = expm(mat * T); |
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131 |
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132 ## replace Ac |
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133 aa(crng,crng) = matexp(crng,crng); ## discretized homegenous diff eqn |
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134 |
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135 ## replace Bc |
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136 bb(crng,:) = matexp(crng,n+(1:m)); |
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137 |
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138 ## replace Acd |
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139 if(nz) |
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140 aa(crng,drng) = matexp(crng,n+m+(1:nz)); |
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141 end |
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142 |
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143 stnames = sysgetsignals(sys,"st"); ## continuous states renamed below |
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144 innames = sysgetsignals(sys,"in"); |
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145 outnames = sysgetsignals(sys,"out"); |
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146 outlist = 1:p; |
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147 dsys = ss2sys(aa,bb,cc,dd,T,0,n+nz,stnames,innames, ... |
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148 outnames,outlist); |
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149 ## rename states |
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150 for ii=1:n |
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151 strval = sprintf("%s_d",sysgetsignals(dsys,"st",ii,1)); |
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152 dsys = syssetsignals(dsys,"st",strval,ii); |
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153 endfor |
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154 |
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155 elseif(strcmp(opt,"bi")) |
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156 if(is_digital(sys)) |
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157 error("c2d: system is already digital") |
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158 else |
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159 ## convert with bilinear transform |
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160 [a,b,c,d,tsam,n,nz,stname,inname,outname,yd] = sys2ss(sys); |
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161 IT = (2/T)*eye(size(a)); |
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162 A = (IT+a)/(IT-a); |
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163 iab = (IT-a)\b; |
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164 tk=2/sqrt(T); |
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165 B = tk*iab; |
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166 C = tk*(c/(IT-a)); |
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167 D = d + (c*iab); |
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168 stnamed = strappend(stname,"_d"); |
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169 dsys = ss2sys(A,B,C,D,T,0,rows(A),stnamed,inname,outname); |
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170 endif |
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171 else |
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172 error(["Bad option=",opt]) |
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173 endif |
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174 |
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175 endfunction |
