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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} {[@var{a}, @var{b}, @var{c}, @var{d}] =} tf2ss (@var{num}, @var{den}) |
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21 ## Conversion from tranfer function to state-space. |
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22 ## The state space system: |
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23 ## @iftex |
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24 ## @tex |
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25 ## $$ \dot x = Ax + Bu $$ |
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26 ## $$ y = Cx + Du $$ |
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27 ## @end tex |
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28 ## @end iftex |
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29 ## @ifinfo |
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30 ## @example |
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31 ## . |
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32 ## x = Ax + Bu |
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33 ## y = Cx + Du |
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34 ## @end example |
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35 ## @end ifinfo |
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36 ## is obtained from a transfer function: |
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37 ## @iftex |
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38 ## @tex |
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39 ## $$ G(s) = { { \rm num }(s) \over { \rm den }(s) } $$ |
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40 ## @end tex |
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41 ## @end iftex |
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42 ## @ifinfo |
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43 ## @example |
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44 ## num(s) |
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45 ## G(s)=------- |
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46 ## den(s) |
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47 ## @end example |
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48 ## @end ifinfo |
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49 ## |
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50 ## The vector @var{den} must contain only one row, whereas the vector |
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51 ## @var{num} may contain as many rows as there are outputs @var{y} of |
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52 ## the system. The state space system matrices obtained from this function |
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53 ## will be in controllable canonical form as described in @cite{Modern Control |
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54 ## Theory}, (Brogan, 1991). |
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55 ## @end deftypefn |
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56 |
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57 ## Author: R. Bruce Tenison <btenison@eng.auburn.edu> |
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58 ## Created: June 22, 1994 |
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59 ## mod A S Hodel July, Aug 1995 |
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60 |
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61 function [a, b, c, d] = tf2ss (num, den) |
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62 |
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63 if(nargin != 2) error("tf2ss: wrong number of input arguments") |
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64 elseif(isempty(num)) error("tf2ss: empty numerator"); |
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65 elseif(isempty(den)) error("tf2ss: empy denominator"); |
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66 elseif(!isvector(num)) |
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67 error(sprintf("num(%dx%d) must be a vector",rows(num),columns(num))); |
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68 elseif(!isvector(den)) |
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69 error(sprintf("den(%dx%d) must be a vector",rows(den),columns(den))); |
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70 endif |
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71 |
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72 ## strip leading zeros from num, den |
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73 nz = find(num != 0); |
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74 if(isempty(nz)) num = 0; |
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75 else num = num(nz(1):length(num)); endif |
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76 nz = find(den != 0); |
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77 if(isempty(nz)) error("denominator is 0."); |
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78 else den = den(nz(1):length(den)); endif |
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79 |
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80 ## force num, den to be row vectors |
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81 num = vec(num)'; den = vec(den)'; |
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82 nn = length(num); nd = length(den); |
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83 if(nn > nd) error(sprintf("deg(num)=%d > deg(den)= %d",nn,nd)); endif |
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84 |
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85 ## Check sizes |
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86 if (nd == 1) a = []; b = []; c = []; d = num(:,1) / den(1); |
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87 else |
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88 ## Pad num so that length(num) = length(den) |
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89 if (nd-nn > 0) num = [zeros(1,nd-nn), num]; endif |
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90 |
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91 ## Normalize the numerator and denominator vector w.r.t. the leading |
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92 ## coefficient |
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93 d1 = den(1); num = num / d1; den = den(2:nd)/d1; |
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94 sw = nd-1:-1:1; |
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95 |
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96 ## Form the A matrix |
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97 if(nd > 2) a = [zeros(nd-2,1),eye(nd-2,nd-2);-den(sw)]; |
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98 else a = -den(sw); endif |
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99 |
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100 ## Form the B matrix |
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101 b = zeros(nd-1,1); b(nd-1,1) = 1; |
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102 |
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103 ## Form the C matrix |
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104 c = num(:,2:nd)-num(:,1)*den; c = c(:,sw); |
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105 |
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106 ## Form the D matrix |
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107 d = num(:,1); |
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108 endif |
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109 |
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110 endfunction |
