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1 ## Copyright (C) 1996, 1998, 2000, 2002, 2004, 2005, 2007 |
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2 ## Auburn University. All rights reserved. |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} tf2ss (@var{num}, @var{den}) |
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22 ## Conversion from transfer function to state-space. |
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23 ## The state space system: |
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24 ## @iftex |
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25 ## @tex |
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26 ## $$ \dot x = Ax + Bu $$ |
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27 ## $$ y = Cx + Du $$ |
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28 ## @end tex |
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29 ## @end iftex |
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30 ## @ifinfo |
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31 ## @example |
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32 ## . |
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33 ## x = Ax + Bu |
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34 ## y = Cx + Du |
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35 ## @end example |
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36 ## @end ifinfo |
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37 ## is obtained from a transfer function: |
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38 ## @iftex |
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39 ## @tex |
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40 ## $$ G(s) = { { \rm num }(s) \over { \rm den }(s) } $$ |
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41 ## @end tex |
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42 ## @end iftex |
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43 ## @ifinfo |
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44 ## @example |
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45 ## num(s) |
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46 ## G(s)=------- |
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47 ## den(s) |
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48 ## @end example |
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49 ## @end ifinfo |
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50 ## |
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51 ## The vector @var{den} must contain only one row, whereas the vector |
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52 ## @var{num} may contain as many rows as there are outputs @var{y} of |
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53 ## the system. The state space system matrices obtained from this function |
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54 ## will be in controllable canonical form as described in @cite{Modern Control |
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55 ## Theory}, (Brogan, 1991). |
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56 ## @end deftypefn |
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57 |
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58 ## Author: R. Bruce Tenison <btenison@eng.auburn.edu> |
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59 ## Created: June 22, 1994 |
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60 ## mod A S Hodel July, Aug 1995 |
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61 |
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62 function [a, b, c, d] = tf2ss (num, den) |
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63 |
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64 if (nargin != 2) |
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65 print_usage (); |
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66 elseif (isempty (num)) |
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67 error ("tf2ss: empty numerator"); |
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68 elseif (isempty (den)) |
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69 error ("tf2ss: empy denominator"); |
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70 elseif (! isvector (num)) |
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71 error ("num(%dx%d) must be a vector", rows (num), columns (num)); |
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72 elseif (! isvector (den)) |
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73 error ("den(%dx%d) must be a vector", rows (den), columns (den)); |
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74 endif |
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75 |
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76 ## strip leading zeros from num, den |
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77 nz = find (num != 0); |
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78 if (isempty (nz)) |
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79 num = 0; |
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80 else |
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81 num = num(nz(1):length(num)); |
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82 endif |
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83 nz = find (den != 0); |
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84 if (isempty (nz)) |
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85 error ("denominator is 0."); |
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86 else |
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87 den = den(nz(1):length(den)); |
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88 endif |
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89 |
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90 ## force num, den to be row vectors |
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91 num = vec (num)'; |
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92 den = vec (den)'; |
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93 nn = length (num); |
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94 nd = length (den); |
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95 if (nn > nd) |
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96 error ("deg(num)=%d > deg(den)= %d", nn, nd); |
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97 endif |
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98 |
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99 ## Check sizes |
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100 if (nd == 1) |
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101 a = b = c = []; |
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102 d = num(:,1) / den(1); |
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103 else |
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104 ## Pad num so that length(num) = length(den) |
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105 if (nd-nn > 0) |
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106 num = [zeros(1,nd-nn), num]; |
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107 endif |
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108 |
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109 ## Normalize the numerator and denominator vector w.r.t. the leading |
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110 ## coefficient |
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111 d1 = den(1); |
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112 num = num / d1; |
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113 den = den(2:nd)/d1; |
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114 sw = nd-1:-1:1; |
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115 |
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116 ## Form the A matrix |
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117 if (nd > 2) |
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118 a = [zeros(nd-2,1), eye(nd-2,nd-2); -den(sw)]; |
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119 else |
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120 a = -den(sw); |
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121 endif |
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122 |
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123 ## Form the B matrix |
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124 b = zeros (nd-1, 1); |
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125 b(nd-1,1) = 1; |
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126 |
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127 ## Form the C matrix |
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128 c = num(:,2:nd)-num(:,1)*den; |
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129 c = c(:,sw); |
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130 |
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131 ## Form the D matrix |
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132 d = num(:,1); |
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133 endif |
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134 |
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135 endfunction |
