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1 # Copyright (C) 1996 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 function moddemo() |
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20 # Octave Controls toolbox demo: Model Manipulations demo |
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21 # Written by David Clem August 15, 1994 |
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22 |
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23 # a s hodel: updated to reflect updated output order in ss2zp |
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24 |
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25 while (1) |
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26 clc |
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27 disp('Octave Model Manipulations Demo') |
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28 disp('=======================================') |
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29 disp(' 1) Perform continuous to discrete time conversion (c2d)') |
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30 disp(' 2) Convert from state space to zero / pole form (ss2zp)') |
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31 disp(' Convert from zero / pole to state space form (zp2ss)') |
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32 disp(' 3) Convert from state space to transfer function form (ss2tf)') |
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33 disp(' Convert from transfer function to state space form (tf2ss)') |
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34 disp(' 4) Convert from transfer function to zero / pole form (tf2zp)') |
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35 disp(' Convert from zero / pole to transfer function form (zp2tf)') |
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36 disp(' 5) Return to main demo menu') |
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37 disp(' ') |
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38 k=6; |
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39 while(k > 5 || k < 1) |
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40 k = input('Please enter a number:'); |
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41 endwhile |
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42 if (k == 1) |
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43 clc |
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44 disp('Perform continuous to discrete time conversion (c2d)\n') |
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45 disp('Example #1, Consider the following continuous time state space system:\n') |
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46 a=[0 1;-25 -4] |
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47 b=[0;1] |
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48 c=[1 1] |
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49 d=1 |
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50 prompt |
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51 disp('\nTo convert this to a discrete time system (using a zero order hold),') |
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52 disp('use the following commands:\n') |
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53 cmd="sys=ss2sys(a,b,c,d);"; |
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54 run_cmd |
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55 cmd="dsys = c2d(sys,0.2);"; |
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56 run_cmd |
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57 cmd="sysout(dsys);"; |
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58 run_cmd |
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59 disp('Function check\n') |
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60 disp('Check the poles of sys vs dsys:\n') |
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61 cmd="[da,db]=sys2ss(dsys);"; |
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62 run_cmd |
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63 cmd="lam = eig(a);"; |
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64 run_cmd |
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65 disp('Discretize the continuous time eigenvalues using the matrix exponential:\n') |
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66 disp('lambc = exp(lam*0.2)\n') |
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67 lambc = exp(lam*0.2) |
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68 disp('Check the eigenvalues of da\n') |
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69 lambd = eig(da) |
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70 disp('Calculate the difference between lambd and lambc:\n') |
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71 cmd = 'error = sort(lambd)-sort(lambc)\n'; |
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72 run_cmd |
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73 disp("The error is on the order of roundoff noise, so we're o.k.") |
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74 prompt |
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75 clc |
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76 elseif (k == 2) |
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77 clc |
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78 disp('Convert from state space to zero / pole form (ss2zp)\n') |
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79 disp('Example #1, Consider the following state space system:\n') |
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80 a=[0 3 1;-2 -4 5;5 8 2] |
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81 b=[0;5;2.5] |
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82 c=[6 -1.9 2] |
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83 d=[-20] |
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84 prompt |
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85 disp(' ') |
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86 disp('\nTo find the poles and zeros of this sytstem, use the following command:\n') |
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87 disp('\n[zer, pol] = ss2zp(a, b, c, d)\n') |
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88 prompt |
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89 disp('Results:\n') |
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90 [zer, pol] = ss2zp(a, b, c, d) |
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91 disp('Variable Description:\n') |
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92 disp('zer, pol => zeros and poles of the state space system') |
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93 disp('a, b, c, d => state space system\n') |
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94 prompt |
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95 clc |
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96 disp('Convert from zero / pole to state space form (zp2ss)\n') |
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97 disp('Example #1, Consider the following set of zeros and poles:\n') |
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98 zer |
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99 pol |
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100 prompt |
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101 disp('\nTo find an equivalent state space representation for this set of poles') |
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102 disp('and zeros, use the following commands:\n') |
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103 k=1 |
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104 disp('\n[na, nb, nc, nd] = zp2ss(zer, pol, k)\n') |
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105 prompt |
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106 disp('Results:\n') |
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107 [na, nb, nc, nd] = zp2ss(zer, pol, k) |
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108 disp('Variable Description:\n') |
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109 disp('na, nb, nc, nd => state space system equivalent to zero / pole input') |
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110 disp('zer, pol => zeros and poles of desired state space system') |
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111 disp('k => gain associated with the zeros\n') |
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112 prompt |
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113 disp('Function check\n') |
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114 disp('Are the eigenvalues of the origonal state space system the same as the') |
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115 disp('eigenvalues of the newly constructed state space system ?\n') |
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116 disp('Find the difference between the two sets of eigenvalues') |
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117 disp('error = sort(eig(a)) - sort(eig(na))\n') |
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118 error = sort(eig(a)) - sort(eig(na)) |
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119 prompt |
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120 clc |
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121 elseif (k == 3) |
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122 clc |
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123 disp('Convert from state space to transfer function (ss2tf)\n') |
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124 disp('Example #1, Consider the following state space system:\n') |
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125 a=[0 1;-2 -3] |
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126 b=[1;1] |
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127 c=[1 9] |
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128 d=[1] |
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129 prompt |
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130 disp('\nTo find an equivalent transfer function for this system, use') |
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131 disp('the following command:\n') |
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132 disp('[num, den] = ss2tf(a, b, c, d)\n') |
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133 prompt |
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134 disp('Results:\n') |
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135 [num,den] = ss2tf(a, b, c, d) |
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136 disp('Variable Description:\n') |
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137 disp('num, den => numerator and denominator of transfer function that is') |
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138 disp(' equivalent to the state space system') |
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139 disp('a, b, c, d => state space system\n') |
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140 prompt |
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141 clc |
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142 disp('Convert from transfer function to state space form (tf2ss)\n') |
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143 disp('Example #1, Consider the following transfer function:\n') |
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144 num |
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145 den |
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146 prompt |
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147 disp('\nTo find an equivalent state space representation for this system, use') |
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148 disp('the following command:\n') |
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149 disp('[a, b, c, d] = tf2ss(num, den)\n') |
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150 prompt |
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151 disp('Results:\n') |
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152 [a, b, c, d] = tf2ss(num, den) |
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153 disp('Variable Description:\n') |
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154 disp('a, b, c, d => state space system equivalent to transfer function input') |
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155 disp('num, den => numerator and denominator of transfer function that is equivalent') |
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156 disp(' to the state space system\n') |
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157 prompt |
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158 clc |
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159 elseif (k == 4) |
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160 clc |
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161 disp('Convert from transfer function to zero / pole form (tf2zp)\n') |
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162 disp('Example #1, Consider the following transfer function:\n') |
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163 num=[1 2 3 4 5 ] |
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164 den=[1 2 3 4 5 6 7] |
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165 prompt |
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166 disp('\nTo find the zeros and poles of this system, use the following command:\n') |
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167 disp('[zer,pol] = tf2zp(num,den)\n') |
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168 prompt |
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169 disp('Results:\n') |
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170 [zer,pol] = tf2zp(num,den) |
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171 disp('Variable Description:\n') |
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172 disp('zer,pol => zeros and poles of the transfer function') |
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173 disp('num, den => numerator and denominator of transfer function\n') |
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174 prompt |
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175 clc |
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176 disp('Convert from zero / pole to transfer function (zp2tf)\n') |
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177 disp('Example #1, Consider the following set of zeros and poles:\n') |
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178 zer |
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179 pol |
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180 prompt |
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181 disp('\nTo find an equivalent transfer function representation for this set') |
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182 disp('of poles and zeros, use the following commands:\n') |
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183 k=1 |
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184 disp('\n[num, den] = zp2tf(zer, pol, k)\n') |
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185 prompt |
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186 disp('Results:\n') |
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187 [num, den] = zp2tf(zer, pol, k) |
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188 disp('Variable Description:\n') |
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189 disp('[num, den] => transfer function representation of desired set of zeros') |
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190 disp(' and poles') |
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191 disp('a, b, c, d => state space system') |
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192 disp('zer, pol => zeros and poles of desired state space system') |
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193 disp('k => gain associated with the zeros\n') |
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194 prompt |
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195 clc |
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196 elseif (k == 5) |
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197 return |
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198 endif |
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199 endwhile |
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200 endfunction |
