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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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301 USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} moddemo (@var{inputs}) |
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22 ## Octave Control toolbox demo: Model Manipulations demo. |
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23 ## @end deftypefn |
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24 |
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25 ## Author: David Clem |
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26 ## Created: August 15, 1994 |
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27 ## a s hodel: updated to reflect updated output order in ss2zp |
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28 |
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29 function moddemo () |
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30 |
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31 while (1) |
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32 clc |
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33 disp("Octave Model Manipulations Demo") |
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34 disp("=======================================") |
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35 disp(" 1) Perform continuous to discrete time conversion (c2d)") |
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36 disp(" 2) Convert from state space to zero / pole form (ss2zp)") |
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37 disp(" Convert from zero / pole to state space form (zp2ss)") |
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38 disp(" 3) Convert from state space to transfer function form (ss2tf)") |
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39 disp(" Convert from transfer function to state space form (tf2ss)") |
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40 disp(" 4) Convert from transfer function to zero / pole form (tf2zp)") |
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41 disp(" Convert from zero / pole to transfer function form (zp2tf)") |
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42 disp(" 5) Return to main demo menu") |
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43 disp(" ") |
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44 k=6; |
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45 while(k > 5 || k < 1) |
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46 k = input("Please enter a number:"); |
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47 endwhile |
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48 if (k == 1) |
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49 clc |
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50 disp("Perform continuous to discrete time conversion (c2d)\n") |
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51 disp("Example #1, Consider the following continuous time state space system:\n") |
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52 a=[0, 1; -25, -4] |
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53 b=[0; 1] |
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54 c=[1, 1] |
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55 d=1 |
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56 prompt |
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57 disp("\nTo convert this to a discrete time system (using a zero order hold),") |
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58 disp("use the following commands:\n") |
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59 cmd="sys=ss(a,b,c,d);"; |
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60 run_cmd |
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61 cmd="dsys = c2d(sys,0.2);"; |
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62 run_cmd |
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63 cmd="sysout(dsys);"; |
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64 run_cmd |
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65 disp("Function check\n") |
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66 disp("Check the poles of sys vs dsys:\n") |
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67 cmd="[da,db]=sys2ss(dsys);"; |
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68 run_cmd |
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69 cmd="lam = eig(a);"; |
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70 run_cmd |
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71 disp("Discretize the continuous time eigenvalues using the matrix exponential:\n") |
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72 disp("lambc = exp(lam*0.2)\n") |
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73 lambc = exp(lam*0.2) |
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74 disp("Check the eigenvalues of da\n") |
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75 lambd = eig(da) |
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76 disp("Calculate the difference between lambd and lambc:\n") |
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77 cmd = "error = sort(lambd)-sort(lambc)\n"; |
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78 run_cmd |
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79 disp("The error is on the order of roundoff noise, so we're o.k.") |
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80 prompt |
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81 clc |
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82 elseif (k == 2) |
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83 clc |
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84 disp("Convert from state space to zero / pole form (ss2zp)\n") |
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85 disp("Example #1, Consider the following state space system:\n") |
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86 a=[0, 3, 1; -2, -4, 5; 5, 8, 2] |
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87 b=[0; 5; 2.5] |
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88 c=[6, -1.9, 2] |
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89 d=[-20] |
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90 prompt |
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91 disp(" ") |
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92 disp("\nTo find the poles and zeros of this sytstem, use the following command:\n") |
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93 disp("\n[zer, pol] = ss2zp(a, b, c, d)\n") |
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94 prompt |
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95 disp("Results:\n") |
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96 [zer, pol] = ss2zp(a, b, c, d) |
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97 disp("Variable Description:\n") |
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98 disp("zer, pol => zeros and poles of the state space system") |
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99 disp("a, b, c, d => state space system\n") |
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100 prompt |
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101 clc |
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102 disp("Convert from zero / pole to state space form (zp2ss)\n") |
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103 disp("Example #1, Consider the following set of zeros and poles:\n") |
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104 zer |
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105 pol |
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106 prompt |
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107 disp("\nTo find an equivalent state space representation for this set of poles") |
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108 disp("and zeros, use the following commands:\n") |
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109 k=1 |
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110 disp("\n[na, nb, nc, nd] = zp2ss(zer, pol, k)\n") |
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111 prompt |
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112 disp("Results:\n") |
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113 [na, nb, nc, nd] = zp2ss(zer, pol, k) |
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114 disp("Variable Description:\n") |
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115 disp("na, nb, nc, nd => state space system equivalent to zero / pole input") |
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116 disp("zer, pol => zeros and poles of desired state space system") |
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117 disp("k => gain associated with the zeros\n") |
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118 prompt |
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119 disp("Function check\n") |
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120 disp("Are the eigenvalues of the origonal state space system the same as the") |
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121 disp("eigenvalues of the newly constructed state space system ?\n") |
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122 disp("Find the difference between the two sets of eigenvalues") |
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123 disp("error = sort(eig(a)) - sort(eig(na))\n") |
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124 error = sort(eig(a)) - sort(eig(na)) |
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125 prompt |
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126 clc |
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127 elseif (k == 3) |
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128 clc |
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129 disp("Convert from state space to transfer function (ss2tf)\n") |
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130 disp("Example #1, Consider the following state space system:\n") |
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131 a=[0, 1; -2, -3] |
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132 b=[1; 1] |
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133 c=[1, 9] |
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134 d=[1] |
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135 prompt |
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136 disp("\nTo find an equivalent transfer function for this system, use") |
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137 disp("the following command:\n") |
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138 disp("[num, den] = ss2tf(a, b, c, d)\n") |
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139 prompt |
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140 disp("Results:\n") |
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141 [num,den] = ss2tf(a, b, c, d) |
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142 disp("Variable Description:\n") |
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143 disp("num, den => numerator and denominator of transfer function that is") |
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144 disp(" equivalent to the state space system") |
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145 disp("a, b, c, d => state space system\n") |
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146 prompt |
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147 clc |
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148 disp("Convert from transfer function to state space form (tf2ss)\n") |
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149 disp("Example #1, Consider the following transfer function:\n") |
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150 num |
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151 den |
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152 prompt |
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153 disp("\nTo find an equivalent state space representation for this system, use") |
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154 disp("the following command:\n") |
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155 disp("[a, b, c, d] = tf2ss(num, den)\n") |
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156 prompt |
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157 disp("Results:\n") |
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158 [a, b, c, d] = tf2ss(num, den) |
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159 disp("Variable Description:\n") |
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160 disp("a, b, c, d => state space system equivalent to transfer function input") |
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161 disp("num, den => numerator and denominator of transfer function that is equivalent") |
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162 disp(" to the state space system\n") |
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163 prompt |
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164 clc |
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165 elseif (k == 4) |
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166 clc |
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167 disp("Convert from transfer function to zero / pole form (tf2zp)\n") |
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168 disp("Example #1, Consider the following transfer function:\n") |
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169 num=[1, 2, 3, 4, 5, ] |
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170 den=[1, 2, 3, 4, 5, 6, 7] |
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171 prompt |
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172 disp("\nTo find the zeros and poles of this system, use the following command:\n") |
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173 disp("[zer,pol] = tf2zp(num,den)\n") |
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174 prompt |
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175 disp("Results:\n") |
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176 [zer,pol] = tf2zp(num,den) |
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177 disp("Variable Description:\n") |
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178 disp("zer,pol => zeros and poles of the transfer function") |
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179 disp("num, den => numerator and denominator of transfer function\n") |
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180 prompt |
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181 clc |
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182 disp("Convert from zero / pole to transfer function (zp2tf)\n") |
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183 disp("Example #1, Consider the following set of zeros and poles:\n") |
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184 zer |
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185 pol |
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186 prompt |
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187 disp("\nTo find an equivalent transfer function representation for this set") |
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188 disp("of poles and zeros, use the following commands:\n") |
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189 k=1 |
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190 disp("\n[num, den] = zp2tf(zer, pol, k)\n") |
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191 prompt |
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192 disp("Results:\n") |
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193 [num, den] = zp2tf(zer, pol, k) |
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194 disp("Variable Description:\n") |
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195 disp("[num, den] => transfer function representation of desired set of zeros") |
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196 disp(" and poles") |
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197 disp("a, b, c, d => state space system") |
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198 disp("zer, pol => zeros and poles of desired state space system") |
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199 disp("k => gain associated with the zeros\n") |
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200 prompt |
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201 clc |
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202 elseif (k == 5) |
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203 return |
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204 endif |
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205 endwhile |
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206 endfunction |
