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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 ## -*- texinfo -*- |
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20 ##@deftypefn {Function File} {@var{outputs} =} rldemo (@var{inputs}) |
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21 ##Octave Controls toolbox demo: Root Locus demo |
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22 ##@end deftypefn |
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23 |
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24 ## Author: David Clem |
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25 ## Created: August 15, 1994 |
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26 ## Updated by John Ingram December 1996 |
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27 |
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28 function rldemo () |
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29 |
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30 while (1) |
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31 clc |
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32 k = menu("Octave Root Locus Demo", ... |
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33 "Display continuous system's open loop poles and zeros (pzmap)", ... |
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34 "Display discrete system's open loop poles and zeros (pzmap)", ... |
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35 "Display root locus diagram of SISO continuous system (rlocus)", ... |
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36 "Display root locus diagram of SISO discrete system (rlocus)", ... |
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37 "Return to main demo menu"); |
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38 gset autoscale |
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39 if (k == 1) |
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40 clc |
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41 help pzmap |
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42 prompt |
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43 |
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44 clc |
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45 disp("Display continuous system's open loop poles and zeros (pzmap)\n"); |
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46 disp("Example #1, Consider the following continuous transfer function:"); |
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47 cmd = "sys1 = tf2sys([1.5, 18.5, 6], [1, 4, 155, 302, 5050]);"; |
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48 disp(cmd); |
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49 eval(cmd); |
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50 cmd ="sysout(sys1);"; |
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51 disp(cmd); |
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52 eval(cmd); |
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53 disp("\nPole-zero form can be obtained as follows:"); |
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54 cmd = "sysout(sys1,""zp"");"; |
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55 disp(cmd); |
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56 eval(cmd); |
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57 disp("View the system's open loop poles and zeros with the command:") |
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58 cmd = "pzmap(sys1);"; |
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59 run_cmd |
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60 prompt |
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61 |
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62 clc |
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63 disp("Example #2, Consider the following set of poles and zeros:"); |
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64 cmd = "sys2 = zp2sys([-1, 5, -23],[-1, -10, -7+5i, -7-5i],5);"; |
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65 disp(cmd); |
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66 eval(cmd); |
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67 cmd = "sysout(sys2);"; |
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68 disp(cmd); |
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69 eval(cmd); |
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70 disp("\nThe pzmap command for the zp form is the same as the tf form:") |
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71 cmd = "pzmap(sys2);"; |
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72 run_cmd; |
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73 disp("\nThe internal representation of the system is not important;"); |
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74 disp("pzmap automatically sorts it out internally."); |
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75 prompt; |
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76 |
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77 clc |
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78 disp("Example #3, Consider the following state space system:\n"); |
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79 cmd = "sys3=ss2sys([0, 1; -10, -11], [0; 1], [0, -2], 1);"; |
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80 disp(cmd); |
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81 eval(cmd); |
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82 cmd = "sysout(sys3);"; |
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83 disp(cmd); |
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84 eval(cmd); |
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85 disp("\nPole-zero form can be obtained as follows:"); |
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86 cmd = "sysout(sys3,""zp"");"; |
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87 disp(cmd); |
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88 eval(cmd); |
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89 disp("\nOnce again, the pzmap command is the same:"); |
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90 cmd = "pzmap(sys3);"; |
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91 run_cmd; |
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92 prompt; |
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93 |
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94 closeplot |
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95 clc |
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96 |
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97 elseif (k == 2) |
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98 clc |
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99 help pzmap |
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100 prompt |
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101 |
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102 clc |
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103 disp("\nDisplay discrete system's open loop poles and zeros (pzmap)\n"); |
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104 disp("First we must define a sampling time, as follows:\n"); |
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105 cmd = "Tsam = 1;"; |
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106 run_cmd; |
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107 disp("Example #1, Consider the following discrete transfer function:"); |
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108 cmd = "sys1 = tf2sys([1.05, -0.09048], [1, -2, 1],Tsam);"; |
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109 disp(cmd); |
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110 eval(cmd); |
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111 cmd ="sysout(sys1);"; |
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112 disp(cmd); |
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113 eval(cmd); |
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114 disp("\nPole-zero form can be obtained as follows:"); |
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115 cmd = "sysout(sys1,""zp"");"; |
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116 disp(cmd); |
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117 eval(cmd); |
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118 disp("View the system's open loop poles and zeros with the command:") |
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119 cmd = "pzmap(sys1);"; |
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120 run_cmd |
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121 prompt |
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122 |
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123 clc |
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124 disp("Example #2, Consider the following set of discrete poles and zeros:"); |
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125 cmd = "sys2 = zp2sys(-0.717, [1, -0.368], 3.68, Tsam);"; |
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126 disp(cmd); |
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127 eval(cmd); |
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128 cmd = "sysout(sys2);"; |
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129 disp(cmd); |
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130 eval(cmd); |
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131 disp("\nThe pzmap command for the zp form is the same as the tf form:") |
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132 cmd = "pzmap(sys2);"; |
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133 run_cmd; |
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134 disp("\nThe internal representation of the system is not important;"); |
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135 disp("pzmap automatically sorts it out internally."); |
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136 prompt; |
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137 |
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138 clc |
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139 disp("Example #3, Consider the following discrete state space system:\n"); |
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140 cmd = "sys3=ss2sys([1, 0.0952; 0, 0.905], [0.00484; 0.0952], [1, 0], 0, Tsam);"; |
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141 disp(cmd); |
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142 eval(cmd); |
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143 cmd = "sysout(sys3);"; |
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144 disp(cmd); |
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145 eval(cmd); |
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146 disp("\nPole-zero form can be obtained as follows:"); |
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147 cmd = "sysout(sys3,""zp"");"; |
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148 disp(cmd); |
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149 eval(cmd); |
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150 disp("\nOnce again, the pzmap command is the same:"); |
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151 cmd = "pzmap(sys3);"; |
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152 run_cmd; |
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153 prompt; |
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154 |
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155 closeplot |
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156 clc |
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157 |
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158 elseif (k == 3) |
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159 clc |
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160 help rlocus |
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161 prompt; |
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162 |
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163 clc |
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164 disp("Display root locus of a continuous SISO system (rlocus)\n") |
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165 disp("Example #1, Consider the following continuous transfer function:"); |
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166 cmd = "sys1 = tf2sys([1.5, 18.5, 6],[1, 4, 155, 302, 5050]);"; |
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167 disp(cmd); |
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168 eval(cmd); |
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169 cmd ="sysout(sys1);"; |
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170 disp(cmd); |
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171 eval(cmd); |
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172 disp("\nPole-zero form can be obtained as follows:"); |
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173 cmd = "sysout(sys1,""zp"");"; |
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174 disp(cmd); |
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175 eval(cmd); |
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176 disp("\nWhen using rlocus, inital system poles are displayed as X's.") |
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177 disp("Moving poles are displayed as diamonds. Zeros are displayed as") |
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178 disp("boxes. The simplest form of the rlocus command is as follows:") |
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179 cmd = "rlocus(sys1);"; |
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180 run_cmd |
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181 disp("\nrlocus automatically selects the minimum and maximum gains based") |
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182 disp("on the real-axis locus breakpoints. The plot limits are chosen") |
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183 disp("to be no more than 10 times the maximum magnitude of the open") |
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184 disp("loop poles/zeros."); |
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185 prompt |
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186 |
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187 clc |
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188 disp("Example #2, Consider the following set of poles and zeros:"); |
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189 cmd = "sys2 = zp2sys([],[0, -20, -2, -0.1],5);"; |
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190 disp(cmd); |
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191 eval(cmd); |
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192 cmd = "sysout(sys2);"; |
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193 disp(cmd); |
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194 eval(cmd); |
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195 disp("\nThe rlocus command for the zp form is the same as the tf form:") |
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196 cmd = "rlocus(sys2);"; |
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197 run_cmd; |
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198 disp("\nThe internal representation of the system is not important;"); |
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199 disp("rlocus automatically sorts it out internally."); |
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200 prompt; |
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201 |
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202 clc |
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203 disp("Example #3, Consider the following state space system:\n"); |
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204 cmd = "sys3=ss2sys([0, 1; -10, -11], [0; 1], [0, -2], 0);"; |
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205 disp(cmd); |
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206 eval(cmd); |
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207 cmd = "sysout(sys3);"; |
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208 disp(cmd); |
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209 eval(cmd); |
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210 disp("\nPole-zero form can be obtained as follows:"); |
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211 cmd = "sysout(sys3,""zp"");"; |
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212 disp(cmd); |
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213 eval(cmd); |
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214 disp("\nOnce again, the rlocus command is the same:"); |
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215 cmd = "rlocus(sys3);"; |
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216 run_cmd; |
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217 |
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218 disp("\nNo matter what form the system is in, the rlocus command works the"); |
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219 disp("the same."); |
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220 prompt; |
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221 |
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222 closeplot |
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223 clc |
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224 |
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225 elseif (k == 4) |
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226 clc |
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227 help rlocus |
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228 prompt |
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229 |
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230 clc |
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231 disp("Display root locus of a discrete SISO system (rlocus)\n") |
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232 disp("First we must define a sampling time, as follows:\n"); |
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233 cmd = "Tsam = 1;"; |
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234 run_cmd; |
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235 disp("Example #1, Consider the following discrete transfer function:"); |
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236 cmd = "sys1 = tf2sys([1.05, -0.09048],[1, -2, 1],Tsam);"; |
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237 disp(cmd); |
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238 eval(cmd); |
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239 cmd ="sysout(sys1);"; |
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240 disp(cmd); |
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241 eval(cmd); |
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242 disp("\nPole-zero form can be obtained as follows:"); |
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243 cmd = "sysout(sys1,""zp"");"; |
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244 disp(cmd); |
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245 eval(cmd); |
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246 disp("\nWhen using rlocus, inital system poles are displayed as X's.") |
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247 disp("Moving poles are displayed as diamonds. Zeros are displayed as") |
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248 disp("boxes. The simplest form of the rlocus command is as follows:") |
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249 cmd = "rlocus(sys1);"; |
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250 run_cmd |
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251 disp("\nrlocus automatically selects the minimum and maximum gains based") |
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252 disp("on the real-axis locus breakpoints. The plot limits are chosen") |
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253 disp("to be no more than 10 times the maximum magnitude of the open") |
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254 disp("loop poles/zeros."); |
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255 prompt |
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256 |
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257 clc |
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258 disp("Example #2, Consider the following set of discrete poles and zeros:"); |
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259 cmd = "sys2 = zp2sys(-0.717, [1, -0.368], 3.68, Tsam);"; |
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260 disp(cmd); |
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261 eval(cmd); |
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262 cmd = "sysout(sys2);"; |
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263 disp(cmd); |
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264 eval(cmd); |
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265 disp("\nThe rlocus command for the zp form is the same as the tf form:") |
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266 cmd = "rlocus(sys2);"; |
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267 run_cmd; |
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268 disp("\nThe internal representation of the system is not important;"); |
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269 disp("rlocus automatically sorts it out internally. Also, it does not"); |
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270 disp("matter if the system is continuous or discrete. rlocus also sorts"); |
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271 disp("this out automatically"); |
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272 prompt; |
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273 |
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274 clc |
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275 disp("Example #3, Consider the following discrete state space system:\n"); |
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276 cmd = "sys3=ss2sys([1, 0.0952; 0, 0.905], [0.00484; 0.0952], [1, 0], 0, Tsam);"; |
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277 disp(cmd); |
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278 eval(cmd); |
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279 cmd = "sysout(sys3);"; |
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280 disp(cmd); |
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281 eval(cmd); |
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282 disp("\nPole-zero form can be obtained as follows:"); |
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283 cmd = "sysout(sys3,""zp"");"; |
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284 disp(cmd); |
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285 eval(cmd); |
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286 disp("\nOnce again, the rlocus command is the same:"); |
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287 cmd = "rlocus(sys3);"; |
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288 run_cmd; |
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289 |
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290 disp("\nNo matter what form the system is in, the rlocus command works the"); |
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291 disp("the same."); |
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292 |
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293 prompt; |
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294 |
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295 closeplot |
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296 clc |
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297 |
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298 elseif (k == 5) |
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299 return |
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300 endif |
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301 endwhile |
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302 endfunction |
