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1 ## Copyright (C) 1996, 1998 Kai P. Mueller |
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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} {} dhinfdemo () |
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21 ## Demonstrate the functions available to design a discrete |
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22 ## @iftex |
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23 ## @tex |
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24 ## $ { \cal H }_\infty $ |
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25 ## @end tex |
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26 ## @end iftex |
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27 ## @ifinfo |
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28 ## H-infinity |
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29 ## @end ifinfo |
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30 ## controller. This is not a true discrete design. The |
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31 ## design is carried out in continuous time while the effect of sampling |
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32 ## is described by a bilinear transformation of the sampled system. |
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33 ## This method works quite well if the sampling period is "small" |
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34 ## compared to the plant time constants. |
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35 ## |
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36 ## Continuous plant: |
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37 ## @iftex |
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38 ## @tex |
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39 ## $$ G(s) = { 1 \over (s+2) (s+1) } $$ |
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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 ## @group |
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45 ## 1 |
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46 ## G(s) = -------------- |
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47 ## (s + 2)(s + 1) |
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48 ## @end group |
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49 ## @end example |
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50 ## @end ifinfo |
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51 ## |
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52 ## Discretised plant with @acronym{ZOH} (Sampling period = @var{Ts} = 1 second): |
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53 ## @iftex |
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54 ## @tex |
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55 ## $$ G(z) = { 0.39958z + 0.14700 \over (z - 0.36788) (z - 0.13533) } $$ |
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56 ## @end tex |
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57 ## @end iftex |
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58 ## @ifinfo |
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59 ## @example |
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60 ## @group |
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61 ## 0.39958z + 0.14700 |
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62 ## G(z) = -------------------------- |
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63 ## (z - 0.36788)(z - 0.13533) |
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64 ## @end group |
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65 ## @end example |
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66 ## @end ifinfo |
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67 ## |
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68 ## @example |
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69 ## @group |
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70 ## +----+ |
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71 ## -------------------->| W1 |---> v1 |
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72 ## z | +----+ |
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73 ## ----|-------------+ || T || => min. |
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74 ## | | vz infty |
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75 ## | +---+ v +----+ |
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76 ## *--->| G |--->O--*-->| W2 |---> v2 |
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77 ## | +---+ | +----+ |
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78 ## | | |
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79 ## | +---+ | |
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80 ## -----| K |<------- |
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81 ## +---+ |
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82 ## @end group |
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83 ## @end example |
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84 ## |
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85 ## @noindent |
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86 ## W1 and W2 are the robustness and performancs weighting functions. |
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87 ## @end deftypefn |
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88 |
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89 ## K. Mueller, <mueller@ifr.ing.tu-bs.de> |
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90 ## Technical University of Braunschweig, IfR |
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91 |
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92 echo off |
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93 disp(" "); |
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94 disp(" --------------------------------------------------"); |
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95 disp(" Discrete H_infinity optimal control for the plant:"); |
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96 disp(" "); |
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97 disp(" 0.39958z + 0.14700"); |
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98 disp(" G(s) = --------------------------"); |
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99 disp(" (z - 0.36788)(z - 0.13533)"); |
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100 disp(" --------------------------------------------------"); |
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101 disp(" "); |
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102 |
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103 disp("sampling time:") |
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104 cmd = "Ts = 1.0;"; |
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105 disp(cmd); |
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106 eval(cmd); |
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107 disp("weighting on actuator value u"); |
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108 cmd = "W1 = wgt1o(0.1, 200.0, 50.0);"; |
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109 disp(cmd); |
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110 eval(cmd); |
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111 disp("weighting on controlled variable y"); |
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112 cmd = "W2 = wgt1o(350.0, 0.05, 0.0002);"; |
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113 disp(cmd); |
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114 eval(cmd); |
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115 ## omega axis (column vector) |
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116 ww = vec(logspace(-4.99, 3.99, 100)); |
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117 |
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118 disp("Create ZOH equivalent model of a continuous plant"); |
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119 cmd = "G = tf(2,[1 3 2]); Gd = c2d(G, Ts);"; |
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120 run_cmd |
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121 |
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122 ## w-plane (continuous representation of the sampled system) |
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123 disp("W-plane transform of discrete time system:"); |
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124 cmd = "Gw = d2c(Gd, \"bi\");"; |
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125 run_cmd |
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126 |
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127 disp(" "); |
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128 disp(" o building P..."); |
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129 ## need One as the pseudo transfer function One = 1 |
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130 cmd = "One = ugain(1);"; |
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131 disp(cmd); |
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132 eval(cmd); |
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133 cmd = " psys = buildssic([1 4;2 4;3 1],[3],[2 3 5],[3 4],Gw,W1,W2,One);"; |
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134 run_cmd; |
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135 disp(" o controller design..."); |
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136 cmd = "[K, gfin, GWC] = hinfsyn(psys, 1, 1, 0.1, 10.0, 0.02);"; |
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137 run_cmd |
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138 |
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139 disp(" "); |
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140 fig_n = 1; |
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141 yn = input(" * Plot magnitudes of W1KS and W2S? [n]: ","S"); |
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142 if (length(yn) >= 1) |
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143 if ((yn(1) == "y") || (yn(1) == 'Y')) |
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144 disp(" o magnitudes of W1KS and W2S..."); |
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145 gwx = sysprune(GWC, 1, 1); |
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146 mag1 = bode(gwx, ww); |
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147 if (columns(mag1) > 1); mag1 = mag1'; endif |
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148 gwx = sysprune(GWC, 2, 1); |
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149 mag2 = bode(gwx, ww); |
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150 if (columns(mag2) > 1); mag2 = mag2'; endif |
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151 figure(fig_n) |
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152 fig_n = fig_n + 1; |
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153 __gnuplot_set__ grid |
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154 loglog(ww, [mag1 mag2]); |
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155 endif |
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156 endif |
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157 |
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158 Kd = c2d(K, "bi", Ts); |
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159 GG = buildssic([1 2; 2 1], [], [1 2], [-2], Gd, Kd); |
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160 disp(" o closed loop poles..."); |
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161 damp(GG); |
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162 |
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163 disp(" "); |
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164 yn = input(" * Plot closed loop step responses? [n]: ","S"); |
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165 if (length(yn) >= 1) |
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166 if ((yn(1) == "y") || (yn(1) == 'Y')) |
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167 disp(" o step responses of T and KS..."); |
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168 figure(fig_n) |
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169 step(GG, 1, 10); |
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170 endif |
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171 endif |
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172 |
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173 ## --------- End of dhinfdemo/kpm |
