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1 # ------------------------------------------------------------ |
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2 # dhinfdemo Design of a discrete H_infinity controller. |
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3 # This is not a true discrete design. The design |
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4 # is carried out in continuous time while the |
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5 # effect of sampling is described by a bilinear |
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6 # transformation of the sampled system. |
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7 # This method works quite well if the sampling |
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8 # period is "small" compared to the plant time |
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9 # constants. |
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10 # |
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11 # This is a script file for OCTAVE. |
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12 # ------------------------------------------------------------ |
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13 # |
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14 # continuous plant: |
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15 # 1 |
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16 # G(s) = -------------- |
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17 # (s + 2)(s + 1) |
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18 # |
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19 # discretised plant with ZOH (Sampling period = Ts = 1 second) |
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20 # |
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21 # 0.39958z + 0.14700 |
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22 # G(s) = -------------------------- |
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23 # (z - 0.36788)(z - 0.13533) |
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24 # |
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25 # +----+ |
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26 # -------------------->| W1 |---> v1 |
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27 # z | +----+ |
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28 # ----|-------------+ || T || => min. |
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29 # | | vz infty |
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30 # | +---+ v +----+ |
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31 # *--->| G |--->O--*-->| W2 |---> v2 |
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32 # | +---+ | +----+ |
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33 # | | |
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34 # | +---+ | |
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35 # -----| K |<------- |
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36 # +---+ |
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37 # |
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38 # W1 and W2 are the robustness and performancs weighting |
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39 # functions |
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40 |
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41 # K. Mueller, <mueller@ifr.ing.tu-bs.de> |
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42 # Technical University of Braunschweig, IfR |
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3229
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43 # $Revision: 2.0.0.2 $ $Date: 1998/12/08 23:29:27 $ |
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44 # |
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45 |
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46 echo off |
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47 disp(" "); |
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48 disp(" --------------------------------------------------"); |
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49 disp(" Discrete H_infinity optimal control for the plant:"); |
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50 disp(" "); |
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51 disp(" 0.39958z + 0.14700"); |
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52 disp(" G(s) = --------------------------"); |
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53 disp(" (z - 0.36788)(z - 0.13533)"); |
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54 disp(" --------------------------------------------------"); |
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55 disp(" "); |
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56 |
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57 disp("sampling time:") |
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58 cmd = "Ts = 1.0;"; |
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59 disp(cmd); |
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60 eval(cmd); |
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61 disp("weighting on actuator value u"); |
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62 cmd = "W1 = wgt1o(0.1, 200.0, 50.0);"; |
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63 disp(cmd); |
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64 eval(cmd); |
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65 disp("weighting on controlled variable y"); |
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66 cmd = "W2 = wgt1o(350.0, 0.05, 0.0002);"; |
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67 disp(cmd); |
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68 eval(cmd); |
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69 # omega axis (column vector) |
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70 ww = vec(logspace(-4.99, 3.99, 100)); |
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71 |
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72 disp("Create ZOH equivalent model of a continuous plant"); |
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73 cmd = "G = tf2sys(2,[1 3 2]); Gd = c2d(G, Ts);"; |
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74 run_cmd |
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75 |
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76 # w-plane (continuous representation of the sampled system) |
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77 disp("W-plane transform of discrete time system:"); |
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78 cmd = "Gw = d2c(Gd, \"bi\");"; |
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79 run_cmd |
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80 |
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81 disp(" "); |
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82 disp(" o building P..."); |
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83 # need One as the pseudo transfer function One = 1 |
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84 cmd = "One = ugain(1);"; |
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85 disp(cmd); |
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86 eval(cmd); |
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87 cmd = " psys = buildssic([1 4;2 4;3 1],[3],[2 3 5],[3 4],Gw,W1,W2,One);"; |
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88 run_cmd; |
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89 disp(" o controller design..."); |
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90 cmd = "[K, gfin, GWC] = hinfsyn(psys, 1, 1, 0.1, 10.0, 0.02);"; |
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91 run_cmd |
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92 |
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93 disp(" "); |
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94 fig_n = 1; |
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95 yn = input(" * Plot magnitudes of W1KS and W2S? [n]: ","S"); |
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96 if (length(yn) >= 1) |
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97 if ((yn(1) == "y") || (yn(1) == 'Y')) |
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98 disp(" o magnitudes of W1KS and W2S..."); |
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99 gwx = sysprune(GWC, 1, 1); |
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100 mag1 = bode(gwx, ww); |
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101 if (columns(mag1) > 1); mag1 = mag1'; endif |
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102 gwx = sysprune(GWC, 2, 1); |
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103 mag2 = bode(gwx, ww); |
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104 if (columns(mag2) > 1); mag2 = mag2'; endif |
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105 figure(fig_n) |
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106 fig_n = fig_n + 1; |
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107 gset grid |
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108 loglog(ww, [mag1 mag2]); |
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109 endif |
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110 endif |
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111 |
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112 Kd = c2d(K, "bi", Ts); |
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113 GG = buildssic([1 2; 2 1], [], [1 2], [-2], Gd, Kd); |
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114 disp(" o closed loop poles..."); |
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115 damp(GG); |
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116 |
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117 disp(" "); |
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118 yn = input(" * Plot closed loop step responses? [n]: ","S"); |
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119 if (length(yn) >= 1) |
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120 if ((yn(1) == "y") || (yn(1) == 'Y')) |
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121 disp(" o step responses of T and KS..."); |
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122 figure(fig_n) |
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123 step(GG, 1, 10); |
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124 endif |
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125 endif |
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126 |
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127 # --------- End of dhinfdemo/kpm |
