|
3236
|
1 # Copyright (C) 1996,1998 Kai Mueller |
|
|
2 # |
|
|
3 # This file is part of Octave. |
|
|
4 # |
|
|
5 # Octave is free software; you can redistribute it and/or modify it |
|
|
6 # under the terms of the GNU General Public License as published by the |
|
|
7 # Free Software Foundation; either version 2, or (at your option) any |
|
|
8 # later version. |
|
|
9 # |
|
|
10 # Octave is distributed in the hope that it will be useful, but WITHOUT |
|
|
11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
|
|
12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
|
|
13 # for more details. |
|
|
14 # |
|
|
15 # You should have received a copy of the GNU General Public License |
|
|
16 # along with Octave; see the file COPYING. If not, write to the Free |
|
3284
|
17 # Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
|
3236
|
18 |
|
3213
|
19 # ------------------------------------------------------------ |
|
|
20 # dhinfdemo Design of a discrete H_infinity controller. |
|
|
21 # This is not a true discrete design. The design |
|
|
22 # is carried out in continuous time while the |
|
|
23 # effect of sampling is described by a bilinear |
|
|
24 # transformation of the sampled system. |
|
|
25 # This method works quite well if the sampling |
|
|
26 # period is "small" compared to the plant time |
|
|
27 # constants. |
|
|
28 # |
|
|
29 # This is a script file for OCTAVE. |
|
|
30 # ------------------------------------------------------------ |
|
|
31 # |
|
|
32 # continuous plant: |
|
|
33 # 1 |
|
|
34 # G(s) = -------------- |
|
|
35 # (s + 2)(s + 1) |
|
|
36 # |
|
|
37 # discretised plant with ZOH (Sampling period = Ts = 1 second) |
|
|
38 # |
|
|
39 # 0.39958z + 0.14700 |
|
|
40 # G(s) = -------------------------- |
|
|
41 # (z - 0.36788)(z - 0.13533) |
|
|
42 # |
|
|
43 # +----+ |
|
|
44 # -------------------->| W1 |---> v1 |
|
|
45 # z | +----+ |
|
|
46 # ----|-------------+ || T || => min. |
|
|
47 # | | vz infty |
|
|
48 # | +---+ v +----+ |
|
|
49 # *--->| G |--->O--*-->| W2 |---> v2 |
|
|
50 # | +---+ | +----+ |
|
|
51 # | | |
|
|
52 # | +---+ | |
|
|
53 # -----| K |<------- |
|
|
54 # +---+ |
|
|
55 # |
|
|
56 # W1 and W2 are the robustness and performancs weighting |
|
|
57 # functions |
|
|
58 |
|
|
59 # K. Mueller, <mueller@ifr.ing.tu-bs.de> |
|
|
60 # Technical University of Braunschweig, IfR |
|
|
61 |
|
|
62 echo off |
|
|
63 disp(" "); |
|
|
64 disp(" --------------------------------------------------"); |
|
|
65 disp(" Discrete H_infinity optimal control for the plant:"); |
|
|
66 disp(" "); |
|
|
67 disp(" 0.39958z + 0.14700"); |
|
|
68 disp(" G(s) = --------------------------"); |
|
|
69 disp(" (z - 0.36788)(z - 0.13533)"); |
|
|
70 disp(" --------------------------------------------------"); |
|
|
71 disp(" "); |
|
|
72 |
|
|
73 disp("sampling time:") |
|
|
74 cmd = "Ts = 1.0;"; |
|
|
75 disp(cmd); |
|
|
76 eval(cmd); |
|
|
77 disp("weighting on actuator value u"); |
|
|
78 cmd = "W1 = wgt1o(0.1, 200.0, 50.0);"; |
|
|
79 disp(cmd); |
|
|
80 eval(cmd); |
|
|
81 disp("weighting on controlled variable y"); |
|
|
82 cmd = "W2 = wgt1o(350.0, 0.05, 0.0002);"; |
|
|
83 disp(cmd); |
|
|
84 eval(cmd); |
|
|
85 # omega axis (column vector) |
|
|
86 ww = vec(logspace(-4.99, 3.99, 100)); |
|
|
87 |
|
|
88 disp("Create ZOH equivalent model of a continuous plant"); |
|
|
89 cmd = "G = tf2sys(2,[1 3 2]); Gd = c2d(G, Ts);"; |
|
|
90 run_cmd |
|
|
91 |
|
|
92 # w-plane (continuous representation of the sampled system) |
|
|
93 disp("W-plane transform of discrete time system:"); |
|
|
94 cmd = "Gw = d2c(Gd, \"bi\");"; |
|
|
95 run_cmd |
|
|
96 |
|
|
97 disp(" "); |
|
|
98 disp(" o building P..."); |
|
|
99 # need One as the pseudo transfer function One = 1 |
|
|
100 cmd = "One = ugain(1);"; |
|
|
101 disp(cmd); |
|
|
102 eval(cmd); |
|
|
103 cmd = " psys = buildssic([1 4;2 4;3 1],[3],[2 3 5],[3 4],Gw,W1,W2,One);"; |
|
|
104 run_cmd; |
|
|
105 disp(" o controller design..."); |
|
|
106 cmd = "[K, gfin, GWC] = hinfsyn(psys, 1, 1, 0.1, 10.0, 0.02);"; |
|
|
107 run_cmd |
|
|
108 |
|
|
109 disp(" "); |
|
|
110 fig_n = 1; |
|
|
111 yn = input(" * Plot magnitudes of W1KS and W2S? [n]: ","S"); |
|
|
112 if (length(yn) >= 1) |
|
|
113 if ((yn(1) == "y") || (yn(1) == 'Y')) |
|
|
114 disp(" o magnitudes of W1KS and W2S..."); |
|
|
115 gwx = sysprune(GWC, 1, 1); |
|
|
116 mag1 = bode(gwx, ww); |
|
|
117 if (columns(mag1) > 1); mag1 = mag1'; endif |
|
|
118 gwx = sysprune(GWC, 2, 1); |
|
|
119 mag2 = bode(gwx, ww); |
|
|
120 if (columns(mag2) > 1); mag2 = mag2'; endif |
|
|
121 figure(fig_n) |
|
|
122 fig_n = fig_n + 1; |
|
|
123 gset grid |
|
|
124 loglog(ww, [mag1 mag2]); |
|
|
125 endif |
|
|
126 endif |
|
|
127 |
|
|
128 Kd = c2d(K, "bi", Ts); |
|
|
129 GG = buildssic([1 2; 2 1], [], [1 2], [-2], Gd, Kd); |
|
|
130 disp(" o closed loop poles..."); |
|
|
131 damp(GG); |
|
|
132 |
|
|
133 disp(" "); |
|
|
134 yn = input(" * Plot closed loop step responses? [n]: ","S"); |
|
|
135 if (length(yn) >= 1) |
|
|
136 if ((yn(1) == "y") || (yn(1) == 'Y')) |
|
|
137 disp(" o step responses of T and KS..."); |
|
|
138 figure(fig_n) |
|
|
139 step(GG, 1, 10); |
|
|
140 endif |
|
|
141 endif |
|
|
142 |
|
|
143 # --------- End of dhinfdemo/kpm |
