|
3432
|
1 ## Copyright (C) 1996, 1998 Kai P. 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 |
|
|
17 ## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
|
|
18 |
|
3452
|
19 ## -*- texinfo -*- |
|
|
20 ## @deftypefn {Function File} {} dhinfdemo () |
|
|
21 ## Demonstrate the functions available for designining a discrete |
|
|
22 ## H_infinity controller. This is not a true discrete design. The |
|
|
23 ## design is carried out in continuous time while the effect of sampling |
|
|
24 ## is described by a bilinear transformation of the sampled system. |
|
|
25 ## This method works quite well if the sampling period is "small" |
|
|
26 ## compared to the plant time constants. |
|
3432
|
27 ## |
|
3452
|
28 ## Continuous plant: |
|
3432
|
29 ## |
|
3452
|
30 ## @example |
|
3432
|
31 ## 1 |
|
|
32 ## G(s) = -------------- |
|
|
33 ## (s + 2)(s + 1) |
|
3452
|
34 ## @end example |
|
3432
|
35 ## |
|
3452
|
36 ## Discretised plant with ZOH (Sampling period = Ts = 1 second): |
|
3432
|
37 ## |
|
3452
|
38 ## @example |
|
3432
|
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 ## +---+ |
|
3452
|
55 ## @end example |
|
3432
|
56 ## |
|
3452
|
57 ## @noindent |
|
|
58 ## W1 and W2 are the robustness and performancs weighting functions. |
|
|
59 ## @end deftypefn |
|
3432
|
60 |
|
|
61 ## K. Mueller, <mueller@ifr.ing.tu-bs.de> |
|
|
62 ## Technical University of Braunschweig, IfR |
|
|
63 |
|
|
64 echo off |
|
|
65 disp(" "); |
|
|
66 disp(" --------------------------------------------------"); |
|
|
67 disp(" Discrete H_infinity optimal control for the plant:"); |
|
|
68 disp(" "); |
|
|
69 disp(" 0.39958z + 0.14700"); |
|
|
70 disp(" G(s) = --------------------------"); |
|
|
71 disp(" (z - 0.36788)(z - 0.13533)"); |
|
|
72 disp(" --------------------------------------------------"); |
|
|
73 disp(" "); |
|
|
74 |
|
|
75 disp("sampling time:") |
|
|
76 cmd = "Ts = 1.0;"; |
|
|
77 disp(cmd); |
|
|
78 eval(cmd); |
|
|
79 disp("weighting on actuator value u"); |
|
|
80 cmd = "W1 = wgt1o(0.1, 200.0, 50.0);"; |
|
|
81 disp(cmd); |
|
|
82 eval(cmd); |
|
|
83 disp("weighting on controlled variable y"); |
|
|
84 cmd = "W2 = wgt1o(350.0, 0.05, 0.0002);"; |
|
|
85 disp(cmd); |
|
|
86 eval(cmd); |
|
|
87 ## omega axis (column vector) |
|
|
88 ww = vec(logspace(-4.99, 3.99, 100)); |
|
|
89 |
|
|
90 disp("Create ZOH equivalent model of a continuous plant"); |
|
4771
|
91 cmd = "G = tf(2,[1 3 2]); Gd = c2d(G, Ts);"; |
|
3432
|
92 run_cmd |
|
|
93 |
|
|
94 ## w-plane (continuous representation of the sampled system) |
|
|
95 disp("W-plane transform of discrete time system:"); |
|
|
96 cmd = "Gw = d2c(Gd, \"bi\");"; |
|
|
97 run_cmd |
|
|
98 |
|
|
99 disp(" "); |
|
|
100 disp(" o building P..."); |
|
|
101 ## need One as the pseudo transfer function One = 1 |
|
|
102 cmd = "One = ugain(1);"; |
|
|
103 disp(cmd); |
|
|
104 eval(cmd); |
|
|
105 cmd = " psys = buildssic([1 4;2 4;3 1],[3],[2 3 5],[3 4],Gw,W1,W2,One);"; |
|
|
106 run_cmd; |
|
|
107 disp(" o controller design..."); |
|
|
108 cmd = "[K, gfin, GWC] = hinfsyn(psys, 1, 1, 0.1, 10.0, 0.02);"; |
|
|
109 run_cmd |
|
|
110 |
|
|
111 disp(" "); |
|
|
112 fig_n = 1; |
|
|
113 yn = input(" * Plot magnitudes of W1KS and W2S? [n]: ","S"); |
|
|
114 if (length(yn) >= 1) |
|
|
115 if ((yn(1) == "y") || (yn(1) == 'Y')) |
|
|
116 disp(" o magnitudes of W1KS and W2S..."); |
|
|
117 gwx = sysprune(GWC, 1, 1); |
|
|
118 mag1 = bode(gwx, ww); |
|
|
119 if (columns(mag1) > 1); mag1 = mag1'; endif |
|
|
120 gwx = sysprune(GWC, 2, 1); |
|
|
121 mag2 = bode(gwx, ww); |
|
|
122 if (columns(mag2) > 1); mag2 = mag2'; endif |
|
|
123 figure(fig_n) |
|
|
124 fig_n = fig_n + 1; |
|
|
125 gset grid |
|
|
126 loglog(ww, [mag1 mag2]); |
|
|
127 endif |
|
|
128 endif |
|
|
129 |
|
|
130 Kd = c2d(K, "bi", Ts); |
|
|
131 GG = buildssic([1 2; 2 1], [], [1 2], [-2], Gd, Kd); |
|
|
132 disp(" o closed loop poles..."); |
|
|
133 damp(GG); |
|
|
134 |
|
|
135 disp(" "); |
|
|
136 yn = input(" * Plot closed loop step responses? [n]: ","S"); |
|
|
137 if (length(yn) >= 1) |
|
|
138 if ((yn(1) == "y") || (yn(1) == 'Y')) |
|
|
139 disp(" o step responses of T and KS..."); |
|
|
140 figure(fig_n) |
|
|
141 step(GG, 1, 10); |
|
|
142 endif |
|
|
143 endif |
|
|
144 |
|
|
145 ## --------- End of dhinfdemo/kpm |
