|
3213
|
1 # Copyright (C) 1993, 1994, 1995 John W. Eaton |
|
|
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, 675 Mass Ave, Cambridge, MA 02139, USA. |
|
|
18 |
|
|
19 function dsys = c2d (sys, opt, T) |
|
245
|
20 |
|
3213
|
21 # Usage: dsys = c2d (sys[, T]) |
|
|
22 # Usage: dsys = c2d (sys[, opt[, T]]) |
|
|
23 # inputs: |
|
|
24 # sys: system data structure (may be mixed discrete/continiuous time) |
|
|
25 # optional arguments: |
|
|
26 # opt: conversion option: |
|
|
27 # "ex" - use the matrix exponential (default) |
|
|
28 # "bi" - use the bilinear transformation |
|
|
29 # 2(z-1) |
|
|
30 # s = ----- |
|
|
31 # T(z+1) |
|
|
32 # FIXME: This option exits with an error if sys is not purely |
|
|
33 # continuous. (The ex can handle mixed systems.) |
|
|
34 # |
|
|
35 # T: sampling time; required if sys is purely continuous. |
|
|
36 # outputs: |
|
|
37 # dsys: discrete time equivalent via zero-order hold, sample each T sec. |
|
|
38 # |
|
|
39 # converts the system described by: |
|
|
40 # . |
|
|
41 # x = Ac x + Bc u |
|
|
42 # |
|
|
43 # into a discrete time equivalent model via the matrix exponential |
|
|
44 # |
|
|
45 # x[n+1] = Ad x[n] + Bd u[n] |
|
|
46 # |
|
|
47 # Note: This function adds _d to the names of the new discrete states. |
|
203
|
48 |
|
3213
|
49 # Written by R.B. Tenison (btenison@eng.auburn.edu) |
|
|
50 # October 1993 |
|
|
51 # Updated by John Ingram for system data structure August 1996 |
|
203
|
52 |
|
3213
|
53 save_val = implicit_str_to_num_ok; # save for later |
|
|
54 implicit_str_to_num_ok = 1; |
|
203
|
55 |
|
3213
|
56 # parse input arguments |
|
|
57 if(nargin < 1 | nargin > 3) |
|
|
58 usage("dsys=c2d(sys[,T])"); |
|
|
59 elseif (!is_struct(sys)) |
|
|
60 error("sys must be a system data structure"); |
|
|
61 elseif (nargin == 1) |
|
|
62 opt = "ex"; |
|
|
63 elseif (nargin == 2 & !isstr(opt) ) |
|
|
64 T = opt; |
|
|
65 opt = "ex"; |
|
203
|
66 endif |
|
|
67 |
|
3213
|
68 # check if sampling period T was passed. |
|
|
69 Ts = sysgettsam(sys); |
|
|
70 if(!exist("T")) |
|
|
71 T = Ts; |
|
|
72 if(T == 0) |
|
|
73 error("sys is purely continuous; no sampling period T provided"); |
|
|
74 endif |
|
|
75 elseif (T != Ts & Ts > 0) |
|
|
76 warning(["c2d: T=",num2str(T),", system tsam==",num2str(Ts), ... |
|
|
77 ": using T=", num2str(min(T,Ts))]); |
|
|
78 T = min(T,Ts); |
|
|
79 endif |
|
203
|
80 |
|
3213
|
81 if (!is_sample(T)) |
|
|
82 error("sampling period T must be a postive, real scalar"); |
|
|
83 elseif( ! (strcmp(opt,"ex") | strcmp(opt,"bi") ) ) |
|
|
84 error(["illegal option passed: ",opt]) |
|
203
|
85 endif |
|
|
86 |
|
3213
|
87 sys = sysupdate(sys,"ss"); |
|
|
88 [n,nz,m,p] = sysdimensions(sys); |
|
|
89 |
|
|
90 if (n == 0) |
|
|
91 warning("c2d: sys has no continuous states; setting outputs to discrete"); |
|
3228
|
92 dsys = syssetsignals(sys,"yd",ones(1:p)); |
|
3213
|
93 elseif(strcmp(opt,"ex")) |
|
|
94 # construct new state-space (a,b,c,d) for continuous subsystem |
|
|
95 [csys,Acd] = syscont(sys); # extract continuous subsystem |
|
|
96 [csys_a, csys_b, csys_c, csys_d] = sys2ss(csys); |
|
|
97 [ sys_a, sys_b, sys_c, sys_d] = sys2ss( sys); |
|
3228
|
98 if(isempty(Acd)) Bmat = sys_b; |
|
|
99 elseif(isempty(csys_b)) Bmat = Acd; |
|
3238
|
100 else Bmat = [Acd, csys_b]; endif |
|
3213
|
101 |
|
|
102 row_zer = columns(Bmat); |
|
3228
|
103 csysn = sysdimensions(csys); |
|
|
104 col_zer = csysn + row_zer; |
|
3213
|
105 |
|
3228
|
106 [csysa,csysb,csysc,csysd] = sys2ss(csys); |
|
3213
|
107 if(isempty(Bmat) ) |
|
|
108 warning("c2d: no inputs to continuous subsystem."); |
|
3228
|
109 mat = csysa; |
|
3213
|
110 else |
|
3238
|
111 mat = [csysa, Bmat ; zeros( row_zer,col_zer) ]; |
|
3213
|
112 endif |
|
|
113 |
|
|
114 matexp = expm(mat * T); |
|
|
115 |
|
3228
|
116 Abar = matexp( 1:csysn , 1:(csysn + columns(Acd)) ); |
|
|
117 Bbar = matexp( 1:csysn , (columns(Abar) + 1):columns(matexp) ); |
|
3213
|
118 |
|
3228
|
119 newnz = rows(Abar); |
|
|
120 outlist = ones(1,rows(csysc)); |
|
|
121 [stnames,innames,outnames] = sysgetsignals(csys); |
|
|
122 dsys = ss2sys(Abar,Bbar,csysc,csysd,T,0,newnz,stnames,innames, ... |
|
|
123 outnames,outlist); |
|
|
124 # rename states |
|
|
125 for ii=1:newnz |
|
|
126 strval = sprintf("%s_d",sysgetsignals(dsys,"st",ii,1)); |
|
|
127 dsys = syssetsignals(dsys,"st",strval,ii); |
|
3213
|
128 endfor |
|
203
|
129 |
|
3213
|
130 elseif(strcmp(opt,"bi")) |
|
|
131 if(is_digital(sys)) |
|
|
132 error("c2d: system is already digital") |
|
|
133 else |
|
|
134 # convert with bilinear transform |
|
|
135 [a,b,c,d,tsam,n,nz,stname,inname,outname,yd] = sys2ss(sys); |
|
|
136 IT = (2/T)*eye(size(a)); |
|
|
137 A = (IT+a)/(IT-a); |
|
|
138 iab = (IT-a)\b; |
|
|
139 tk=2/sqrt(T); |
|
|
140 B = tk*iab; |
|
|
141 C = tk*(c/(IT-a)); |
|
|
142 D = d + (c*iab); |
|
3228
|
143 stnamed = strappend(stname,"_d"); |
|
3213
|
144 dsys = ss2sys(A,B,C,D,T,0,rows(A),stnamed,inname,outname); |
|
|
145 endif |
|
|
146 else |
|
|
147 error(["Bad option=",opt]) |
|
|
148 endif |
|
|
149 |
|
|
150 implicit_str_to_num_ok = save_val; # restore value |
|
203
|
151 |
|
|
152 endfunction |
