1 ## Copyright (C) 2011 Lukas F. Reichlin
3 ## This file is part of LTI Syncope.
5 ## LTI Syncope is free software: you can redistribute it and/or modify
6 ## it under the terms of the GNU General Public License as published by
7 ## the Free Software Foundation, either version 3 of the License, or
8 ## (at your option) any later version.
10 ## LTI Syncope is distributed in the hope that it will be useful,
11 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 ## GNU General Public License for more details.
15 ## You should have received a copy of the GNU General Public License
16 ## along with LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
19 ## Convert the discrete SS model into its continuous-time equivalent.
21 ## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
22 ## Created: September 2011
25 function sys = __d2c__ (sys, tsam, method = "zoh", w0 = 0)
28 case {"z", "s"} # {"zoh", "std"}
29 [sys.a, sys.b, sys.c, sys.d, sys.e] = __dss2ss__ (sys.a, sys.b, sys.c, sys.d, sys.e);
30 [n, m] = size (sys.b); # n: states, m: inputs
31 tmp = logm ([sys.a, sys.b; zeros(m,n), eye(m)]) / tsam;
32 if (norm (imag (tmp), inf) > sqrt (eps))
33 warning ("ss: d2c: possibly inaccurate results");
35 sys.a = real (tmp(1:n, 1:n));
36 sys.b = real (tmp(1:n, n+1:n+m));
38 case {"t", "b", "p"} # {"tustin", "bilin", "prewarp"}
39 if (method(1) == "p") # prewarping
40 beta = w0 / tan (w0*tsam/2);
45 [sys.a, sys.b, sys.c, sys.d] = slab04md (sys.a, sys.b, sys.c, sys.d, 1, beta, true);
47 [sys.a, sys.b, sys.c, sys.d, sys.e] = __dss_bilin__ (sys.a, sys.b, sys.c, sys.d, sys.e, beta, true);
51 error ("ss: d2c: %s is an invalid or missing method", method);