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1 # Copyright (C) 1993, 1994 John W. Eaton |
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2 # |
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3 # This file is part of Octave. |
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4 # |
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5 # Octave is free software; you can redistribute it and/or modify it |
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6 # under the terms of the GNU General Public License as published by the |
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7 # Free Software Foundation; either version 2, or (at your option) any |
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8 # later version. |
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9 # |
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10 # Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 # for more details. |
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14 # |
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15 # You should have received a copy of the GNU General Public License |
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16 # along with Octave; see the file COPYING. If not, write to the Free |
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17 # Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. |
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18 |
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19 function [Ad, Bd] = c2d (Ac, Bc, T) |
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20 |
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21 # Usage: [Ad, Bd] = c2d (Ac, Bc, T) |
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22 # |
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23 # converts the continuous time system described by: |
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24 # . |
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25 # x = Ac x + Bc u |
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26 # |
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27 # into a discrete time equivalent model via the matrix exponential |
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28 # |
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29 # x[n+1] = Ad x[n] + Bd u[n] |
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30 # |
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31 # assuming a zero-order hold on the input and sample time T. |
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32 |
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33 # Written by R.B. Tenison (btenison@eng.auburn.edu) |
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34 # October 1993 |
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35 |
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36 # check args |
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37 if (nargin != 3) |
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38 usage ("c2d (Ac, Bc, T)"); |
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203
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39 endif |
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40 |
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41 [ma, na] = size (Ac); |
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42 [mb, nb] = size (Bc); |
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43 |
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44 if (ma != na) |
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45 error ("c2d: Ac must be square"); |
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46 endif |
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47 |
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48 if (ma != mb) |
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49 error ("c2d: Ac and Bc must have the same number of rows"); |
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50 endif |
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51 |
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52 matexp = expm ([[Ac, Bc] * T; zeros (nb, na+nb)]); |
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53 |
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54 Ad = matexp (1:na, 1:na); |
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55 Bd = matexp (1:na, na+1:na+nb); |
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56 |
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57 endfunction |
