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1 ## Copyright (C) 1996 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 |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License 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, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## Usage: [Ad, Bd] = c2d (Ac, Bc, T) |
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21 ## |
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22 ## converts the continuous time system described by: |
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23 ## . |
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24 ## x = Ac x + Bc u |
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25 ## |
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26 ## into a discrete time equivalent model via the matrix exponential |
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27 ## |
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28 ## x[n+1] = Ad x[n] + Bd u[n] |
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29 ## |
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30 ## assuming a zero-order hold on the input and sample time T. |
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31 |
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32 ## Author: R.B. Tenison <btenison@eng.auburn.edu> |
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33 ## Created: October 1993 |
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34 ## Adapted-By: jwe |
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35 |
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36 function [Ad, Bd] = c2d (Ac, Bc, T) |
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37 |
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38 ## check args |
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39 if (nargin != 3) |
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40 usage ("c2d (Ac, Bc, T)"); |
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203
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41 endif |
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42 |
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43 [ma, na] = size (Ac); |
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44 [mb, nb] = size (Bc); |
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45 |
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46 if (ma != na) |
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47 error ("c2d: Ac must be square"); |
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48 endif |
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49 |
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50 if (ma != mb) |
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51 error ("c2d: Ac and Bc must have the same number of rows"); |
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52 endif |
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53 |
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54 matexp = expm ([[Ac, Bc] * T; (zeros (nb, na+nb))]); |
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55 |
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56 Ad = matexp (1:na, 1:na); |
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57 Bd = matexp (1:na, na+1:na+nb); |
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58 |
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59 endfunction |
