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1 ## Copyright (C) 1996 Auburn University. All rights reserved. |
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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, 59 Temple Place, Suite 330, Boston, MA 02111 USA. |
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18 ## |
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19 ## Written by A. S. Hodel a.s.hodel@eng.auburn.edu |
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20 |
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21 function [retsys, nc, no, cflg, oflg] = sysmin (sys, flg); |
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22 |
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23 ## [retsys,nc,no] = sysmin(sys{,flg}); |
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24 ## return a minimal (or reduced order) system |
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25 ## inputs: |
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26 ## sys: system data structure |
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27 ## flg: 0 [default] return minimal system; state names lost |
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28 ## : 1 return system with physical states removed that |
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29 ## are either uncontrollable or unobservable |
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30 ## (cannot reduce further without discarding physical |
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31 ## meaning of states) |
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32 ## outputs: |
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33 ## retsys: returned system |
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34 ## nc: number of controllable states in the returned system |
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35 ## no: number of observable states in the returned system |
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36 ## cflg: is_controllable(retsys) |
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37 ## oflg: is_observable(retsys) |
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38 |
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39 switch(nargin) |
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40 case(1), flg = 0; |
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41 case(2), jnk = flg; # dummy operation |
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42 otherwise, |
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43 usage("[retsys,nc,no] = sysmin(sys{,flg})"); |
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44 endswitch |
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45 dflg = is_digital(sys,flg); |
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46 Ts = sysgettsam(sys); |
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47 switch(flg) |
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48 case(0), |
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49 ## reduce to a minimal system |
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50 [aa,bb,cc,dd] = sys2ss(sys); |
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51 [cflg,Uc] = is_controllable(aa,bb); |
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52 if(!cflg) |
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53 ## reduce to controllable states |
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54 if(!isempty(Uc)) |
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55 aa = Uc'*aa*Uc; |
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56 bb = Uc'*bb; |
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57 cc = cc*Uc; |
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58 else |
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59 aa = bb = cc = []; |
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60 endif |
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61 endif |
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62 if(!isempty(aa)) |
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63 [oflg,Uo] = is_observable(aa,cc); |
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64 if(!oflg) |
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65 if(!isempty(Uo)) |
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66 aa = Uo'*aa*Uo; |
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67 bb = Uo'*bb; |
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68 cc = cc*Uo; |
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69 else |
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70 aa = bb = cc = []; |
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71 endif |
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72 endif |
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73 endif |
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74 switch(dflg) |
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75 case(0), |
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76 nc = no = nn = columns(aa); |
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77 nz = 0; |
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78 case(1), |
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79 nc = no = nz = columns(aa); |
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80 nn = 0; |
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81 endswitch |
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82 inname = sysgetsignals(sys,"in"); |
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83 outname= sysgetsignals(sys,"out"); |
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84 retsys = ss2sys(aa,bb,cc,dd,Ts,nn,nz,[],inname,outname); |
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85 case(1), |
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86 ## reduced model with physical states |
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87 [cflg,Uc] = is_controllable(sys); xc = find(max(abs(Uc')) != 0); |
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88 [oflg,Uo] = is_observable(sys); xo = find(max(abs(Uo')) != 0); |
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89 xx = intersection(xc,xo); |
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90 if(isempty(xx)) xx = 0; endif # signal no states in reduced model |
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91 retsys = sysprune(sys,[],[],xx); |
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92 otherwise, |
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93 error("illegal value of flg=%d",flg); |
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94 endswitch |
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95 if(sysdimensions(retsys,"st") > 0) |
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96 [cflg,Uc] = is_controllable(retsys); nc = columns(Uc); |
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97 [oflg,Uo] = is_observable(retsys); no = columns(Uo); |
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98 else |
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99 nc = no = 0; |
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100 endif |
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101 endfunction |
