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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 |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{retsys}, @var{nc}, @var{no}] =} sysmin (@var{sys}, @var{flg}) |
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21 ## Returns a minimal (or reduced order) system |
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22 ## |
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23 ## @strong{Inputs} |
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24 ## @table @var |
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25 ## @item sys |
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26 ## System data structure |
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27 ## @item flg |
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28 ## When equal to 0 (default value), returns minimal system, |
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29 ## in which state names are lost; when equal to 1, returns system |
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30 ## with physical states removed that are either uncontrollable or |
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31 ## unobservable (cannot reduce further without discarding physical |
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32 ## meaning of states). |
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33 ## @end table |
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34 ## @strong{Outputs} |
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35 ## @table @var |
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36 ## @item retsys |
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37 ## Returned system. |
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38 ## @item nc |
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39 ## Number of controllable states in the returned system. |
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40 ## @item no |
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41 ## Number of observable states in the returned system. |
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42 ## @item cflg |
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43 ## @code{is_controllable(retsys)}. |
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44 ## @item oflg |
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45 ## @code{is_observable(retsys)}. |
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46 ## @end table |
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47 ## @end deftypefn |
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48 |
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49 ## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu> |
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50 |
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51 function [retsys, nc, no, cflg, oflg] = sysmin (sys, flg) |
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52 |
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53 switch(nargin) |
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54 case(1), flg = 0; |
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55 case(2), jnk = flg; # dummy operation |
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56 otherwise, |
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57 print_usage (); |
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58 endswitch |
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59 dflg = is_digital(sys,2); |
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60 [n,nz,m,p] = sysdimensions(sys); |
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61 if(n*nz > 0) |
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62 # both continuous and discrete states |
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63 [aa,bb,cc,dd,tsam,n,nz,stnam,innam,outnam,yd] = sys2ss(sys); |
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64 crng = 1:n; |
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65 drng = n+(1:nz); |
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66 |
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67 # get minimal realization of continuous part |
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68 Ac = aa(crng,crng); |
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69 Acd = aa(crng,drng); |
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70 Adc = aa(drng,crng); |
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71 Ad = aa(drng,drng); |
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72 Bc = bb(crng,:); |
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73 Bd = bb(drng,:); |
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74 Cc = cc(:,crng); |
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75 Cd = cc(:,drng); |
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76 |
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77 cstnam = stnam(crng); |
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78 dstnam = stnam(drng); |
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79 cinnam = __sysconcat__(innam,stnam(drng)); |
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80 coutnam = __sysconcat__(outnam,stnam(drng)); |
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81 csys = ss(Ac,[Bc,Acd],[Cc;Adc]); |
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82 csys = syssetsignals(csys,"st",cstnam); |
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83 csys = syssetsignals(csys,"in",cinnam); |
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84 csys = syssetsignals(csys,"out",coutnam); |
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85 |
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86 # reduce continuous system, recombine with discrete part |
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87 csys = sysmin(csys,flg); |
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88 cn = sysdimensions(csys); |
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89 |
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90 if(cn == 0) |
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91 # continuous states are removed; just reduce the discrete part |
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92 sys = sysprune(sys,1:p,1:m,drng); |
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93 retsys = sysmin(sys,flg); |
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94 else |
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95 # extract updated parameters from reduced continuous system |
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96 [caa,cbb,ccc,cdd,ctsam,cn,cnz,cstnam,cinnam,coutnam] = sys2ss(csys); |
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97 crng = 1:cn; |
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98 Ac = caa; |
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99 Bc = cbb(:,1:m); |
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100 Acd = cbb(:,m+(1:nz)); |
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101 Cc = ccc(1:p,:); |
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102 Adc = ccc(p + (1:nz),:); |
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103 |
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104 # recombine to reduce discrete part of the system |
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105 dinnam = __sysconcat__(innam,cstnam); |
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106 doutnam = __sysconcat__(outnam,cstnam); |
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107 dsys = ss(Ad,[Bd,Adc],[Cd;Acd],[],tsam); |
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108 dsys = syssetsignals(dsys,"st",dstnam); |
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109 dsys = syssetsignals(dsys,"in",dinnam); |
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110 dsys = syssetsignals(dsys,"out",doutnam); |
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111 |
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112 # reduce discrete subsystem |
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113 dsys = sysmin(dsys); |
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114 [n1,nz] = sysdimensions(dsys); |
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115 if(nz == 0) |
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116 # discrete subsystem is not needed |
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117 retsys = sysprune(csys,1:p,1:m); |
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118 else |
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119 # combine discrete, continuous subsystems |
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120 [Ad,dbb,dcc] = sys2ss(dsys); |
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121 dstnam = sysgetsignals(dsys,"st"); |
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122 Bd = dbb(:,1:m); |
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123 Adc = dbb(:,m+(1:cn)); |
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124 Cd = dcc(1:p,:); |
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125 Acd = dcc(p+(1:cn),:); |
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126 stnam = __sysconcat__(cstnam,dstnam); |
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127 aa = [Ac, Acd; Adc, Ad]; |
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128 bb = [Bc; Bd]; |
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129 cc = [Cc, Cd]; |
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130 retsys = ss([Ac, Acd; Adc, Ad], [Bc ; Bd], [Cc, Cd], dd, tsam, ... |
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131 cn, nz, stnam, innam, outnam, find(yd == 1)); |
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132 end |
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133 endif |
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134 else |
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135 Ts = sysgettsam(sys); |
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136 switch(flg) |
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137 case(0), |
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138 ## reduce to a minimal system |
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139 [aa,bb,cc,dd] = sys2ss(sys); |
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140 [cflg,Uc] = is_controllable(aa,bb); |
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141 if(!cflg) |
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142 ## reduce to controllable states |
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143 if(!isempty(Uc)) |
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144 aa = Uc'*aa*Uc; |
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145 bb = Uc'*bb; |
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146 cc = cc*Uc; |
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147 else |
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148 aa = bb = cc = []; |
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149 endif |
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150 endif |
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151 if(!isempty(aa)) |
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152 [oflg,Uo] = is_observable(aa,cc); |
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153 if(!oflg) |
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154 if(!isempty(Uo)) |
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155 aa = Uo'*aa*Uo; |
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156 bb = Uo'*bb; |
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157 cc = cc*Uo; |
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158 else |
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159 aa = bb = cc = []; |
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160 endif |
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161 endif |
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162 endif |
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163 switch(dflg) |
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164 case(0), |
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165 nc = no = nn = columns(aa); |
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166 nz = 0; |
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167 case(1), |
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168 nc = no = nz = columns(aa); |
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169 nn = 0; |
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170 endswitch |
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171 innam = sysgetsignals(sys,"in"); |
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172 outnam= sysgetsignals(sys,"out"); |
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173 retsys = ss(aa,bb,cc,dd,Ts,nn,nz,[],innam,outnam); |
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174 case(1), |
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175 ## reduced model with physical states |
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176 [cflg,Uc] = is_controllable(sys); xc = find(max(abs(Uc')) != 0); |
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177 [oflg,Uo] = is_observable(sys); xo = find(max(abs(Uo')) != 0); |
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178 xx = intersection(xc,xo); |
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179 if(isempty(xx)) xx = 0; endif # signal no states in reduced model |
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180 retsys = sysprune(sys,[],[],xx); |
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181 otherwise, |
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182 error ("invalid value of flg = %d", flg); |
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183 endswitch |
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184 if(sysdimensions(retsys,"st") > 0) |
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185 [cflg,Uc] = is_controllable(retsys); nc = columns(Uc); |
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186 [oflg,Uo] = is_observable(retsys); no = columns(Uo); |
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187 else |
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188 nc = no = 0; |
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189 endif |
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190 endif |
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191 endfunction |
