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1 ## Copyright (C) 1996, 1998 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 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[K}, @var{gain}, @var{kc}, @var{kf}, @var{pc}, @var{pf}] = h2syn (@var{asys}, @var{nu}, @var{ny}, @var{tol}) |
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21 ## Design H2 optimal controller per procedure in |
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22 ## Doyle, Glover, Khargonekar, Francis, "State Space Solutions to Standard |
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23 ## H2 and Hinf Control Problems", IEEE TAC August 1989 |
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24 ## |
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25 ## Discrete time control per Zhou, Doyle, and Glover, ROBUST AND OPTIMAL |
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26 ## CONTROL, Prentice-Hall, 1996 |
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27 ## |
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28 ## @strong{Inputs} input system is passed as either |
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29 ## @table @var |
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30 ## @item asys |
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31 ## system data structure (see ss, sys2ss) |
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32 ## @itemize @bullet |
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33 ## @item controller is implemented for continuous time systems |
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34 ## @item controller is NOT implemented for discrete time systems |
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35 ## @end itemize |
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36 ## @item nu |
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37 ## number of controlled inputs |
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38 ## @item ny |
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39 ## number of measured outputs |
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40 ## @item tol |
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41 ## threshhold for 0. Default: 200*eps |
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42 ## @end table |
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43 ## |
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44 ## @strong{Outputs} |
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45 ## @table @var |
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46 ## @item k |
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47 ## system controller |
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48 ## @item gain |
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49 ## optimal closed loop gain |
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50 ## @item kc |
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51 ## full information control (packed) |
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52 ## @item kf |
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53 ## state estimator (packed) |
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54 ## @item pc |
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55 ## ARE solution matrix for regulator subproblem |
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56 ## @item pf |
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57 ## ARE solution matrix for filter subproblem |
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58 ## @end table |
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59 ## @end deftypefn |
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60 |
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61 ## Updated for System structure December 1996 by John Ingram |
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62 |
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63 function [K, gain, Kc, Kf, Pc, Pf] = h2syn (Asys, nu, ny, tol) |
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64 |
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65 if ((nargin < 3) | (nargin > 4)) |
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66 usage("[K,gain, Kc, Kf, Pc, Pf] = h2syn(Asys,nu,ny[,tol])"); |
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67 elseif(nargin == 3 ) |
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68 [chkdgkf,dgs] = is_dgkf(Asys,nu,ny); |
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69 elseif(nargin == 4) |
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70 [chkdgkf,dgs] = is_dgkf(Asys,nu,ny,tol); |
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71 endif |
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72 |
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73 if (!chkdgkf ) |
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74 disp("h2syn: system does not meet required assumptions") |
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75 help is_dgkf |
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76 error("h2syn: exit"); |
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77 endif |
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78 |
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79 ## extract dgs information |
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80 nw = dgs.nw; nu = dgs.nu; |
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81 A = dgs.A; Bw = dgs.Bw; Bu = dgs.Bu; |
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82 Cz = dgs.Cz; Dzw = dgs.Dzw; Dzu = dgs.Dzu; nz = dgs.nz; |
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83 Cy = dgs.Cy; Dyw = dgs.Dyw; Dyu = dgs.Dyu; ny = dgs.ny; |
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84 d22nz = dgs.Dyu_nz; |
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85 dflg = dgs.dflg; |
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86 |
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87 if(norm(Dzw,Inf) > norm([Dzw, Dzu ; Dyw, Dyu],Inf)*1e-12) |
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88 warning("h2syn: Dzw nonzero; feedforward not implemented") |
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89 Dzw |
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90 D = [Dzw, Dzu ; Dyw, Dyu] |
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91 endif |
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92 |
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93 ## recover i/o transformations |
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94 Ru = dgs.Ru; Ry = dgs.Ry; |
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95 [ncstates, ndstates, nout, nin] = sysdimensions(Asys); |
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96 Atsam = sysgettsam(Asys); |
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97 [Ast, Ain, Aout] = sysgetsignals(Asys); |
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98 |
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99 if(dgs.dflg == 0) |
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100 Pc = are(A,Bu*Bu',Cz'*Cz); # solve control, filtering ARE's |
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101 Pf = are(A',Cy'*Cy,Bw*Bw'); |
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102 F2 = -Bu'*Pc; # calculate feedback gains |
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103 L2 = -Pf*Cy'; |
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104 |
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105 AF2 = A + Bu*F2; |
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106 AL2 = A + L2*Cy; |
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107 CzF2 = Cz + (Dzu/Ru)*F2; |
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108 BwL2 = Bw+L2*(Ry\Dyw); |
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109 |
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110 else |
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111 ## discrete time solution |
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112 error("h2syn: discrete-time case not yet implemented") |
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113 Pc = dare(A,Bu*Bu',Cz'*Cz); |
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114 Pf = dare(A',Cy'*Cy,Bw*Bw'); |
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115 endif |
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116 |
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117 nn = ncstates + ndstates; |
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118 In = eye(nn); |
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119 KA = A + Bu*F2 + L2*Cy; |
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120 Kc1 = ss(AF2,Bw,CzF2,zeros(nz,nw)); |
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121 Kf1 = ss(AL2,BwL2,F2,zeros(nu,nw)); |
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122 |
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123 g1 = h2norm(Kc1); |
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124 g2 = h2norm(Kf1); |
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125 |
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126 ## compute optimal closed loop gain |
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127 gain = sqrt ( g1*g1 + g2*g2 ); |
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128 |
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129 if(nargout) |
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130 Kst = strappend(Ast,"_K"); |
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131 Kin = strappend(Aout((nout-ny+1):(nout)),"_K"); |
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132 Kout = strappend(Ain((nin-nu+1):(nin)),"_K"); |
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133 |
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134 ## compute systems for return |
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135 K = ss(KA,-L2/Ru,Ry\F2,zeros(nu,ny),Atsam,ncstates,ndstates,Kst,Kin,Kout); |
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136 endif |
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137 |
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138 if (nargout > 2) |
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139 ## system full information control state names |
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140 stname2 = strappend(Ast,"_FI"); |
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141 |
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142 ## system full information control input names |
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143 inname2 = strappend(Ast,"_FI_in"); |
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144 |
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145 ## system full information control output names |
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146 outname2 = strappend(Aout(1:(nout-ny)),"_FI_out"); |
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147 |
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148 nz = rows (Cz); |
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149 nw = columns (Bw); |
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150 |
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151 Kc = ss(AF2, In, CzF2, zeros(nz,nn), Atsam, ... |
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152 ncstates, ndstates, stname2, inname2, outname2); |
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153 endif |
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154 |
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155 if (nargout >3) |
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156 ## fix system state estimator state names |
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157 stname3 = strappend(Ast,"_Kf"); |
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158 |
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159 ## fix system state estimator input names |
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160 inname3 = strappend(Ast,"_Kf_noise"); |
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161 |
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162 ## fix system state estimator output names |
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163 outname3 = strappend(Ast,"_est"); |
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164 |
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165 Kf = ss(AL2, BwL2, In, zeros(nn,nw),Atsam, ... |
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166 ncstates, ndstates, stname3, inname3,outname3); |
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167 endif |
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168 |
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169 endfunction |
