Mercurial > octave
view scripts/control/lqg.m @ 3346:8dd4718801fd
[project @ 1999-11-09 18:18:12 by jwe]
author | jwe |
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date | Tue, 09 Nov 1999 18:18:37 +0000 |
parents | f7e4a95916f2 |
children | 69b167451491 |
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# Copyright (C) 1996, 1997 Auburn University. All Rights Reserved # # This file is part of Octave. # # Octave is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the # Free Software Foundation; either version 2, or (at your option) any # later version. # # Octave is distributed in the hope that it will be useful, but WITHOUT # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License # for more details. # # You should have received a copy of the GNU General Public License # along with Octave; see the file COPYING. If not, write to the Free # Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA. ## -*- texinfo -*- ## @deftypefn {Function File } {[@var{K}, @var{Q}, @var{P}, @var{Ee}, @var{Er}] =} lqg(@var{sys}, @var{Sigw}, @var{Sigv}, @var{Q}, @var{R}, @var{in_idx}) ## Design a linear-quadratic-gaussian optimal controller for the system ## @example ## dx/dt = A x + B u + G w [w]=N(0,[Sigw 0 ]) ## y = C x + v [v] ( 0 Sigv ]) ## @end example ## or ## @example ## x(k+1) = A x(k) + B u(k) + G w(k) [w]=N(0,[Sigw 0 ]) ## y(k) = C x(k) + v(k) [v] ( 0 Sigv ]) ## @end example ## ## @strong{Inputs} ## @table @var ## @item sys ## system data structure ## @item Sigw, Sigv ## intensities of independent Gaussian noise processes (as above) ## @item Q, R ## state, control weighting respectively. Control ARE is ## @item in_idx ## indices of controlled inputs ## ## default: last dim(R) inputs are assumed to be controlled inputs, all ## others are assumed to be noise inputs. ## @end table ## @strong{Outputs} ## @table @var ## @item K ## system data structure format LQG optimal controller ## (Obtain A,B,C matrices with @code{sys2ss}, @code{sys2tf}, or @code{sys2zp} as appropriate) ## @item P ## Solution of control (state feedback) algebraic Riccati equation ## @item Q ## Solution of estimation algebraic Riccati equation ## @item Ee ## estimator poles ## @item Es ## controller poles ## @end table ## @end deftypefn ## See also: h2syn, lqe, lqr function [K,Q1,P1,Ee,Er] = lqg(sys,Sigw,Sigv,Q,R,input_list) # Written by A. S. Hodel August 1995; revised for new system format # August 1996 sav_val = implicit_str_to_num_ok; implicit_str_to_num_ok = 1; if ( (nargin < 5) | (nargin > 6)) usage("[K,Q1,P1,Ee,Er] = lqg(sys,Sigw, Sigv,Q,R{,input_list})"); elseif(!is_struct(sys) ) error("sys must be in system data structure"); endif DIG = is_digital(sys); [A,B,C,D,tsam,n,nz,stname,inname,outname] = sys2ss(sys); [n,nz,nin,nout] = sysdimensions(sys); if(nargin == 5) #construct default input_list input_list = (columns(Sigw)+1):nin; endif if( !(n+nz) ) error(["lqg: 0 states in system"]); elseif(nin != columns(Sigw)+ columns(R)) error(["lqg: sys has ",num2str(nin)," inputs, dim(Sigw)=", ... num2str(columns(Sigw)),", dim(u)=",num2str(columns(R))]) elseif(nout != columns(Sigv)) error(["lqg: sys has ",num2str(nout)," outputs, dim(Sigv)=", ... num2str(columns(Sigv)),")"]) elseif(length(input_list) != columns(R)) error(["lqg: length(input_list)=",num2str(length(input_list)), ... ", columns(R)=", num2str(columns(R))]); endif varname = list("Sigw","Sigv","Q","R"); for kk=1:length(varname); eval(sprintf("chk = is_square(%s);",nth(varname,kk))); if(! chk ) error("lqg: %s is not square",nth(varname,kk)); endif endfor # permute (if need be) if(nargin == 6) all_inputs = sysreorder(nin,input_list); B = B(:,all_inputs); inname = inname(all_inputs); endif # put parameters into correct variables m1 = columns(Sigw); m2 = m1+1; G = B(:,1:m1); B = B(:,m2:nin); # now we can just do the design; call dlqr and dlqe, since all matrices # are not given in Cholesky factor form (as in h2syn case) if(DIG) [Ks, P1, Er] = dlqr(A,B,Q,R); [Ke, Q1, jnk, Ee] = dlqe(A,G,C,Sigw,Sigv); else [Ks, P1, Er] = lqr(A,B,Q,R); [Ke, Q1, Ee] = lqe(A,G,C,Sigw,Sigv); endif Ac = A - Ke*C - B*Ks; Bc = Ke; Cc = -Ks; Dc = zeros(rows(Cc),columns(Bc)); # fix state names stname1 = strappend(stname,"_e"); # fix controller output names outname1 = strappend(inname(m2:nin),"_K"); # fix controller input names inname1 = strappend(outname,"_K"); if(DIG) K = ss2sys(Ac,Bc,Cc,Dc,tsam,n,nz,stname1,inname1,outname1,1:rows(Cc)); else K = ss2sys(Ac,Bc,Cc,Dc,tsam,n,nz,stname,inname1,outname1); endif implicit_str_to_num_ok = sav_val; endfunction