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diff --git a/modules/cacsd/macros/findABCD.sci b/modules/cacsd/macros/findABCD.sci new file mode 100755 index 000000000..b57e74f11 --- /dev/null +++ b/modules/cacsd/macros/findABCD.sci @@ -0,0 +1,115 @@ +function [sys,K,Q,Ry,S,rcnd]=findABCD(s,n,l,R,meth,nsmpl,tol,printw) + sys=[];K=[];Q=[];Ry=[];S=[];rcnd=[]; + [nargout,nargin] = argn(0) + //FINDABCD Finds the system matrices and the Kalman gain of a discrete-time + // system, given the system order and the relevant part of the + // R factor of the concatenated block-Hankel matrices, using subspace + // identification techniques (MOESP and/or N4SID). + // + // [SYS,K] = FINDABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW) computes a state- + // space realization SYS = (A,B,C,D) (an ss object), and the Kalman + // predictor gain K (if NSMPL > 0). The model structure is: + // + // x(k+1) = Ax(k) + Bu(k) + Ke(k), k >= 1, + // y(k) = Cx(k) + Du(k) + e(k), + // + // where x(k) and y(k) are vectors of length N and L, respectively. + // + // [SYS,K,Q,Ry,S,RCND] = FINDABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW) also + // returns the state, output, and state-output (cross-)covariance + // matrices Q, Ry, and S (used for computing the Kalman gain), as well as + // the vector RCND of length lr containing the reciprocal condition numbers + // of the matrices involved in rank decisions, least squares or Riccati + // equation solutions, where + // lr = 4, if Kalman gain matrix K is not required, and + // lr = 12, if Kalman gain matrix K is required. + // + // S is the number of block rows in the block-Hankel matrices. + // + // METH is an option for the method to use: + // METH = 1 : MOESP method with past inputs and outputs; + // = 2 : N4SID method; + // = 3 : combined method: A and C via MOESP, B and D via N4SID. + // Default: METH = 3. + // Matrix R, computed by FINDR, should be determined with suitable arguments + // METH and JOBD. METH = 1 and JOBD = 1 must be used in findR, for METH = 1 + // in FINDABCD; METH = 1 must be used in FINDR, for METH = 3 in FINDABCD. + // + // NSMPL is the total number of samples used for calculating the covariance + // matrices and the Kalman predictor gain. This parameter is not needed if + // the covariance matrices and/or the Kalman predictor gain matrix are not + // desired. If NSMPL = 0, then K, Q, Ry, and S are not computed. + // Default: NSMPL = 0. + // + // TOL is the tolerance used for estimating the rank of matrices. + // If TOL > 0, then the given value of TOL is used as a lower bound + // for the reciprocal condition number. + // Default: prod(size(matrix))*epsilon_machine where epsilon_machine + // is the relative machine precision. + // + // PRINTW is a select for printing the warning messages. + // PRINTW = 1: print warning messages; + // = 0: do not print warning messages. + // Default: PRINTW = 0. + // + // The number of output arguments may vary, but should correspond to the + // input arguments, e.g., + // SYS = FINDABCD(S,N,L,R,METH) or + // [SYS,RCND] = FINDABCD(S,N,L,R,METH) just return SYS, or SYS and RCND. + // + // See also FINDAC, FINDBD, FINDBDK, FINDR, ORDER, SIDENT + // + + // V. Sima 18-01-2000. + // + // Revisions: + // + + nin = nargin; + nout = nargout; + // + if nin<8 then + printw = 0; + end + if nin<7 then tol = 0;end + if tol==[] then tol = 0;end + + if nin<6 then nsmpl = 0;end + if nsmpl==[] then nsmpl = 0;end + + if nin<5 then meth = 3;end + if meth==[] then meth = 3;end + + if nin<4 then + error(msprintf(gettext("%s: Wrong number of input arguments: %d to %d expected.\n"),"findABCD",4,8)); + end + // + // Compute all system matrices. + job = 1; + if nout==1 then + [A,C,B,D] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + elseif nout>=2 then + if nsmpl==0 then + // Here K means rcnd. + [A,C,B,D,K] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + elseif nout==2 then + [A,C,B,D,K] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + elseif nout==3 then + [A,C,B,D,K,Q] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + elseif nout==4 then + [A,C,B,D,K,Q,Ry] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + elseif nout==5 then + [A,C,B,D,K,Q,Ry,S] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + elseif nout==6 then + [A,C,B,D,K,Q,Ry,S,rcnd] = sident(meth,job,s,n,l,R,tol,nsmpl,[],[],printw); + else + error(msprintf(gettext("%s: Wrong number of output arguments: %d to %d expected.\n"),"findABCD",1,6)); + end + else + error(msprintf(gettext("%s: Wrong number of output arguments: %d to %d expected.\n"),"findABCD",1,6)); + end + // + sys = syslin(1,A,B,C,D); + // + // end findABCD +endfunction |