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diff --git a/modules/cacsd/macros/findBDK.sci b/modules/cacsd/macros/findBDK.sci new file mode 100755 index 000000000..85730d0a3 --- /dev/null +++ b/modules/cacsd/macros/findBDK.sci @@ -0,0 +1,123 @@ +function [B,D,K,Q,Ry,S,rcnd]=findBDK(s,n,l,R,A,C,meth,job,nsmpl,tol,printw) + B=[];D=[];K=[];Q=[];Ry=[];S=[];rcnd=[]; + [nargout,nargin] = argn(0) + //FINDBDK Finds the system matrices B and D and the Kalman gain of a discrete-time + // system, given the system order, the matrices A and C, and the relevant + // part of the R factor of the concatenated block-Hankel matrices, using + // subspace identification techniques (MOESP or N4SID). + // + // [B,D,K] = FINDBDK(S,N,L,R,A,C,METH,JOB,NSMPL,TOL,PRINTW) computes the + // system matrices B (if JOB = 1), B and D (if JOB = 2), 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. + // + // [B,D,RCND] = FINDBDK(S,N,L,R,A,C,METH,JOB) also returns the vector + // RCND of length 4 containing the reciprocal condition numbers of the + // matrices involved in rank decisions. + // + // [B,D,K,Q,Ry,S,RCND] = FINDBDK(S,N,L,R,A,C,METH,JOB,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 12 containing the reciprocal condition numbers + // of the matrices involved in rank decisions, least squares or Riccati + // equation solutions. + // + // 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. + // Default: METH = 2. + // 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 FINDBDK. Using METH = 1 in FINDR and METH = 2 in FINDBDK is allowed. + // + // JOB is an option specifying which system matrices should be computed: + // JOB = 1 : compute the matrix B; + // = 2 : compute the matrices B and D. + // Default: JOB = 2. + // + // 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., + // B = FINDBDK(S,N,L,R,A,C,METH,1) or + // [B,D] = FINDBDK(S,N,L,R,A,C,METH,2) or + // [B,D,RCND] = FINDBDK(S,N,L,R,A,C,METH,2) + // return B, or B and D, or B, D, and RCND, respectively. + // + // See also FINDABCD, FINDAC, FINDBD, FINDR, ORDER, SIDENT + // + + // V. Sima 18-01-2000. + // + // Revisions: + // V. Sima, July 2000. + // + + nin = nargin; + nout = nargout; + // + if nin<11 then printw = 0;end + if nin<10 then tol = 0;end + if tol==[] then tol = 0,end + if nin<9 then nsmpl = 0;end + if nsmpl==[] then nsmpl = 0;end + if nin<8 then job = 2;end + if job==[] then job = 2;end + if nin<7 then meth = 2;end + if meth == [] then meth = 2;end + if nin<6 then + error(msprintf(gettext("%s: Wrong number of input arguments: %d to %d expected.\n"),"findBDK",6,11)); + end + // + jobl = job+2; + // + // Compute system matrices B and D. + if nout==1 then + B = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + elseif nout==2 then + // If job = 1 and nsmpl > 0, D means K. + // If job = 1 and nsmpl = 0, D means rcnd. + [B,D] = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + elseif nout==3 then + // If below, job = 1 and nsmpl = 0, D means rcnd, K is not assigned. + // If job = 1 and nsmpl > 0, D means K, K means Q. + [B,D,K] = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + elseif nout==4 then + // If job = 1 and nsmpl > 0, D means K, K means Q, Q means Ry. + [B,D,K,Q] = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + elseif nout==5 then + // If job = 1 and nsmpl > 0, D means K, K means Q, Q means Ry, Ry means S. + [B,D,K,Q,Ry] = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + elseif nout==6 then + // If job = 1 and nsmpl > 0, D means K, K means Q, Q means Ry, + // Ry means S, S means rcnd. + [B,D,K,Q,Ry,S] = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + elseif nout==7 then + [B,D,K,Q,Ry,S,rcnd] = sident(meth,jobl,s,n,l,R,tol,nsmpl,A,C,printw); + else + error(msprintf(gettext("%s: Wrong number of output arguments: %d to %d expected.\n"),"findBDK",1,7)); + end + // + // end findBDK +endfunction |