findAC - discrete-time system subspace identification

Calling Sequence

[A,C] = findAC(S,N,L,R,METH,TOL,PRINTW)

[A,C,RCND] = findAC(S,N,L,R,METH,TOL,PRINTW)

Parameters

• S : integer, the number of block rows in the block-Hankel matrices
• N : integer
• L : integer
• R : matrix, relevant part of the R factor of the concatenated block-Hankel matrices computed by a call to findr.
• METH : integer, an option for the method to use
  • = 1 : MOESP method with past inputs and outputs;
  • = 2 : N4SID method;

  Default: METH = 3.

• TOL : 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 : integer, switch for printing the warning messages.
  • PRINTW = 1: print warning messages;
  • = 0 : do not print warning messages.

  Default: PRINTW = 0.

• A : matrix, state system matrix
• C : matrix, output system matrix
• RCND : vector of length 4, condition numbers of the matrices involved in rank decision

Description

finds the system matrices A and C 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 or N4SID).

*[A,C] = findAC(S,N,L,R,METH,TOL,PRINTW) computes the system matrices A and C. 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.

*[A,C,RCND] = findAC(S,N,L,R,METH,TOL,PRINTW) also returns the vector RCND of length 4 containing the condition numbers of the matrices involved in rank decisions.

Matrix R, computed by findR, should be determined with suitable arguments METH and JOBD.

Examples

//generate data from a given linear system
A = [ 0.5, 0.1,-0.1, 0.2;
      0.1, 0,  -0.1,-0.1;      
     -0.4,-0.6,-0.7,-0.1;  
      0.8, 0,  -0.6,-0.6];      
B = [0.8;0.1;1;-1];
C = [1 2 -1 0];
SYS=syslin(0.1,A,B,C);
nsmp=100;
U=prbs_a(nsmp,nsmp/5);
Y=(flts(U,SYS)+0.3*rand(1,nsmp,'normal'));

// Compute R
S=15;L=1;
[R,N,SVAL] = findR(S,Y',U');

N=3;
METH=3;TOL=-1;
[A,C] = findAC(S,N,L,R,METH,TOL);
 
  

See Also

findABCD ,   findBD ,   findBDK ,   findR ,   sorder ,   sident ,