<< armax1 Identification findAC >>

Scilab Help >> Control Systems - CACSD > Identification > findABCD

findABCD

discrete-time system subspace identification

Syntax

SYS        = findABCD(S, N, L, R, METH)
[SYS, RCND] = findABCD(S, N, L, R, METH)
[SYS, K] = findABCD(S,N,L,R,METH,NSMPL,TOL,PRINTW)
[SYS, K, Q, Ry, S, RCND] = findABCD(S, N, L, R, METH, NSMPL, TOL, PRINTW)

Arguments

S

integer, the number of block rows in the block-Hankel matrices

N

integer, the system order

L

integer, the number of output

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;

= 3

combined method: A and C via MOESP, B and D via N4SID.

Default: METH = 3.

NSMPL

integer, 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

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;

PRINTW

= 0: do not print warning messages.

Default: PRINTW = 0.

SYS

computes a state-space realization SYS = (A,B,C,D) (an syslin object)

K

the Kalman predictor gain K (if NSMPL > 0)

Q

state covariance

Ry

output covariance

S

state-output cross-covariance

RCND

vector, reciprocal condition numbers of the matrices involved in rank decisions, least squares or Riccati equation solutions

Description

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).

lr = 4,  if Kalman gain matrix K is not required, and
lr = 12, if Kalman gain matrix K is required.

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.

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;
[R,N1,SVAL] = findR(S,Y',U');
N=3;
SYS1 = findABCD(S,N,1,R) ;SYS1.dt=0.1;

SYS1.X0 = inistate(SYS1,Y',U');

Y1=flts(U,SYS1);
clf();plot2d((1:nsmp)',[Y',Y1'])

See also


Report an issue
<< armax1 Identification findAC >>