In this paper, we propose a deterministic off-line identification method performed by using input and output data with a constant steady-state output response. The method can directly acquire any order of reduced model without knowing the real order of a plant, in such a way that the intermediate parameters are uniquely determined so as to be orthogonal with respect to 0-N-tuple integral values of output error and irrelevant to the unmodeled dynamics. From the intermediate parameters, the co-efficients of a rational transfer function are calculated. In consequence, the method can be executed for any linear single-input single-output plant without knowing or estimating its order at the beginning. The effectiveness of the method is illustrated by numerical simulations and also by applying it to a two-mass system.

1.
So¨derstro¨m, T., and Stoica, P., 1989, System Identification, Prentice-Hall, Englewood Cliffs, NJ.
2.
Ljung, L., 1987, System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, NJ.
3.
Wang
,
Z.
, and
Unbehauen
,
H.
,
1999
, “
Model Reduction Based on Regional Pole and Covariance Equivalent Realizations
,”
IEEE Trans. Autom. Control
,
44
(
10
), pp.
1889
1893
.
4.
De Moor, B., Moonen, M., Vandenberghe, L., and Vandewalle, J., 1988, “Identification of Linear State Space Models With SVD Using Canonical Correlation Analysis,” Singular Value Decomposition and Signal Processing, E. Deprettere, ed., Elsevier Science and Technology Books, North-Holland, Amsterdam, pp. 161–169.
5.
Moonen
,
M.
,
De Moor
,
B.
,
Vandenberghe
,
L.
, and
Vandewalle
,
J.
,
1989
, “
On- and Off-Line Identification of Linear State-Space Models
,”
Int. J. Control
,
49
(
1
), pp.
219
232
.
6.
Van Overschee, P., and De Moor, B., 1996, Subspace Identification for Linear Systems, Kluwer Academic, Dordrecht, The Netherlands.
7.
Van der Veen
,
A. J.
,
Deprettere
,
E. F.
, and
Swindlehurst
,
A.
,
1993
, “
Subspace-Based Signal Analysis Using Singular Value Decomposition
,”
Proc. IEEE
,
81
(
9
), pp.
1277
1308
.
1.
Verhaegen
,
M.
, and
Dewilde
,
P.
,
1992
, “
Subspace Model Identification, Parts 1 and 2
,”
Int. J. Control
,
56
(
5
), pp.
1187
1210
, 1211/1241;
2.
1993
, Part 3,
58
(
3
), pp.
555
586
.
1.
Viberg
,
M.
,
1995
, “
Subspace-Based Methods for Identification of Linear Time-Invariant Systems
,”
Automatica
,
31
(
12
), pp.
1835
1851
.
2.
Ljung, L., 1997, System Identification Toolbox, The Math Works, Inc., Natick, MA.
3.
Zang, Z., Bitmead, R. R., and Gevers, M., 1991, “H2 Iterative Model Refinement and Control Robustness Enhancement,” Proc. of 30th IEEE Conference on Decision and Control, Brighton, England, pp. 279–284.
4.
Zang, Z., Bitmead, R. R., and Gevers, M., 1992, “Disturbance Rejection: On-Line Refinement of Controllers by Closed-Loop Modeling,” Proc. of American Control Conference, Chicago, Ill., pp. 2829–2833.
5.
Zang
,
Z.
,
Bitmead
,
R. R.
, and
Gevers
,
M.
,
1995
, “
Iterative Weighted Least-Squares Identification and Weighted LQG Control Design
,”
Automatica
,
31
(
11
), pp.
1577
1594
.
6.
Hakvoort, R. G., Schrama, R. J. P., and Van den Hof, P. M. J., 1992, “Approximate Identification in View of LQG Feedback Design,” Proc of American Control Conference, Chicago, Ill., pp. 2824–2828.
7.
Wahlberg
,
B.
, and
Ljung
,
L.
,
1986
, “
Design Variables for Bias Distribution in Transfer Function Estimation
,”
IEEE Trans. Autom. Control
,
31
(
2
), pp.
134
144
.
8.
Kailath, T., 1979, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ.
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