» Download Article

Authors
Marion Gilson; Hugues Garnier; Peter Young; Paul Van den Hof

Identifier
10.3182/20060329-3-AU-2901.00143

Index Terms
system identification,closed-loop identification,optimal instrumental variable

Abstract
This paper describes an optimal instrumental variable method for identifying discrete-time transfer function models of the Box-Jenkins transfer function form in the closed-loop situation. This method is based on the Refined Instrumental Variable (RIV) algorithm which, because of an appropriate choice of particular design variables, achieves minimum variance estimation of the model parameters. The Box-Jenkins model is the most natural since it does not constrain the process and the noise models to have common polynomials. The performance of the proposed approach is evaluated by Monte Carlo analysis in comparison with other alternative closed loop estimation methods.

References

[1] Broersen, P. M. T. (2002). Automatic spectral
    analysis with time series models. IEEE
    Transactions on Instrumental Measurement
    51(2), 211-216.
[2] Forssell, U. and L. Ljung (1999). Closed-loop identification
     revisited. Automatica 35(7), 1215-
    1241.
[3] Gilson, M. and P. Van den Hof (2001). On the relation
     between a bias-eliminated least-squares
    (BELS) and an IV estimator in closed-loop
    identification. Automatica 37(10), 1593-1600.
[4] Gilson, M. and P. Van den Hof (2005). Instrumental
     variable methods for closed-loop system
    identification. Automatica 41(2), 241-249.
[5] Ljung, L. (1999). System identification : theory for
    the user - Second Edition. Prentice-Hall.
[6] Söderström, T. and P. Stoica (1983). Instrumental
     variable methods for system identification.
    Springer-Verlag.
[7] Söderström, T., P. Stoica and E. Trulsson (1987).
    Instrumental variable methods for closed-loop
     systems. In: 10th IFAC World Congress
    on Automatic Control. Munich - Germany.
    pp. 363-368.
[8] Van den Hof, P. M. J. (1998). Closed-loop issues
    in system identification. Annual Reviews in
    Control 22, 173-186.
[9] Young, P. C. (1976). Some observations on instrumental
     variable methods of time-series
    analysis. International Journal of Control
    23(5), 593-612.
[10] Young, P. C. (1970). An instrumental variable
     method for real-time identification of a noisy
     process. Automatica 6, 271-287.
[11] Young, P. C. (1984). Recursive estimation and
     time-series analysis. Springer-Verlag. Berlin.
[12] Young, P. C. (1985a). Recursive identification, estimation
      and control. In: Handbook of Statistics
      5: Time Series in the Time Domain. E.
     J. Hannan, P. R. Krishnaiah and M. M. Rao
     (eds.). pp. 213-256.
[13] Young, P. C. (1985b). The instrumental variable
     method: a practical approach to identification
     and system parameter estimation In: Identification
      and System Parameter Estimation.
     H. A. Barker and P. C. Young (eds). Pergamon
     Press: Oxford, pp. 1-16.