» Download Article

Authors
Jonas Gillberg; Lennart Ljung

Identifier
10.3182/20060329-3-AU-2901.00028

Index Terms
continuous-time systems,parameter estimation,continuous-time,output error,B-splines

Abstract
This paper treats the identification of continuous-time output error (OE) models based on sampled data. The exact method for doing this is well known both for data given in the time and frequency domains. The time domain approach however, becomes somewhat complex, especially for non-uniformly sampled data. In this paper we assume that the system input is a zero order hold signal and that the sampling rate is so high that for high frequencies the system behaves as a set of integrators. The conclusion is that if the system has relative degree l then the output should be interpolated using an l order polynomial spline function.

References

[1] Brillinger, D. R. (1981). Time Series. Holden-Day.
    San Francisco, CA.
[2] de Boor, C. (1978). A Practical Guide to Splines.
    Springer-Verlag. New York.
[3] de Boor, C. (2004). Spline Toolbox. 7th ed., The
    MathWorks Inc. Natick, MA.
[4] Gillberg, J. (2004). Methods for frequency domain
    estimation of continuous-time models. Lic.
    Dissertation Linköping Studies in Science and
    Technology Thesis No. 1133. Department of
    Electrical Engineering, Linköping University.
    SE-581 83 Linköping, Sweden.
[5] Gillberg, J. and L. Ljung (2005). Frequency-domain
     identification of continuous-time
    ARMA models from sampled data. In: Proceedings
     of the 16th IFAC World Congress,
    Prague.
[6] Ljung, L. (1999). System Identification-Theory
    for the User. 2nd ed., Prentice-Hall. Upper
    Saddle River, NJ.
[7] Ljung, L. (2003). System Identification Toolbox for
    use with MATLAB. Version 6. 6th ed., The
    MathWorks Inc. Natick, MA.
[8] Mensler, M. (1999). Analyse et etude comparative
    de methodes d'identification des systemes a
    representation continue. PhD thesis. Centre
    de Recherche en Automatique de Nancy, Universite
     Henri Poincare, Nancy.
[9] Rao, G. P. and H. Garnier (2002). Numerical illustrations
     of the relevance of direct continuous-time
     model identification. In: Proc. of the 15th
    IFAC World Congress, Barcelona.
[10] Rolain, Y., J. Schoukens and G. Vandersteen
     (1998). Signal reconstruction for nonequidistant
      finite length sample sets: a 'kis' approach.
      In: Proceedings of the Instrumentation
      and Measurement Technology Conference
     .
[11] Schoenberg, I. J. (1973). Cardinal Spline Interpolation
     . SIAM. Philadelphia, PA.
[12] Åström, K. J., P. Hagander and J. Sternby
     (1984). Zeros of sampled systems. Automatica
      20(1), 31-38.
[13] Unbehauen, H. and G. P. Rao (1990). Continuous-time
      approaches to system identification - a
     survey. Automatica 26(1), 23-35.
[14] Unser, M., A. Aldroubi and M. Eden (1993a). B-spline
      signal processing: Part I - theory. IEEE
     Transations on Signal Processing 41(2), 821-
     833.
[15] Unser, M., A. Aldroubi and M. Eden (1993b).
     B-spline signal processing: Part II - efficient
     design and application. IEEE Transactions
     on Signal Processing 41(2), 834-847.
[16] Wahlberg, B. (1988). Limit results for sampled
     systems. International Journal of Control
     48(3), 1267-1283.
[17] Weller, S. R., W. Moran, B. Ninnes and A. D.
     Pollinton (2001). Sampling zeros and the
     Euler-Frobenius polynomials. IEEE Transactions
      on Automatic Control 46(2), 340-343.
[18] Yuz, J., G. C. Goodwin and H. Garnier (2005).
     Generalized hold functions for fast sampling
     rates. In: Proceedings of the 43rd IEEE Conference
      on Decision and Control.