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Applications of Approximate Stochastic Sampled-Data Models

  • Juan I. Yuz
  • Graham C. Goodwin
Part of the Communications and Control Engineering book series (CCE)

Abstract

This chapter explores several applications of approximate stochastic sampled-data models. It is shown that, in some applications, an understanding of the role of sampling zero dynamics can be crucial in obtaining accurate results. In particular, parameter and state estimation problems are considered where the use of a restricted bandwidth may be crucial to correctly account for the artifacts of sampling.

Keywords

Incremental Model Sampling Zero Restricted Bandwidth Maximum Sampling Interval Unmodelled High Frequency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Further Reading

The fact that the ordinary least squares method leads to biased estimates in the identification of continuous-time AR models from sampled data was first observed in

  1. Söderström T, Fan H, Carlsson B, Bigi S (1997) Least squares parameter estimation of continuous-time ARX models from discrete-time data. IEEE Trans Autom Control 42(5):659–673 CrossRefzbMATHGoogle Scholar

That the cause of the difficulty was sampling zeros was first pointed out in

  1. Larsson EK (2003) Identification of stochastic continuous-time systems. PhD thesis, Division of Systems and Control, Uppsala University, Sweden Google Scholar
  2. Larsson EK (2005) Limiting sampling results for continuous-time ARMA systems. Int J Control 78(7):461–473 MathSciNetCrossRefzbMATHGoogle Scholar

The resolution of the problem using asymptotic sampling zero dynamics as a pre-filter is discussed in more detail in

  1. Yuz JI, Goodwin GC (2008) Robust identification of continuous-time systems from sampled data. In: Garnier H, Wang L (eds) Continuous-time model identification from sampled data. Springer, Berlin Google Scholar

Robust estimation using a limited frequency range is described in

  1. Aguero JC et al. (2012) Dual time-frequency domain system identification. Automatica 48(12):3031–3041 MathSciNetCrossRefGoogle Scholar
  2. Yuz JI, Goodwin GC (2008) Robust identification of continuous-time systems from sampled data. In: Garnier H, Wang L (eds) Continuous-time model identification from sampled data. Springer, Berlin Google Scholar

Circular complex distributions are described in

  1. Brillinger DR (1974) Fourier analysis of stationary processes. Proc IEEE 62(12):1628–1643 MathSciNetCrossRefGoogle Scholar
  2. Brillinger DR (1981) Time series: data analysis and theory. McGraw-Hill, New York zbMATHGoogle Scholar

Further information regarding frequency-domain identification can be found in

  1. Gillberg J, Ljung L (2009) Frequency-domain identification of continuous-time ARMA models from sampled data. Automatica 45(6):1371–1378 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Pintelon R, Schoukens J (2007) Frequency domain maximum likelihood estimation of linear dynamic errors-in-variables models. Automatica 43(4):621–630 MathSciNetCrossRefzbMATHGoogle Scholar
  3. Pintelon R, Schoukens J, Rolain Y (2008) Frequency-domain approach to continuous-time system identification: some practical aspects. In: Garnier H, Wang L (eds) Continuous-time model identification from sampled data. Springer, Berlin, pp 215–248 CrossRefGoogle Scholar

The section on identification based on non-uniformly fast-sampled data draws heavily on

  1. Yuz JI, Alfaro J, Agüero JC, Goodwin GC (2011) Identification of continuous-time state-space models from non-uniform fast-sampled data. IET Control Theory Appl 5(7):842–855 MathSciNetCrossRefGoogle Scholar

Other papers describing alternative approaches to the identification of continuous systems from non-uniform data include

  1. Ding F, Qiu L, Chen T (2009) Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 45(2):324–332 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Gillberg J, Ljung L (2010) Frequency domain identification of continuous-time output error models, part II: non-uniformly sampled data and B-spline output approximation. Automatica 46(1):11–18 MathSciNetCrossRefzbMATHGoogle Scholar
  3. Larsson E, Söderström T (2002) Identification of continuous-time AR processes from unevenly sampled data. Automatica 38:709–718 CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Juan I. Yuz
    • 1
  • Graham C. Goodwin
    • 2
  1. 1.Departamento de ElectrónicaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.School of Electrical Engineering & Computer ScienceUniversity of NewcastleCallaghanAustralia

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