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.
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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
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
That the cause of the difficulty was sampling zeros was first pointed out in
Larsson EK (2003) Identification of stochastic continuous-time systems. PhD thesis, Division of Systems and Control, Uppsala University, Sweden
Larsson EK (2005) Limiting sampling results for continuous-time ARMA systems. Int J Control 78(7):461–473
The resolution of the problem using asymptotic sampling zero dynamics as a pre-filter is discussed in more detail in
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
Robust estimation using a limited frequency range is described in
Aguero JC et al. (2012) Dual time-frequency domain system identification. Automatica 48(12):3031–3041
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
Circular complex distributions are described in
Brillinger DR (1974) Fourier analysis of stationary processes. Proc IEEE 62(12):1628–1643
Brillinger DR (1981) Time series: data analysis and theory. McGraw-Hill, New York
Further information regarding frequency-domain identification can be found in
Gillberg J, Ljung L (2009) Frequency-domain identification of continuous-time ARMA models from sampled data. Automatica 45(6):1371–1378
Pintelon R, Schoukens J (2007) Frequency domain maximum likelihood estimation of linear dynamic errors-in-variables models. Automatica 43(4):621–630
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
The section on identification based on non-uniformly fast-sampled data draws heavily on
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
Other papers describing alternative approaches to the identification of continuous systems from non-uniform data include
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
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
Larsson E, Söderström T (2002) Identification of continuous-time AR processes from unevenly sampled data. Automatica 38:709–718
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Yuz, J.I., Goodwin, G.C. (2014). Applications of Approximate Stochastic Sampled-Data Models. In: Sampled-Data Models for Linear and Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-5562-1_19
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DOI: https://doi.org/10.1007/978-1-4471-5562-1_19
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