Modelling and identification of non-linear deterministic systems in the delta-domain

Authors:
S. R. Anderson;V. Kadirkamanathan
Affiliations:
Department of Psychology, University of Sheffield, Western Bank, Sheffield S10 2TP, UK;Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Abstract

This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta-domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure.