Identification of a magnetic levitator using NARX-OBF models and genetic algorithm

Abstract

The Volterra models using orthonormal basis functions (OBFs) are very common in the system identification literature. These models are called Volterra-OBF and they only use polynomial operations with the filtered input signals to capture the behaviour of dynamic systems. The extension of this idea to the filtered output, combined with the filtered input signals, leads to the nonlinear auto regressive with exogenous input - orthonormal basis function (NARX-OBF) models. Within this context, the goal of this paper is to identify a nonlinear system with a NARX-OBF model and compare its results to the one obtained using a Volterra-OBF model. In order to determine the model parameters, some heuristic optimisation methods are presented. The identification of a magnetic levitator is presented in order to exemplify the use of these models. Regarding the comparison between NARX-OBF and Volterra-OBF, in nonlinear system identification, one can conclude that NARX-OBF models have reached smaller mean square error (MSE) in tested cases.