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

Authors: Elder Oroski; Rafael Holdorf Lopez; Adolfo Bauchspiess

Addresses: Laboratory of Technological Innovation (LIT), Technological University of Paraná, UTFPR, Av. Sete de Setembro, 3165, Rebouças, CEP 80230-901, Curitiba, Paraná, Brazil ' Center for Optimization and Reliability in Engineering (CORE), University of Santa Catarina, UFSC, R. João Pio Duarte Silva, 241, Córrego Grande, CEP 88037-000, Florianópolis, Santa Catarina, Brazil ' Laboratory of Automation and Robotic (LARA), University of Brasília, UnB, Campus Universitrio Darcy Ribeiro, CEP 70910-900, Brasília, Distrito Federal, Brazil

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.

Keywords: system identification; Volterra and NARX models; orthonormal basis functions; OBFs; genetic algorithm.

DOI: 10.1504/IJMIC.2017.087031

International Journal of Modelling, Identification and Control, 2017 Vol.28 No.4, pp.307 - 316

Available online: 23 Aug 2017 *

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