Identification of NARX Models for Compensation Design

TL;DR

This paper demonstrates the identification of NARX models for three different systems, including numerical and experimental examples, using a combination of ERR, AIC, and ELS methods to achieve accurate models with minimal terms.

Contribution

It introduces a structured approach combining ERR, AIC, and ELS for effective NARX model identification across diverse nonlinear systems.

Findings

Successful identification of systems with no more than five terms

Effective structure selection using ERR and AIC methods

Models suitable for nonlinearity compensation in future applications

Abstract

This report presents the modeling results for three systems, two numerical and one experimental. In the numerical examples, we use mathematical models previously obtained in the literature as the systems to be identified. The first numerical example is a heating system with a polynomial nonlinearity that is described by a Hammerstein model. The second is a Bouc-Wen model that represents the hysteretic behavior in a piezoelectric actuator. Finally, the experimental example is a pneumatic valve that presents a variety of nonlinearities, including hysteresis. For each example, a Nonlinear AutoRegressive model with eXogenous inputs (NARX) is identified using two well-established techniques together, the Error Reduction Ratio (ERR) method to hierarchically select the regressors and the Akaike's Information Criterion (AIC) to truncate the number of terms. Using both approaches, the structure selection is achieved. The design of the excitation input is based on preserving the frequencies of interest and force the system to achieve different points of operation. Hence, having the structure previously selected with ERR and AIC, we use the Extended Least Squares (ELS) algorithm to estimate the parameters. The results show that it is possible to identify the referred systems with no more than five terms. These identified models will be used for nonlinearity compensation in future works.