Identification and nonlinearity compensation of hysteresis using NARX models
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ORIGINAL PAPER
Identification and nonlinearity compensation of hysteresis using NARX models Petrus E. O. G. B. Abreu · Lucas A. Tavares · Bruno O. S. Teixeira · Luis A. Aguirre
Received: 10 January 2020 / Accepted: 1 September 2020 © Springer Nature B.V. 2020
Abstract This paper deals with two problems: the identification and compensation of hysteresis nonlinearity in dynamical systems using nonlinear polynomial autoregressive models with exogenous inputs (NARX). First, based on gray-box identification techniques, some constraints on the structure and parameters of NARX models are proposed to ensure that the identified models display a key feature of hysteresis. In addition, a more general framework is developed to explain how hysteresis occurs in such models. Second, two strategies to design hysteresis compensators are presented. In one strategy, the compensation law is obtained through simple algebraic manipulations performed on the identified models. In the second strategy, the compensation law is directly identified from the data. Both numerical and experimental results are presented to illustrate the efficiency of the proposed procedures. Also, it has been found that the compensators based on gray-box models outperform the cases with models identified using black-box techniques.
P. E. O. G. B. Abreu (B)· L. A. Tavares Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil e-mail: [email protected] B. O. S. Teixeira · L. A. Aguirre Department of Electronic Engineering, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil
Keywords Hysteresis · Gray-box identification · Compensation of nonlinearities · NARX model
1 Introduction Hysteresis is a nonlinear behavior that is present in several systems and devices. It is commonly related to the phenomena of ferromagnetism, plasticity, and friction, among others [56]. Some examples include mechanical, electronic and biomedical systems, as well as sensors and actuators such as magnetorheological dampers, piezoelectric actuators, and pneumatic control valves [20,46,50]. An intrinsic feature of such systems is the memory effect, meaning that the output depends on the history of the corresponding input. In addition to the memory effect, the literature provides different definitions and conditions to distinguish such systems and characterize the hysteretic behavior. In some cases, the occurrence of hysteresis has been associated with the existence of several fixed points whenever these systems are subject to a constant [41] or time-varying [37] input signal. Additionally, hysteresis has also been defined as a hard nonlinearity that depends on the magnitude and rate of the input signal. These aspects can pose various performance limitations if not properly taken into account during the control design [50,55]. Hence, a common goal is to attenuate the hysteretic behavior of the system [18,57,63] prior to feedback control design.
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