Adaptive compound control based on generalized Bouc–Wen inverse hysteresis modeling in piezoelectric actuators

Abstract

This paper focuses on the study of the dynamic hysteresis compensation and control of piezoelectric actuators so as to improve the swing accuracy of the piezoelectric fast steering mirror mechanism in the photoelectric compound-axis control system. Moreover, in view of the rate dependence and asymmetry of piezoelectric hysteresis, and the complex inversion process of the generalized Bouc–Wen hysteresis model, the Hammerstein dynamic inverse hysteresis model of the piezoelectric actuator is established. To be specific, the static nonlinearity and rate dependence of the piezoelectric inverse hysteresis are represented by the generalized Bouc–Wen inverse model and the auto-regressive exogenous model, respectively, and the parameters of the model are identified by the adaptive beetle swarm optimization algorithm. In the process of the open-loop feedforward compensation, the dynamic positioning accuracy of the piezoelectric actuator is greatly affected by various disturbances and the uncertainty of the hysteresis compensation model. In this context, a compound control strategy that combines the feedforward compensation with the single-neuron adaptive proportion-integration-differentiation control is proposed based on the Hammerstein dynamic inverse hysteresis model of the piezoelectric actuator. The experimental results verify the effectiveness and superiority of the proposed control strategy.

A survey of Bouc-Wen hysteretic models applied to piezo-actuated mechanical systems: Modeling, identification, and control

“…In general, mechanical systems with hysteresis can be divided into Hammerstein structure (Pawlak, 1991), Wiener structure (Giri et al, 2013), Wiener- Hammerstein (Mzyk and Wachel, 2017), and Hammerstein-Wiener (Wills et al, 2013) in the light of the different number and position of hysteretic nonlinear model and linear dynamics model. In the BW hysteretic model, the Hammerstein structure is commonly adopted (Zhang et al, 2021a(Zhang et al, , 2021b, as illustrated in Figure 6. According to the different mechanical structures and performance requirements, mechanical systems can be divided to a BW hysteretic model and a linear dynamics model, whose detailed descriptions are addressed in this section.…”

“…Thus, it is vital to build a mathematical model accurately for mechanical systems to achieve an efficient and accurate output performance. Many models have been introduced to characterize hysteretic properties, such as Preisach model (Hughes and Wen, 1997; Jiaqiang et al, 2015; Li et al, 2014a; Mayergoyz, 1991; Nguyen et al, 2018; Wolf et al, 2012; Xiao and Li, 2013), Prandt-Ishlinskii model (Al Janaideh and Krejčí, 2012; Fan and Tan, 2019; Gan et al, 2016; Li and Xu, 2011; Qin et al, 2017; Xie et al, 2020; Yi et al, 2019; Zhang et al, 2021a, 2021b), Bouc-Wen (BW) model (Chen et al, 2022; Ikhouane and Rodellar, 2007; Wang and Zhu, 2011), Maxwell model (Cao et al, 2013; Juhász et al, 2011; Liu et al, 2016a, 2016b), Duhem model (Lin and Lin, 2012; Macki et al, 1993; Ouyang and Jayawardhana, 2014; Wang and Chen, 2017), Dahl model (Xu and Li, 2010), Jiles–Atherton model (Zaman and Matin, 2015; Zirka et al, 2012), Krasnosel’skii-Pokrovskii model (Zhou et al, 2015), Polynomial-based hysteretic model (Jung et al, 2001), and neural network model (Xu and Zhou, 2018).…”

Precision Flux Control of Linear Reluctance Actuator Using the Integral Sliding Mode Method

“…To describe the characteristics of hysteresis, various model structures are proposed. The most representative methods include physical modeling, mathematical operator modeling, and intelligent modeling (Li M. et al, 2019;Al Janaideh et al, 2021;Zhang et al, 2021;Cheng et al, 2022;Flores et al, 2022;Otieno et al, 2022). Specifically, the Bouc-Wen model sorted by the physical method is the most popular one since its parameters have definite physical meaning and are easily obtained (Ismail et al, 2009;Hassani et al, 2014).…”