Digital controller design for Bouc–Wen model with high-order hysteretic nonlinearities through approximated scalar sign function

Abstract

In the models of piezoelectric actuator (PEA) systems, the hysteresis effects are often described by the concise Bouc-Wen models; however, these models are nonlinear and non-smooth because of the existence of terms which involve the absolute-value function. In particular, a challenging control problem is posed when, due to the properties of certain materials, such absolute-value terms are of high order. This control problem has been rarely studied. This article proposes the use of the approximated scalar sign function (ASSF), which is a numerically stable and differentiable nonlinear function, to represent the hysteresis function, with single-order or high-order absolute-value terms. This innovative step leads to a nonlinear but sufficiently smooth model. Then, a systematic digital design methodology is presented, which involves the following steps: (1) establish an optimal linear model based upon the resulting smooth model, (2) adopt a PI-based analogue controller and (3) apply the predictionbased digital redesign technique for digital implementation. A digital observer is also developed for state reconstruction, and to improve the input disturbance rejection. The positioning control of a PEA system with a high-order hysteretic Bouc-Wen model is implemented to demonstrate the effectiveness of the proposed ASSF based modelling and controller design approaches.

Synchronization of Discrete Sprott Chaotic Systems and Its Application in Secure Communication

“…Over the past few years, it has been reported to many practical control systems. Several design methods of discrete-time SMC have been found in the literature [Hoz et al (2014)], [Yang et al (1996)], [Chee et al (2003)], [Wu et al (2010)], [Zhou et al (2008)], [Yan et al (2008)], [Lin et al (2010)].…”