Abstract
The hysteresis property in a smart structure has attracted much attention from researchers for several decades. Hysteresis not only affects the response precision of the smart structure but also threatens the stability of the system. This paper focuses on how the hysteresis property influences the control effect of vibration suppression for a smart beam. Furthermore, the Bouc–Wen model is adopted to describe the hysteresis property of a smart beam and the hysteresis parameters of the hysteresis model are identified with a genetic algorithm. Based on the identification results, the hysteresis model is validated to represent the hysteresis property of the smart beam. Based on the hysteresis model, model reference adaptive control is designed to explore the influence of hysteresis on the vibration control of the smart beam. With some simulations and experiments, it is found that the vibration control effect is influenced when the hysteresis item changes. The vibration control effect will be improved when the hysteresis coefficient in the Bouc–Wen model, as the expected objective model of the adaptive reference model, is within a proper numerical range where the control system is stable. Furthermore, when the time delay is considered in the closed-loop control system, the principle of the hysteresis influence is different. The results indicate that the hysteresis property affects not only the control effect but also the stability of the control system for a smart cantilever beam.
Highlights
Hysteresis is a common nonlinearity of piezoelectric materials [1,2,3]
PID control was implemented to damp both the free and forced vibrations of a thin-walled structure and compared with LQR optimal control [8], a new intelligent methodology was introduced to mitigate the vibration response of flexible cantilever plates [9], and a minimax-linear quadratic Gaussian controller was designed based on an uncertain system model for the positioning of a piezoelectric tube scanner used in an atomic force microscope [10]. ese linear control approaches are limited in terms of their applications to linear system models
The model reference adaptive control [23, 27] is adopted to explore the influence of hysteresis on the control effect of vibration suppression of smart structures with the Bouc–Wen model in this paper
Summary
Hysteresis is a common nonlinearity of piezoelectric materials [1,2,3]. Hysteresis is a lagging phenomenon where a physical effect on the smart material lags behind its cause. Some linear control laws are commonly designed based on a linear model for the smart structure. Erefore, modeling the hysteresis nonlinearities of smart structures is important for designing a controller to explore the influence of hysteresis on the control of the smart structures. Based on the two types of models, the main control laws were adopted with only their inverse hysteresis model as open-loop control to compensate for the hysteresis property of the smart structure [17, 18]. Compared with other control methods, the adaptive control has strongly robust, adaptive, and anti-interference properties Because of these advantages, the model reference adaptive control [23, 27] is adopted to explore the influence of hysteresis on the control effect of vibration suppression of smart structures with the Bouc–Wen model in this paper.
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