Practical tracking control of piezoelectric actuators with time-delay estimation and nonsingular terminal sliding mode

¹ Hangzhou Vocational and Technical College, Hangzhou 310018, China
² Aerospace System Engineering Shanghai, Shanghai 200000, China
³ Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
⁴ Wenzhou Polytechnic, Wenzhou 325000, China

^* Corresponding author: jinyuma@nuaa.edu.cn

Abstract

A novel type of nonlinear robust control strategy is proposed in view of uncertain nonlinear factors, such as hysteresis, creep, and high-frequency vibration, of piezoelectric actuators (PEAs). This strategy can be used for the precise trajectory tracking of PEAs. The Bouc–Wen dynamic model is reasonably simplified to facilitate engineering application. The hysteresis term is summarized as an unknown term to avoid its nonlinear parameter identification. The controller robustness is achieved due to the nonsingular terminal sliding mode control, and the online estimation of unknown disturbances is realized because of the delay estimation technology; thus, no prior knowledge of the unknown boundary of the system is required. The precision robust differentiator is used to estimate the speed and acceleration signals in real time on the basis of the obtained displacement signals. The closed-loop stability of the system is proved by the Lyapunov criterion. Experimental results show that the proposed control strategy performs better than the traditional time-delay estimation control in terms of control accuracy and energy conservation. Therefore, the proposed control strategy can play an important role in the micro/nanofield driven by PEAs.