Nonlinear tracking differentiator and PD controller for piezoelectric actuators in a robotic hand

This article deals with the modeling and control design for piezoelectric actuators of a micro-robotic system. Piezoelectric actuators generally exhibit complex and nonlinear behavior due to their inherent asymmetric hysteresis phenomenon, creep nonlinearity, and oscillatory characteristics. Moreover, these actuators are subject to an external disturbance force caused by the interaction with the manipulated objects. It has been shown in practice that these characteristics have a negative and significant impact on the performance of piezoelectric actuators, which increases the difficulty of their control. The main objective of this paper is to account simultaneously for all undesired and complex characteristics outlined above. To this end, our main idea is to lump the hysteresis and creep phenomena, as well as the disturbing manipulation force together as one total disturbance term. The total disturbance is first estimated in real-time via a nonlinear tracking differentiator, then feedback control law is designed to compensate for the disturbance and achieve a good transient profile. To validate and demonstrate the efficacy of the proposed approach, experiments are conducted, and results obtained are discussed.