Hierarchical Disturbance-Based Displacement Observer for Piezoelectric Self-Sensing Actuation

Timely and reliable displacement feedback is essential for high-precision manipulation based on piezoelectric actuators, but this is not available in limited workspace. The charge-based self-sensing technique relies on only piezoelectric characteristics is an alternative method for obtaining the displacement. However, the charge–leakage effect caused by inherent actuator defects and measurement errors significantly degrade its sensing accuracy. This study proposes a displacement estimation method, which is divided into the following two parts. 1) The basic part is utilized to observe disturbance and estimate displacement. 2) The extended part is used to keep the inherent drift of charge sensing method in a tolerable level. Convergence conditions for the proposed method are analyzed using the small-gain theorem. Further, experiments are conducted to evaluate the sensing performance, and the feasibility of the proposed method as displacement feedback. Experimental results show that both the root mean square error (RMSE) and charge drift of the proposed method can be kept below 1%, and it reduces the RMSE by 54.1% compared with strain gauge method when acting as displacement feedback in a closed-loop system.