Tracking Control for a Piezoelectric Nanopositioner Using Estimated States and Feedforward Compensation of Hysteresis

Nanopositioning stages utilizing piezoelectric actuators exhibit several undesired features inhibiting good reference tracking performance. The most salient features are lightly damped mechanical resonances, hysteresis, and creep. In addition, sensor noise can limit the resolution achievable when applying closed-loop control schemes. In order to reduce sensor noise when using closed-loop control, we develop a state estimator in the form of an adaptive Luenberger observer. Furthermore, we propose a novel method for compensating the hysteretic behavior in piezoelectric actuators when tracking a reference trajectory, and present a method for online identification of the parameters of the system, aiming for simplicity and ease of implementation. The backstepping framework is used to obtain an adaptive control law and to analyze stability and boundedness of the tracking error. Experimental results are presented in order to assess the performance of the proposed hysteresis compensation, as well as the backstepping control law, on a flexure-based nanopositioner using piezoelectric actuators.