Robust adaptive backstepping control for piezoelectric nano-manipulating systems

In this paper we present a systematic modeling and control approach for nano-manipulations of a two-dimensional PZT (piezoelectric transducer) actuated servo stage. The major control challenges associated with piezoelectric nano-manipulators typically include the nonlinear dynamics of hysteresis, model uncertainties, and various disturbances. The adverse effects of these complications will result in significant performance loss, unless effectively eliminated. The primary goal of the paper is on the ultra high precision control of such systems by handling various model uncertainties and disturbances simultaneously. To this end, a novel robust adaptive backstepping-like control approach is developed such that parametric uncertainties can be estimated adaptively while the nonlinear dynamics and external disturbances are treated as bounded disturbances for robust elimination. Meanwhile, the L2-gain of the closed-loop system is considered, and an H∞ optimization problem is formulated to improve the tracking accuracy. Numerical simulations and real time experiments are finally conducted, which significantly outperform conventional PID methods and achieve around 1% tracking error for circular contouring tasks.