Sliding mode disturbance observer-based adaptive integral backstepping control of a piezoelectric nano-manipulator

Abstract

This paper investigates a systematic modeling and control methodology for a multi-axis PZT (piezoelectric transducer) actuated servo stage supporting nano-manipulations. A sliding mode disturbance observer-based adaptive integral backstepping control method with an estimated inverse model compensation scheme is proposed to achieve ultra high precision tracking in the presence of the hysteresis nonlinearities, model uncertainties, and external disturbances. By introducing a time rate of the input signal, an enhanced rate-dependent Prandtl–Ishlinskii model is developed to describe the hysteresis behaviors, and its inverse is also constructed to mitigate their adverse effects. In particular, the corresponding inverse compensation error is analyzed and its boundedness is proven. Subsequently, the sliding mode disturbance observer-based adaptive integral backstepping controller is designed to guarantee the convergence of the tracking error, where the sliding mode disturbance observer can track the total disturbances in a finite time, while the integral action is incorporated into the adaptive backstepping design to improve the steady-state control accuracy. Finally, real time implementations of the proposed algorithm are applied on the PZT actuated servo system, where excellent tracking performance with tracking precision error around 6‰ for circular contour tracking is achieved in the experimental results.