Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

Abstract

This paper presents a new Global Fast Non-singular Terminal Sliding Mode Controller (GFNTSMC) that delivers high-precision tracking of high-frequency trajectories when applied to a piezo-driven nanopositioner. The control scheme is realized by combing inverse hysteresis model and global fast non-singular terminal sliding mode compensation. The inverse Bouc–Wen hysteresis model is used to calculate the required hysteresis-compensating feedforward control voltage according to the reference signal. The key uniqueness of the proposed control strategy is it’s red global fast convergence, achieved with high accuracy and high bandwidth. The stability of the reported GFNTSMC controller is proved with the Lyapunov theory. Its performance is verified through experimentally recorded tracking results, and its superiority over three benchmark control approaches, namely the Proportional–Integral–Derivative (PID), the Positive Position Feedback with integral action (PPF+I) and the conventional linear high-order sliding mode controller (LHOSMC) is demonstrated through comparative tracking error analysis. Its wide-band stability as well as its significant robustness to parameter uncertainty is also showcased.