Finite-time adaptive sliding mode control for high-precision tracking of piezo-actuated stages

Piezo-actuated stages are widely used in nanopositioning applications. However, they not only have inherent static hysteresis characteristics but also have dynamic rate-dependent hysteresis nonlinearity. Therefore, to address dynamic hysteresis nonlinearity and uncertainty in the model parameters, an adaptive switching-gain sliding mode controller with a proportional-integral-derivative surface is designed. In particular, the combination of Bouc-Wen model and second-order linear system is used to describe the dynamic hysteresis process. To improve the robustness and reduce chattering in the sliding mode control method, an adaptive switching-gain is added to the controller without knowing in advance the upper bound of uncertainties. Finite-time convergence conditions of the closed-loop system are also analyzed. Finally, the proposed control method is implemented in real time on an ARM experimental platform. Comparative experimental results demonstrate excellent tracking performance and robustness. The dynamic hysteresis characteristics are suppressed effectively, and this result provides a powerful reference for engineering applications.