A modified adaptive disturbance observer-based sliding mode control for piezoelectric actuator-driven nanopositioning system with enhanced disturbance rejection

Piezoelectric actuator-driven nanopositioning systems offer advantages such as fast response and high resolution. However, owing to inherent hysteresis nonlinearities and external disturbances, achieving both high-speed and high-precision trajectory tracking remains challenging for such systems. Therefore, this paper proposes a reaching-phase free recursive terminal sliding mode control (RPF-RTSMC) based on a modified adaptive Hammerstein disturbance observer-based (MAH-DOB) approach. First, the RPF-RTSMC is designed on the basis of a recursive combination of fast terminal and integral sliding modes. Then, through optimization of the initial value configuration, the convergence of the sliding mode is accelerated. This adjustment enables the system to maintain global robustness capability throughout the entire control process. Furthermore, the MAH-DOB approach is integrated into the RPF-RTSMC for the estimation and compensation of lumped disturbances (e.g., rate-dependent hysteresis and uncertainties), thus improving disturbance rejection and mitigating control chattering. A stability analysis of the composite closed-loop system is performed via Lyapunov theory. Finally, experimental results demonstrate that the proposed method outperforms conventional fast nonsingular terminal sliding-mode controller schemes based on a nonlinear disturbance observer in terms of convergence error suppression and disturbance rejection capability.