Prescribed-time sliding mode control for nanopositioning stages via extended state observer

This paper proposes a synergistic control framework combining a novel prescribed-time extended state observer (PTESO) with a chattering-free prescribed-time sliding mode controller (PTSMC) to achieve high-precision trajectory tracking for piezoelectric nanopositioning stages. The proposed PTESO employs a continuous, bounded time-varying function to accurately estimate lumped disturbances within a user-defined time, thereby obviating the need for complex switching mechanisms. A PTSMC method combining precise disturbance estimation and hyperbolic tangent functions is proposed, which significantly suppresses control chattering while ensuring prescribed-time convergence of the tracking error. Experimental validation demonstrates that our approach achieves superior tracking accuracy and faster user-definable convergence while producing a control signal with improved smoothness, offering a significant advantage over existing advanced control strategies.