Prescribed-Time Control with Time Transformation Method for Nanopositioning Stages

Conventional sliding mode control methods often lack the capability to accurately predict and regulate convergence times, leading to uncertainties in high-precision applications. This paper introduces a novel prescribed-time control strategy that leverages an advanced time transformation method to ensure reliable trajectory tracking. This approach ingeniously maps the operational domain from a finite interval [0, ࣎) onto an extended infinite time horizon [0, λ), which significantly streamlines the stability analysis and eases the synthesis of the control law. The efficacy of the proposed controller is validated through simulations involving piezoelectric nanopositioning stages, wherein the results confirm its ability to maintain prescribed-time stability.