Precision Synchronous Control of Multiple Motion Systems: A Tube-Based MPC Approach

Lithography machines operate in scanning mode for the fabrication of large-scale integrated circuits (ICs), requiring high-precision synchronous motion between the reticle and wafer stages. Disturbances generated by each stage during high-acceleration movements are transmitted through the base frame, resulting in degradation of synchronization performance. To address this challenge, this paper proposes a tube-based model predictive control (tube-MPC) approach for synchronization in lithography machines. First, the proposed modeling method accurately characterizes the coupling disturbances and synchronization dynamics. Subsequently, a tube-MPC approach is developed to ensure that the states of the nominal system are constrained within the terminal constraint set. To reduce the complexity of online computations, an approach is employed to transform online optimization problems into offline problems by creating an online lookup table. This enables the determination of optimal control inputs via a simplified online optimization algorithm. The robustness and trajectory tracking performance of the proposed approach are verified through simulation experiments, demonstrating its effectiveness in enhancing the synchronization performance of multiple motion systems.