Integration of Gaussian Process Regression and Iterative Learning Control for Scanning Stage with Iron-Core Linear Motors

Lithography systems for semiconductor and display manufacturing increasingly require high-speed, high-precision positioning. Based on a scanning-stage architecture driven by iron-core linear motors, controlled magnetic attraction is leveraged to provide lateral actuation without additional actuators. Because the same attraction introduces state-dependent thrust ripple, a feedforward framework is developed that couples iterative learning control (ILC) with Gaussian process regression (GPR) to generalize ILC-refined inputs to previously unseen trajectories. To reduce the burden of time-consuming ILC experiments and the rapid growth of GPR computation with training-set size, a trajectory optimization method is proposed that trades off GP predictive variance against computational cost, enabling accurate prediction with a compact training set. The proposed method is validated on a three-degree-of-freedom experimental platform, in which scanning is performed along the primary axis while lateral and yaw offsets are held constant. Experiments consistently reduce tracking errors across a range of scan conditions, supporting the proposed approach for high-performance lithography stages.