An Adaptive Spatial-Terminal Iterative Learning Strategy in Roll-to-Roll Control Problems

Abstract

Roll-to-Roll (R2R) systems, featuring motorized or idle rollers, are crucial for high-volume, continuous production of flexible substrates. A significant challenge in R2R printing processes is maintaining tight alignment tolerances for multilayer printed electronics. This alignment, known as registration, is complicated by the deformability of flexible substrates and complex roller dynamics, leading to registration errors (RE) caused by variations in substrate tensions and speeds. Despite using real-time feedback controllers like proportional-integral-derivative (PID) or model predictive control for tension control, these systems struggle with transient and angle-periodic disturbances common in R2R systems. We introduce a spatial-terminal iterative learning control (STILC) method with an adaptive basis function to eliminate RE in R2R gravure printing. This function, along with the registration error, updates the STILC compensation profile via a P-type iterative learning control (ILC) law. Our numerical experiments demonstrate that STILC with the adaptive basis function effectively eliminates RE caused by roller-motor axis mismatches and provides better convergence than STILC with an invariant basis function. This novel approach shows promise for various industrial applications involving spatially periodic disturbances, particularly those with unknown dynamics and without given state trajectories to track rigorously, which is common in engineering practice.