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

Abstract Roll-to-Roll (R2R) systems, featuring a series of motorized or idle rollers, are pivotal for high-volume, continuous production of flexible substrates across various industrial applications. One of the significant challenges in R2R printing processes lies in maintaining tight alignment tolerances, as specified by the device resolution for multi-layer printed electronics. The alignment of the printed patterns in different layers is known as registration. However, the inherent deformability of flexible substrates, coupled with the complicated dynamics of rollers result in significant difficulties for high-precision registration control. The registration error (RE) is essentially the positional or dimensional deviation caused by undesired variations in substrate tensions and substrate speeds. Despite the employment of real-time feedback controllers such as Proportional-Integral-Derivative (PID) or Model Predictive Control (MPC) for R2R tension control, they are not responsive enough to transient disturbances and they fail to continually enhance performance in the presence of angle-periodic disturbances, a common scenario in R2R systems due to roller rotations. In this study, we introduce a Spatial-Terminal Iterative Learning Control (STILC) method, incorporating an adaptive basis function, aimed at eradicating RE in an R2R gravure printing process. This basis function, alongside the registration error, is utilized in the update of the STILC compensation profile via a P-type Iterative Learning Control law. Our numerical experiments show that the STILC with the adaptive basis function effectively eliminates the RE caused by roller-motor axis mismatches. Additionally, we also verify by simulations that our method provides better convergence performance than the STILC with an invariant basis function. This novel STILC approach is promising for various industrial applications involving spatially periodic disturbances, especially those with unknown dynamics and without given state trajectories to track rigorously, which is common in engineering practice.