Robust Monotonically Convergent Spatial Iterative Learning Control: Interval Systems Analysis via Discrete Fourier Transform

Abstract

Additive manufacturing (AM) systems use a layer-by-layer paradigm to build three-dimensional structures. There are myriad of advantages to AM; however, challenges with real-time actuation and sensing relegate AM processes to be largely open-loop processes. In this paper, we build upon the spatial iterative learning control (SILC) strategy to close the loop in the iteration domain in AM systems, enabling autonomous process control in the absence of real-time sensing. We approximate the steady-state partial differential equations of AM systems by discrete two-dimensional convolution operators and assume uncertain spatially varying kernels to have a more realistic representation of these complex processes. From this system description, we formalize the robust monotonic convergence (RMC) criterion for SILC. Importantly, we use discrete Fourier transform-based tools to study spatial dynamics, a practical framework for data-rich spatial sensors used in AM. The theoretical results are complemented with experiments on the AM process electrohydrodynamic jet printing, demonstrating that the RMC criterion can predict the design boundary for convergent behavior for norm-optimal SILC.