A hybrid modeling and optimal control framework for layer-by-layer radiative processing of thick sections

This paper introduces a hybrid modeling and optimal control framework for a class of layer-by-layer manufacturing processes. Specifically, a stepped-concurrent layer-by-layer process is offered as a solution for overcoming the challenge of maintaining through-cure during thick-part fabrication using Ultraviolet (UV) radiation inputs that are subject to in-domain attenuation. The layering and curing sequence is modeled as a hybrid system, where the layering steps constitute discrete events on otherwise continuous curing kinetics and thermal processes. It is shown that the UV intensity as well as the inter-layer hold times can be selected optimally by posing an optimal control problem with the objective of minimizing the overall cure deviation in the thick multi-layer part. The necessary conditions for optimality are explicitly derived by adjoining the coupled PDE and ODE constraints of the process model. The potential benefit of the proposed optimization scheme is demonstrated considering simulations of a composite laminate curing process. It is found that, compared to traditional equal-interval layering, optimal layering time control gives significantly improved performance in terms of minimizing cure-level deviation, for comparable total energy usage. There is also some added benefit to optimizing the inter-layer UV input as well.