Hybrid Modeling and Robust Control for Layer-by-Layer Manufacturing Processes

Abstract

This paper presents a hybrid system modeling and robust process optimization and control scheme for a layer-by-layer manufacturing process. In particular, the optimization of the layering times is offered as a solution for overcoming the challenge of maintaining through-cure during thick-part fabrication using ultraviolet radiation inputs that are subjected to in-domain attenuation. The layer deposition and curing sequence is modeled as a hybrid system by treating the underlying cure kinetics and the associated thermal process as a continuous dynamics switched by the discrete layering events. The interlayer hold times are taken as the control variables that can be optimally selected to minimize the final cure deviation across all layers. A robust optimization problem is posed that includes the sensitivity of the objective function to process the model parameter uncertainty. By adjoining the hybrid system model and the associated sensitivity constraints to the objective, the necessary conditions of optimality are derived. The advantages of the proposed robust optimization scheme are then demonstrated by simulating a layer-by-layer thick composite laminate fabrication process. It is shown that, compared with the use of nominal optimal layering time control, robust optimal layering time control significantly improves the performance in terms of closely tracking a desired final cure level distribution in the presence of parametric uncertainty.