Model Predictive Control of PDEs for Temperature Control in 3D-Printing Processes

Processes of additive manufacturing by 3D-printing are typically operated by only using constant references for feed motion and laser power. For adapting properties of workpieces to desired geometries, the control towards changing reference signals is an enabling factor, though. With a focus on temperature control, this paper proposes a scheme of model predictive control for 3D-printing with consideration of constraints and arbitrary references. Starting from partial differential equations to model heat propagation over the geometry, prediction models and optimization problems are formulated as a local part of a more detailed simulation model of the complete workpiece. For laser velocity and power as manipulated variables, optimization problems involving integer variables are solved. Simulation results show how spatial temperature profiles can be adjusted by the proposed approach.