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Modeling and cooling rate control in laser additive manufacturing: 1-D PDE formulation

Laser Additive Manufacturing (LAM) is becoming a versatile tool to manufacture parts with complex geometry. However, controlling the thermal history to optimize the microstructure property of the manufactured part remains challenging and highly experience-based. This paper investigates the real-time control of cooling rate, a commonly-used metrics of the thermal history during the LAM process. We use a one-dimensional Partial Differential Equation (PDE) to predict the conductive heat transfer in a single laser scan, with ambient cooling as a heat sink. Two approaches — based on the perspective in the inertial vs. body frames — are used to analyze the PDE. In the inertial frame, the PDE is projected to the eigenfunctions of the heat equation. In the laser frame, the PDE is transformed to an advection-diffusion-reaction equation, and approximated using the proper orthogonal decomposition (POD) method. For the control objective, we consider and compare two possible definitions of the cooling rate. Cooling rate control consists of two parts: 1. A feedforward control based on the steady-state temperature profile ensures melting and maximize the cooling rate. 2. a proportional-integral (PI) feedback controller regulates the setpoint in the presence of external thermal disturbance and modeling error.