Regulating the melt-pool size to a constant reference value during the build process is a challenging task in Laser Powder Bed Fusion additive manufacturing (LPBF-AM). This paper considers adjusting laser power to achieve a constant melt-pool volume during laser processing of a multi-track build under LPBF-AM. First, a Gaussian Process Regression (GPR) is applied to model the variation of the melt-pool volume along the deposition distance, with physics-informed input features. Then a constrained finite-horizon optimal control problem is formulated, with a quadratic cost function defined to minimize the difference between the melt-pool volume and a reference value. A projected gradient descent algorithm is applied to compute the sequence of laser power in the proposed optimal control problem. The GPR modeling of melt-pool dynamics is trained and tested using simulated data sets generated from a commercial finite-element based AM software, and the same commercial AM software is used to evaluate the control performance. Simulation results demonstrate the effectiveness of the proposed GPR modeling and optimal control in regulating melt-pool volume for building multi-track parts with LPBF-AM.

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