Gaussian Process (GP)-based Learning Control of Selective Laser Melting Process

In-layer Thermal Control of a Multi-layer Selective Laser Melting Process

“…The laser moves along a trajectory µ k : [0, τ k ] → R 2 that defines the sliced geometry of the part at layer k. As in [12], [15] we adopt a Gaussian beam model and take the laser power as our controlled variable. Specifically, the heat flux due to the laser is…”

“…Ideally, the input constraint u(t) ∈ U would be incorporated directly into the optimization problem (15), which would then be solved repeatedly, resulting in an model predictive control (MPC) like structure, e.g., [22]. However, the computational cost of the resulting controller is likely prohibitive for high loop-rates.…”

“…The two main approaches for LPBF control have been proposed in the literature: In-layer (intra-layer) controllers update process inputs during the printing of a single layer, while inter-layer or layer-to-layer (L2L) controllers update the inputs between the layers. In-layer control has been used to adjust melt pool dimensions in experimental setups on single tracks and build parts using PID control [5], [7], [17]- [19], on geometries with overhang features [6], and with datadriven modeling techniques in simulation studies [20]. While providing promising results, these methods rely on controller tuning to get desired process characteristics, which may be time consuming and expensive.…”

“…While demonstrating practical applicability, these controllers do not consider optimal regulation or input constraints of the physical process, and do not capture the multi-layer process dynamics. In [15], a Gaussian Process surrogate model for a single layer process is considered for in-layer closed loop model predictive control (MPC) of the laser power. While MPC provides improved control performance, multi-layer dynamics of the process and heat accumulation from previous layers again is not considered.…”