  Powder Bed Fusion (PBF) is an important Additive Manufacturing (AM) process
that is seeing widespread utilization. However, due to inherent process
variability, it is still very costly and time consuming to certify the process
and the part. This has led researchers to conduct numerous studies in process
modeling, in-situ monitoring and feedback control to better understand the PBF
process and decrease variations, thereby making the process more repeatable. In
this study, we develop a layer-to-layer, spatial, control-oriented thermal PBF
model. This model enables a framework for capturing spatially-driven thermal
effects and constructing layer-to-layer spatial controllers that do not suffer
from inherent temporal delays. Further, this framework is amenable to
voxel-level monitoring and characterization efforts. System output
controllability is analyzed and output controllability conditions are
determined. A spatial Iterative Learning Controller (ILC), constructed using
the spatial modeling framework, is implemented in two experiments, one where
the path and part geometry are layer-invariant and another where the path and
part geometry change each layer. The results illustrate the ability of the
controller to thermally regulate the entire part, even at corners that tend to
overheat and even as the path and part geometry change each layer.
