Additive Manufacturing (AM) is a set of manufacturing processes which has promise in the production of complex, functional structures that cannot be fabricated with conventional manufacturing and the repair of high-value parts. However, a significant challenge to the adoption of additive manufacturing processes to these applications is proper process control. In order to enable closed-loop process control compact models suitable for control design and for describing the layer-by-layer material addition process are needed. This dissertation proposes a two-dimensional modeling and control framework, with an application to a specific metal-based AM process, whereby the deposition of the current layer is affected by both in-layer and layer-to-layer dynamics, both of which are driven by the state of the previous layer. The proposed modeling framework can be used to create two-dimensional dynamic models for the analysis of layer-to-layer stability and as a foundation for the design of layer-to-layer controllers for AM processes. In order to analyze the stability of this class of systems, linear repetitive process results are extended enabling the treatment of the process model as a two-dimensional analog of a discrete time system. For process control, the closed-loop repetitive process is again treated as a two-dimensional analog of a discrete time system for which controllers are designed. The proposed methodologies are applied to a metal-based AM process, Laser Metal Deposition (LMD), which is known to exhibit layer-to-layer unstable behavior and is also of significant interest to high-value manufacturing industries --Abstract, page iii
