Control-oriented modeling of Laser Metal Deposition as a repetitive process

Laser Metal Deposition (LMD) is an additive manufacturing process whose dynamics are driven by complex heat transfer and fluid flow phenomena. The LMD process, along with every additive manufacturing process, is fundamentally a two-dimensional process possessing both temporal (or spatial) domain dynamics and propagation of information from layer to layer. However, modeling the two-dimensionality of the process for use in control has received little attention. Here, a model aimed at capturing the important nonlinear two-dimensional physical processes of the melt pool shape, while maintaining simplicity, is presented. The model is expressed in a form that lends itself to the design of repetitive process control schemes. An analytical tool is used to describe layer-to-layer stability properties of the process using the model, and insights into the fundamental stability limitations of the process are given.