A Loop-Shaping Method for Frequency-Based Design of Layer-to-Layer Control for Laser Metal Deposition

Additive manufacturing processes fabricate parts in a layer-by-layer fashion, depositing material along a predefined path before incrementing to the next layer. Although the thickness of any given layer is bounded, in-layer dynamics can couple with layer-to-layer dynamics such that height defects amplify from one layer to the next. This is considered instability in the layer domain. By considering each layer as an iteration, additive processes can be categorized as repetitive processes. Although Repetitive Process Control (RPC) algorithms exist that can stabilize the process and converge to desired reference, it is typically assumed that the reference and disturbance are constant from layer to layer. In this paper, the problem of tracking references (layer thicknesses) that change from layer to layer is considered. The bandwidth of the changing references is considered bounded in both the spatial and layer domains. A loop-shaping design process is then considered, in which the bounds are mapped to a bound on the two-dimensional sensitivity function and projected onto weighting filters in an LQR control formulation. The layer-to-layer controller is then constructed from traditional LQR methods. The controller is demonstrated on a simulation of laser metal deposition for a wavy wall build having frequency content in both the spatial and layer domains.