Layer-to-Layer Stability of Linear Layerwise Spatially Varying Systems: Applications in Fused Deposition Modeling

Closed-loop control applications for additive manufacturing (AM) technologies introduce unique challenges in control-oriented modeling and controller development. There have been developments in current literature to model the temporal and spatial dynamics of AM processes. The temporal dynamics of AM processes are often modeled using tools from fluid dynamics and mechanics to represent the material deposition and the motion of the deposition system. Spatial dynamics are often modeled by representing the spreading dynamics of the deposited material in the layerwise spatial domain. An important challenge with the spatial dynamics of AM processes is to understand the performance of the layer-to-layer (L2L) spatial dynamics under spatial disturbances in the system. To this end, this article presents a linear layerwise spatially varying (LLSV) systems modeling framework to represent the L2L spatial height evolution of a generic AM process. The proposed unifying modeling framework can easily represent various AM processes. An L2L stability measure is provided as a performance measure for the spatial dynamic state of an AM process. L2L stability is a novel analysis tool to understand and analyze the spatial characteristics of AM processes. Fundamental L2L stability definitions for a nominal system model and a system model with known Gaussian spatial noise are presented. Theoretical robustness bounds for L2L stability are experimentally compared to a fused deposition modeling (FDM) process. The results show that the theoretical robustness bounds given in this work provide an important foundation for developing novel closed-loop L2L spatial control applications.