Control-oriented models for ink-jet 3D printing

This paper proposes two control-oriented models to describe the layer-to-layer height evolution of the ink-jet 3D printing process. While the process has found wide applicability, as with many industrial 3D printing systems, ink-jet 3D printers operated in open loop, even when sensor measurements are available. One of the primary reasons for this is the lack of suitable control-oriented models of the process. To address this issue, two control-oriented models are proposed in this paper, the first is based on droplet geometry superposition, while the other is based on a graph-based characterization of local flow dynamics. The superposition model ignores the flow of the deposited liquid material, while the graph-based dynamic model is able to capture this phenomenon. These two models are compared with an existing flow-based empirical model and validated with experimental results, with the graph-based dynamic model demonstrating between 5 and 14% improvement in layer height prediction. Both the superposition model and the graph-based dynamic model are suitable for closed-loop control algorithm design (as they are discrete layer-to-layer state-space models). We envision that these control-oriented models will ultimately enable the design of model-based closed-loop control for high resolution ink-jet 3D printing.