Non-Linear Dynamic Modeling of Cartesian-Frame FFF 3-D Printer Gantry for Predictive Control

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Date

2023

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University of Texas at Austin

Abstract

This paper presents the development of a dynamic model of an FFF 3-D printer gantry (2-D) that is useful for developing an open-loop predictive control system. This predictive control system based on the mechanics of the system will help to reduce manufacturing defects by minimizing position error in the printing head. A six-dimensional non-linear dynamic model of the printer gantry was derived using Newton-Euler method, followed by a Lagrangian dynamic model to gain additional insight on energy transfer aspects and model validation. A state-space model of the full system was developed for positioning and control. A detailed case-study of an example printer was completed in MATLAB-Simulink to demonstrate the system model with comparisons from the analytical model and physical characterization on a real printer. Finally, a few examples of passive control designs were illustrated for predictive control development. It was concluded that dynamics-based predictive control is a promising, realistic, and practical approach to controlling the dynamic error and dimensional error commonly seen with FFF machines.

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