Control-oriented Modeling and Multirate Feedback Control in Laser Powder Bed Fusion Additive Manufacturing

Abstract

A high-precision additive manufacturing process, laser powder bed fusion (LPBF) has enabled unmatched agile manufacturing of a wide range of products from engine components to medical implants. While finite element modeling and closed-loop control have been identified key for predicting and engineering part qualities in LPBF, existing results in each realm are developed in opposite computational architectures wildly different in time scale. This dissertation builds a first-instance closed-loop simulation framework by integrating high-fidelity finite element modeling with feedback controls originally developed for general mechatronics systems. By utilizing the output signals (e.g., melt pool width) retrieved from the finite element model (FEM) to directly update the control signals (e.g., laser power) sent to the model, the proposed closed-loop framework enables testing the limits of advanced controls in LPBF and surveying the parameter space fully to generate more predictable part qualities. Along the course of formulating the framework, we build and refine an FEM of the thermal response in LPBF and verify the FEM by comparing its results with experimental and analytical solutions. Thereafter, we use the FEM to understand the melt-pool evolution induced by the thermomechanical interactions in LPBF. In addition, we build a new Hammerstein mixed-fidelity model to capture more of the complex spatiotemporal thermal dynamics. Under the architecture of the closed-loop simulation, we discuss general loop-shaping algorithms and specifically develop a multirate fractional-order repetitive control (RC) algorithm that addresses an intrinsic RC limitation when the exogenous signal frequency cannot divide the sampling frequency of the sensor. We also investigate the model inversion techniques---an important piece of the loop-shaping control---and build an $H_\infty$-based optimal inversion that attains model accuracy at the frequency regions of interest while constraining noise amplification elsewhere to guarantee system robustness. Besides, we analyze spectral properties of the closed-loop signals under sample-data control and show that the single-rate high-gain feedback cannot reject disturbances near and beyond the Nyquist frequency. From there, we provide a case study on applying an RC algorithm to greatly attenuate periodic thermal variations in LPBF.