materials Article Model-Based Feedforward Control of Part Height in Directed Energy Deposition Qian Wang 1, *, Jianyi Li 1 , Abdalla R. Nassar 2 , Edward W. Reutzel 2 and Wesley F. Mitchell 2   Citation: Wang, Q.; Li, J.; Nassar, A.R.; Reutzel, E.W.; Mitchell, W.F. Model-Based Feedforward Control of Part Height in Directed Energy Deposition. Materials 2021, 14, 337. https://doi.org/10.3390/ ma14020337 Received: 24 November 2020 Accepted: 4 January 2021 Published: 11 January 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional clai- ms in published maps and institutio- nal affiliations. Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA; gejianyili@gmail.com 2 Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16802, USA; arn5000@arl.psu.edu (A.R.N.); ewr101@arl.psu.edu (E.W.R.); wfm11@arl.psu.edu (W.F.M.) * Correspondence: quw6@psu.edu Abstract: Control of the geometric accuracy of a metal deposit is critical in the repair and fabrication of complex components through Directed Energy Deposition (DED). This paper developed and experimentally evaluated a model-based feedforward control of laser power with the objective of achieving the targeted part height in DED. Specifically, based on the dynamic model of melt- pool geometry derived from our prior work, a nonlinear inverse-dynamics controller was derived in a hatch-by-hatch, layer-by-layer manner to modulate the laser power such that the melt-pool height was regulated during the simulated build process. Then, the laser power trajectory from the simulated closed-loop control under the nonlinear inverse-dynamics controller was implemented as a feedforward control in an Optomec Laser-Engineered Net Shape (LENS) MR-7 system. This paper considered the deposition of L-shaped structures of Ti-6AL-4V as a case study to illustrate the proposed model-based controller. Experimental validation showed that by applying the proposed model-based feed-forward control for laser power, the resulting build had 24–42% reduction in the average build height error with respect to the target build height compared to applying a constant laser power through the entire build or applying a hatch-dependent laser power strategy, for which the laser power values were obtained from experimental trial and error. Keywords: directed energy deposition; additive manufacturing; feedforward control; nonlinear inverse-dynamics control; build height regulation 1. Introduction Additive Manufacturing (AM), also called 3D printing, refers to a process that builds three-dimensional parts directly from the complex Computer-Aided Design (CAD) files by depositing material in a layer-by-layer manner. Directed energy deposition (DED) is one type of AM processes, where focused energy, such as an electron beam or laser beam, is used to melt material as filler material is being deposited [1–3]. Laser-Engineered Net Shape (LENS) and Laser Metal Deposition-powder (LMD-p) are among the typical DED AM processes. For fabrication of complex components through DED, model-based real-time control or optimization of process parameters is often required to ensure build quality and geo- metric accuracy of a build part. Most of the existing real-time controllers for DED were restricted to classical controllers, e.g., on/off bang-bang controller [4], and Proportional– Integral–Derivative (PID) controllers [5–11], to name a few. The PID controllers were designed either based on pure sensing information without a model [6,7,10] or based on relatively simplistic single-input single-output empirical models, e.g., a first-order transfer function [8]; a first-order transfer function plus a time delay [11]; or a knowledge-based empirical model [5,9]. Advanced control methodologies were also investigated in several studies. A fuzzy logic controller was designed to follow the desired clad height in a cladding process by controlling the laser power [12]. A sliding mode controller, together Materials 2021, 14, 337. https://doi.org/10.3390/ma14020337 https://www.mdpi.com/journal/materials