<p>Additive manufacturing, particularly laser-based directed energy deposition (DED-LB), offers advantages over conventional subtractive methods, such as near-net-shape manufacturing. In DED-LB, the surface of the substrate is melted by a laser, while powder is deposited simultaneously, track by track, to form layers and a final part geometry. As the industry requires high-quality part geometries, modelling and prediction of those are essential for manufacturing accuracy. However, coupled physical phenomena, such as remelting, make the prediction challenging. To address this challenge, a controller can react to deviations by adapting process parameters, enabling control over final part geometry characteristics like track height. First, parameters were altered along single tracks, and resulting heights were measured offline using a laser triangulation sensor. Next, the enhanced geometry data provided the basis for the system identification which forms the foundation of a data-based model predictive controller. In order to enhance the behaviour and dynamics of the system, different models were identified and compared, including specifically tailored grey-box models. Based on the results, the nonlinear grey-box models are the most promising approach for a future model predictive controller development for the investigated DED-LB process.</p>