“Optimal Aluminium Extrusion Planning Under Minimum-Taper Constraints”
Authors: Trym A.L. Gabrielsen, Lars Imsland, Peter Singstad, Anne Koren, Fredrik Gjertsen, Trond Aukrust and Ole Johannes Emmerhoff,Affiliation: NTNU, Department of Engineering Cybernetics, Cybernetica, SINTEF and Norsk Hydro
Reference: 2026, Vol 47, No 2, pp. 71-84.
Keywords: aluminium extrusion, process control, optimal control, nonlinear programming, direct collocation
Abstract: The minimum allowable initial billet taper affects the thermal margin available during aluminium extrusion and can therefore constrain the attainable production rate. This paper uses full-horizon dynamic optimization to quantify this trade-off while jointly optimizing the initial billet temperature distribution, ram-speed trajectory, and die-cooling trajectory. The formulation provides a means of predicting targets for the billet heating phase that facilitate minimum-time extrusion while accounting for peak-temperature and other process constraints. The problem is posed as a nonlinear program with extrusion time as its primary objective and with various process constraints, such as peak outlet temperature. We solve the problem with varying degrees of control freedom (ram-speed, cooling, initial taper) to quantify how the available process degrees of freedom affect the attainable extrusion time. In the considered case, under the assumption that extrusion-pressure limits remain inactive within the prescribed operating bounds, the minimum-taper constraint is active at the optimum. Over the investigated range, the corresponding minimum extrusion time increases approximately affinely by about 3.7 s per additional 10 degC per meter of axial taper. An industrial closed-loop simulator exhibits the same qualitative relationship, with a corresponding increase of about 2.5 s per 10 degC per meter.
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BibTeX:
@article{MIC-2026-2-3,
title={{Optimal Aluminium Extrusion Planning Under Minimum-Taper Constraints}},
author={Gabrielsen, Trym A.L. and Imsland, Lars and Singstad, Peter and Koren, Anne and Gjertsen, Fredrik and Aukrust, Trond and Emmerhoff, Ole Johannes},
journal={Modeling, Identification and Control},
volume={47},
number={2},
pages={71--84},
year={2026},
doi={10.4173/mic.2026.2.3},
publisher={Norwegian Society of Automatic Control}
};