WIAS Preprint No. 1402, (2009)

The heat treatment of steel --- A mathematical control problem


  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Kern, Daniela

2010 Mathematics Subject Classification

  • 74P10 80A20 93C20


  • Laser surface hardening, optimal control, pyrometer control




The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control.

Appeared in

  • Materialwiss. Werkstofftech., 40 (2009) pp. 438--442.

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