Application of enthalpy-based feedback control methodology to the two-sided stefan problem

Bryan Petrus, Joseph Bentsman, Brian Thomas

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In [1], the authors introduced a novel control law for the single-phase Stefan problem, a nonlinear partial differential equation, with the eventual goal of applying the result to control of cooling in continuous steel casting. In this paper, the previously published method of controlling the Stefan problem is extended in two key ways that improve the fidelity of the nonlinear PDE as a model of the temperature and solidification of continuous steel casters. First, a non-symmetric temperature distribution is allowed, in which separate Neumann boundary control is applied at either surface. Two convergent control laws are compared in simulation, with one converging significantly faster. Second, saturation of the Neumann boundary control input is considered. Saturation is a significant concern in the actual process. The enthalpy-based algorithm still allows for convergence under saturation. However, as one would expect, severity of the constraints can affect the convergence rate.

Original languageEnglish (US)
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781479932726
StatePublished - 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: Jun 4 2014Jun 6 2014

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2014 American Control Conference, ACC 2014
Country/TerritoryUnited States
CityPortland, OR


  • Distributed parameter systems
  • Materials processing

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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