Solid Boundary Output Feedback Control of the Stefan Problem: The Enthalpy Approach

Bryan Petrus, Zhelin Chen, Hamza El-Kebir, Joseph Bentsman, Brian Thomas

Research output: Contribution to journalArticlepeer-review


By taking enthalpy - an internal energy of a diffusion-type system - as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.

Original languageEnglish (US)
Pages (from-to)3485-3500
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 1 2023


  • control
  • Convergence
  • Enthalpy
  • enthalpy
  • nonlinear partial differential equations
  • Observers
  • Output feedback
  • solidification
  • Steel
  • Stefan problem
  • Temperature control
  • Temperature sensors
  • Control

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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