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Related Experiment Video

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Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

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

Bryan Petrus¹, Zhelin Chen², Hamza El-Kebir²

¹University of Illinois Urbana-Champaign, Champaign, IL 61801 USA. He is now with Nucor Steel Decatur, Decatur, AL 35673 USA.

IEEE Transactions on Automatic Control

|August 7, 2024

Summary

This summary is machine-generated.

This study develops output feedback boundary control laws for the Stefan problem, enabling precise tracking of temperature and phase change interfaces using enthalpy-based system states. The methods ensure stable control and accurate trajectory following for diffusion systems.

Keywords:

Control Stefan problem enthalpy nonlinear partial differential equations solidification

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Area of Science:

Thermodynamics and Heat Transfer
Control Systems Engineering
Mathematical Modeling

Background:

The Stefan problem, a phase change problem with moving boundaries, presents significant challenges in control due to its nonlinear dynamics.
Accurate control of temperature profiles and interface position is crucial for many industrial processes involving phase transitions.

Purpose of the Study:

To develop output feedback boundary control laws for a nonlinear, one-dimensional partial differential equation (PDE) process model representing the Stefan problem.
To achieve trajectory tracking of both the spatiotemporal temperature and the temporal interface position.

Main Methods:

Enthalpy is utilized as the system state, expressed via temperature profile and interface position.
A full-state feedback controller is designed for single-sided boundary control.
A stable observer is developed for full-state reconstruction.
Output feedback control laws are derived by combining the controller and observer.

Main Results:

The developed control laws ensure closed-loop convergence of temperature and interface errors for both single-sided and two-sided Stefan problems.
Simulations demonstrate exponential-like trajectory convergence.
Implementable smooth bounded control signals are achieved.

Conclusions:

The proposed output feedback boundary control strategy effectively addresses the complexities of the Stefan problem.
Stable and accurate trajectory tracking of temperature and phase change interfaces is achievable.
The methodology provides a robust framework for controlling diffusion-type systems with moving boundaries.