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

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 m...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2023-06, Vol.68 (6), p.3485-3500
Main Authors: Petrus, Bryan, Chen, Zhelin, El-Kebir, Hamza, Bentsman, Joseph, Thomas, Brian G.
Format: Article
Language:English
Subjects:
Actuation
Boundary control
Closed loops
Control
Control systems
Control theory
Convergence
Enthalpy
Feedback control
Heat flux
Internal energy
nonlinear partial differential equations
Observers
Output feedback
Solidification
Steel
Stefan problem
Temperature control
Temperature profiles
Temperature sensors
Tracking control
Trajectory control
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3197704