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arXiv · 1607.04345

Backstepping Control of the One-Phase Stefan Problem

Shumon Koga·Mamadou Diagne·Shuxia Tang·Miroslav Krstic
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Abstract

In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A new nonlinear backstepping transformation for moving boundary problem is utilized to transform the original coupled PDE-ODE system into a target system whose exponential stability is proved. The full-state boundary feedback controller ensures the exponential stability of the moving interface to a reference setpoint and the ${\cal H}_1$-norm of the distributed temperature by a choice of the setpint satisfying given explicit inequality between initial states that guarantees the physical constraints imposed by the melting process.

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Shumon Koga, Mamadou Diagne, Shuxia Tang, Miroslav Krstic. 2016-07-14. Backstepping Control of the One-Phase Stefan Problem. https://arxiv.org/abs/1607.04345

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