Backstepping Control of the One-Phase Stefan Problem

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 ${\mathcal{H}}_1$-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.

6 pages, 4 figures, The 2016 American Control Conference

Cited by in corpus (4)

• Output Feedback Control of the One-Phase Stefan Problem
• Stabilization of Filament Production Rate for Screw Extrusion-Based Polymer 3D-Printing
• Single-Boundary Control of the Two-Phase Stefan System
• Control and State Estimation of the One-Phase Stefan Problem via Backstepping Design