Boundary geometric control of a linear Stefan problem

This paper addresses the geometric control. of the position of a liquid solid interface in a melting process of a material known as Stefan problem. The system model is hybrid, i.e. the dynamical behavior of the liquid-phase temperature is modeled by a heat equation while the motion of the moving boundary is described by an ordinary differential equation. The control is applied at one boundary as a heat flux and the second moving boundary represents the liquid solid interface whose position is the controlled variable. The control objective is to ensure a desired position of the liquid solid interface. The control law is designed using the concept of characteristic index, from geometric control theory, directly issued from the hybrid model without any reduction of the partial differential equation. It is shown by use of Lyapunoy stability test that the control law yields an exponentially stable closed-loop system. The performance of the developed control law is evaluated through simulation by considering zinc melting. (C) 2014 Elsevier Ltd. All rights reserved.