Boundary geometric control of a linear Stefan problem |
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| Affiliation: | 1. Laboratoire de Conception et Conduite des Systèmes de Production, Université Mouloud MAMMERI, 15 000 Tizi-Ouzou, Algeria;2. Laboratoire Réactions et Génie des Procédés, UMR 7274-CNRS, Lorraine Université, ENSIC 1, rue Grandville, BP 20451, 54001 Nancy Cedex, France;1. CNRS, Control Systems Department, University of Grenoble, 11, rue des Mathématiques, Domaine Universitaire, 38400 Saint Martin d’Hères, France;2. Schneider Electric, Technology Innovation, Technopole, 37-quai Paul Merlin, 38050 Grenoble cedex, France;1. Institut de Robòtica i Informàtica Industrial (CSIC-UPC), Technical University of Catalonia (UPC), Llorens i Artigas 4-6, 2nd floor, 08028 Barcelona, Spain;2. Department of Automatic Control and Systems Engineering, Faculty of Automatic Control and Computers, “Politehnica” University of Bucharest, 313 Spl. Independentei, 060042 Bucharest, Romania;3. E3S (SUPELEC Systems Sciences), Automatic Control Department, Gif sur Yvette, France;1. Chair of Optimal Control, Technische Universität München, Fakultät für Mathematik, Boltzmannstraße 3, 85748 Garching b. München, Germany;2. Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany;1. Department of Chemical & Biomolecular Engineering, Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong;2. Department of Control Science & Engineering, Zhejiang University, 310027, China;3. Guangzhou Fok Ying Tung Research Institute, Hong Kong University of Science & Technology, Hong Kong, China |
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| Abstract: | 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 Lyapunov 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. |
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| Keywords: | Distributed parameter system Stefan problem Moving boundary Geometric control Characteristic index Exponential stability |
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