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Distributed control of nonlinear diffusion systems by input–output linearization

Authors

  • Ahmed Maidi,

    1. Laboratoire de Conception et de Conduite des Systèmes de Production, Université Mouloud MAMMERI, 15 000 Tizi-Ouzou, Algérie
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  • Jean-Pierre Corriou

    Corresponding author
    1. Laboratoire Réactions et Génie des Procédés, CNRS-ENSIC-INPL, Lorraine Université, Nancy Cedex, France
    • Correspondence to: Jean-Pierre Corriou, Laboratoire Réactions et Génie des Procédés, CNRS-ENSIC-INPL, Lorraine Université, 1, rue Grandville BP 20451, 54001 Nancy Cedex, France

      E-mail: jean-pierre.corriou@ensic.inpl-nancy.fr

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SUMMARY

This paper addresses the distributed control by input–output linearization of a nonlinear diffusion equation that describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model without any approximation or reduction. The main idea consists in the control design in assuming an equivalent linear diffusion equation obtained by use of the Cole–Hopf transformation. This framework helps to demonstrate the closed-loop stability using some concepts from the powerful semigroup theory. The performance of the proposed controller is successfully tested, through simulation, by considering a nonlinear heat conduction problem concerning the control of the temperature of a steel plate modeled by a nonlinear heat equation with Dirichlet boundary conditions. Copyright © 2012 John Wiley & Sons, Ltd.

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