On exponential bistability of equilibrium profiles of nonisothermal axial dispersion tubular reactors

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    Résumé

    Sufficient conditions are established for the exponential stability/instability of the equilibrium profiles for a linearized model of nonisothermal axial dispersion tubular reactors. The considered reactors are assumed to involve a chemical reaction of the form A → B, where A and B denote the reactant and the product, respectively, and where the Peclet numbers appearing in the energy and mass balance partial differential equations are assumed to be equal. First, different kinds of linearization of infinite-dimensional dynamical systems are presented. Then, the considered linearized model around any equilibrium is shown to be well-posed. Moreover, by using a Lyapunov-based approach, exponential stability is addressed. In the case when the reactor can exhibit only one equilibrium, it is shown that the latter is always exponentially stable. When three equilibrium profiles are exhibited, bistability is established, i.e. the stability pattern '(exponentially) stable - unstable - stable' is proven for the linearized model. The results are illustrated by some numerical simulations.

    langue originaleAnglais
    Numéro d'article9159873
    Pages (de - à)3235-3242
    Nombre de pages8
    journalIEEE Transactions on Automatic Control
    Volume66
    Numéro de publication7
    Les DOIs
    Etat de la publicationPublié - juil. 2021

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