On Exponential Bistability of Equilibrium Profiles of Nonisothermal Axial Dispersion Tubular Reactors

• 成果类型: Article
• 署名作者: Hastir, Anthony; Winkin, Joseph J.; Dochain, Denis
• 署名单位: University of Namur; University of Namur; Universite Catholique Louvain
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3014457
• 发表日期: 2021
• 页码: 3235-3242
• 关键词: Equilibrium profile; Gateaux-Frechet derivatives; Lyapunov method; nonisothermal tubular reactor; nonlinear infinite-dimensional system

摘要

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.