TY - JOUR

T1 - On exponential bistability of equilibrium profiles of nonisothermal axial dispersion tubular reactors

AU - Hastir, Anthony

AU - Winkin, Joseph J.

AU - Dochain, Denis

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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 PDEs 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 adressed. 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.

AB - 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 PDEs 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 adressed. 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.

KW - Dispersion

KW - Equilibrium profile

KW - Gateaux-Frechet derivatives

KW - Inductors

KW - Lyapunov method

KW - Mathematical model

KW - Nonisothermal tubular reactor

KW - Nonlinear infinite-dimensional system

KW - Numerical models

KW - Perturbation methods

KW - Stability analysis

KW - Two dimensional displays

UR - http://www.scopus.com/inward/record.url?scp=85089392576&partnerID=8YFLogxK

U2 - 10.1109/TAC.2020.3014457

DO - 10.1109/TAC.2020.3014457

M3 - Article

AN - SCOPUS:85089392576

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

ER -