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 -