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
N1 - Funding Information:
Manuscript received August 19, 2019; revised February 26, 2020; accepted July 26, 2020. Date of publication August 5, 2020; date of current version June 29, 2021. This work was supported by Fonds de la Recherche Scientifique—FNRS. The work of Anthony Hastir was supported by FNRS Research Fellow under the Grant FC 29535. Recommended by Associate Editor Y. Le Gorrec. (Corresponding author: Anthony Hastir.) Anthony Hastir and Joseph J. Winkin are with the Department of Mathematics and Namur Institute for Complex Systems (naXys), University of Namur, B-5000 Namur, Belgium (e-mail: anthony.hastir@unamur.be; joseph.winkin@unamur.be).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/7
Y1 - 2021/7
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 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.
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 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.
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
KW - Gâteaux-Fréchet derivatives
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
SN - 0018-9286
VL - 66
SP - 3235
EP - 3242
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 7
M1 - 9159873
ER -