PI-controlled bioreactor as a generalized Lienard system
Chaotic Dynamics
2007-05-23 v2
Abstract
It is shown that periodic orbits can occur in Cholette's bioreactor model working under the influence of a PI-controller. We find a diffeomorphic coordinate transformation that turns this controlled enzymatic reaction system into a generalized Lienard form. Furthermore, we give sufficient conditions for the existence and uniqueness of limit cycles in the new coordinates. We also perform numerical simulations illustrating the possibility of the existence of a local center (period annulus). A result with possible practical applications is that the oscillation frequency is a function of the integral control gain parameter
Cite
@article{arxiv.nlin/0502049,
title = {PI-controlled bioreactor as a generalized Lienard system},
author = {V. Ibarra-Junquera and H. C. Rosu},
journal= {arXiv preprint arXiv:nlin/0502049},
year = {2007}
}
Comments
15 pages, 5 figures, accepted version at Computers & Chem. Eng