PI-controlled bioreactor as a generalized Lienard system

Details PI-controlled bioreactor as a generalized Lienard system PI-controlled bioreactor as a generalized Lienard system

2005-02-21

arxiv.org/abs/nlin/0502049v2

Computers and Chem. Eng. 31 (2007) 136-141

Nonlinear Sciences

Chaotic Dynamics

15 pages, 5 figures, accepted version at Computers & Chem. Eng

Scientific paper

10.1016/j.compchemeng.2006.05.02

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

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