PI-controlled bioreactor as a generalized Liénard system

Abstract

"It is shown that periodic orbits can emerge in Cholette’s bioreactor model working under the influence of a PI-controller. We find a diffeomorphic coordinate trans-formation that turns this controlled enzymatic reaction system into a general-ized Lie´nard form. Furthermore, we give sufficient conditions for the existence and uniqueness of limit cycles in the new coordinates. We also perform numerical simu-lations 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."