Cell population models for bifurcation analysis and nonlinear control of continuous yeast bioreactors

Abstract

Saccharomyces cerevisiae (baker's yeast) can exhibit sustained oscillations over a wide range of operating conditions when produced in a continuous bioreactor. In this paper the bifurcations leading to these periodic solutions are investigated using an unstructured, segregated model in which the population balance equation (PBE) for the cell mass distribution is coupled to the mass balance of the rate limiting substrate. The PBE model is shown to produce periodic solutions over a range of dilution rates due to the presence of two supercritical Hopf bifurcations. The problem of oscillation attenuation using nonlinear feedback control with four candidate input/output variable pairings is investigated. The controller designs are based on a low dimensional moment representation of the PBE model. The performance of the nonlinear controllers are compared and discussed.