Control of Oscillating Microbial Cultures Described by Population Balance Models

Abstract

Nonlinear feedback control laws are derived which attenuate undesired oscillations or induce synchrony in microbial cultures described by population balance models. The population balance model is solved using a finite difference method. A model suitable for controller design is obtained by expressing the population balance equations in terms of moments of the cell age distribution. Oscillations are damped, and the culture is forced to a desired equilibrium point by designing a feedback linearizing controller which manipulates dilution rate and feed substrate concentration and regulates cell number concentration and substrate concentration. An approximate equilibrium solution to the population balance equations is used to determine setpoint values for the two controlled variables. Cell synchrony is induced by designing a feedback linearizing controller which manipulates feed substrate concentration and regulates substrate concentration to an oscillatory trajectory of a predetermined period. The performance of the nonlinear controllers is evaluated through closed-loop simulations.