Stability analysis of a bioreactor model with delayed feedback control

Abstract

We consider a well known mathematical model, describing the process ofВ anaerobic biological treatment (methane fermentation) of organic wastes in a
continuously stirred tank bioreactor. The model is presented by twoВ non-linear ordinary differential equations and one algebraic equation for the gaseous (methane) output.В We introduce a feedback control law, which depends on the on-line measurable output and involves a discrete delay.В This is a practically oriented problem, becauseВ there is always a time delay between output measurements andВ system's response in industrial applications, cf. [1].
Delayed bioreactor models have been recently investigated by manyВ authors as an attempt to explain different phenomenaВ in practical experiments, see e.~g. [2] and theВ references therein. The aim of the paper is to study the stabilizability of theВ considered closed-loop model with respect to the time delay.В A numerical extremum seeking algorithm, implemented in web-based environment [3] is
applied to optimize the methane flow rate in real time.В Simulation results are presented to illustrate the efficiency of the algorithm.