Modeling-Error Compensation Approach for Extremum-Seeking Control of Continuous Stirred Tank Bioreactors with Unknown Growth Kinetics

Abstract

In this paper, an adaptive extremum seeking control scheme for continuous stirred tank bioreactors is presented. Unknown growth kinetics without considering an explicit mathematical expression is assumed. An adaptive learning technique based on modeling error estimation coupled with a proportional compensation is used to construct a feedback control that maximizes a production function (e.g., biogas production) that depends on the growth kinetics. Also, it is assumed that only the production output and the substrate concentration are available from measurements. It is shown that the resulting controller is equivalent to a proportional–integral compensator. The closed-loop analysis based on singular perturbation techniques showed the stability of the controlled bioreactor at about the optimal equilibrium point. Numerical simulations on a simple example and a more realistic anaerobic digestion case are used to illustrate the stability properties.