Estimation of Substrate and Biomass Concentrations in a Chemostat using an Extended Kalman Filter

Abstract

This paper presents the estimation of substrate and biomass concentrations inside a Chemostat used for waste-water treatment. These concentrations represent the state variables of the process model. Most research in this field used only deterministic models, not accounting for uncertainties and noises on the states and on the output. Hence, the estimation of these concentrations may not be sufficiently accurate. For a more realistic description, we used here a stochastic formulation. Unlike the other research works, we used a stochastic differential equations (SDE) model which provides a better representation of the system in his natural processing scale. This model also includes the aleatory effects in the process which had been discarded in the other works. We then deal with the state estimation problem using an Extended Kalman filter, which proceeds with a linearization of the model around a deterministic trajectory. The classical prediction and update steps of the filter are then carried-out and led to good results. Notice that the system in study has some interesting properties such as discrete-time observations, high noise intensities and slow-time evolution. Results are presented, discussed and compared with the related state-of-the-art researches.

Keywords

• Extended Kalman filter
• State estimation
• Chemostat
• Waste-water treatment