State Observer Design Based on a Model of Chemostat Microbial Cultivation Accounting for the Memory Effects

Abstract

The problem of model-based state observer design for the chemostat microbial cultivation is considered. General chemostat model accounting for the memory (delay) effects is used for the state observer design. The memory effects influencing the process dynamics are described by zero-order exponential memory functions in the expressions of the specific growth rate and specific consumption rate. Two modifications of the general model (µ-type and S-type models) are used for the state observer design. In the first modification, the memory effects are accounted for by weighted averages of the specific growth and consumption rates' past values. The second modification assumes that the memory effects are accounted for by weighted averages of the past values of the substrate concentration only. Particular cases, when the memory effects are taken into account in the specific growth and consumption rates by equal memory functions and when the memory effects are taken into account in the expression of the specific growth rate only, are considered. The proposed procedure is based on the Kalman filtering method under the assumption for full knowledge of the process kinetics and on-line measurement of the limiting substrate concentration. As a case study, a model of the continuous growth of a strain Saccharomyces cerevisiae on a glucose-limited medium is considered. The robustness of the observer with respect to the adaptability parameter variations is studied.