Online Biomass and Specific Growth Rate Estimation Aimed to Control of a Chemostat Microbial Cultivation Accounting for the Memory Effects

Abstract

A general chemostat microbial cultivation model accounting for the memory effects (in two modifications - μ-type and S-type) is used for biomass and growth rate estimation, based on measurements of the substrate concentration. The influence of the memory effects (history of the process) on the process dynamics is accounted for by employing a zero-order memory functions, characterized by different (in general case) adaptability parameters with respect to the specific growth rate and specific consumption rate. Thus, the memory effects are taken into account in both, growth dynamics and limiting substrate consumption dynamics. Two particular cases, which actually correspond to the most common practical situations on one side, and on the other side - the most suitable model structures of the growth rate from a point of view of control synthesis, are also considered. The first one assumes that the memory effects are taken into account in both, biomass and substrate, equations (specific growth and consumption rates expressions) with equal adaptability parameters, and the second one - in the biomass equation only (specific growth rate expression). The proposed procedure, based on the extended Kalman filtering method, is developed under assumption that the process kinetics models are known except for the adaptability parameter(s). Thus the necessity of performing step-response experiments for the sake of adaptability parameter(s) identification could be successfully avoided. As an example, two estimators, based on different kinetic models of continuous growth of a strain Saccharomyces cerevisiae on a glucose limited medium, are designed. The two models have the same structure and kinetic parameters (identified on the basis of steady-state experiments) and differ the way of memory function incorporation only. The estimation performance is studied under different initial conditions. The effect of the estimation error on the control performance, in case of adaptive control of biomass and substrate concentration, is also investigated. The simulation results are discussed with respect to the applicability of the proposed estimators in the framework of adaptive control systems.