State and time delay estimation of continuous microorganisms cultivation

A continuous fermentation model taking into account the culture memory is used for a state estimation design. The influence of the culture memory on the process dynamics is accounted for by a time delay parameter. The proposed procedure of on-line state estimation in the case when the delay has a constant value is based on the extended Kalman observer. The case when the delay parameter is evaluated on-line is also considered. An adaptive state and parameter algorithm on the base of the extended Kalman filter is proposed. The theoretical results are applied to continuous culture for growth of a strain of Saccharomyces cerevisiae.List of Symbols X, S mg/l Biomass concentration and substrate concentration respectively - S ⁰ mg/l Feed substrate concentration - Z mg/l Past substrate concentration - µ h^–1 Specific growth rate taking into account culture memory - h^–1 Specific consumption rate - h Time delay parameter denoting culture memory - D h^–1 Dilution rate - State variables vector - W _ij Gain coefficient for on-line state and parameter estimation - F Substrate feed rate vector - () Gain coefficient matrix - R Square symmetric Riccati matrix - K Matrix of coefficients - K(t) Delay kernel taking account of culture memory - Denote an estimation value The partial support by Bulgarian National Science Research Foundation under Grant SRTS 428/94 Modeling and Control of Fermentation Processes Taking the Memory Effect into Account is gratefully acknowledged.