On-line Biomass Estimation in a Batch Bio-technological Process: Bacillus Thuringiensis δ - Endotoxins Production

Biomass concentration in a biotechnological process is one of the states that characterize a bioprocess. Moreover, it is generally the main direct or indirectly desired product. It is well known that the biomass concentration is not normally measured online because this measurement is not possible or this is economically unprofitable. Therefore, for control purposes it is necessary to replace the unavailable biomass concentration measurements with reliable and robust online estimations. To this aim, several states observers can be found in the literature. A review of commonly used techniques can be found in (Bastin & Dochain, 1990; Dochain, 2003) and references therein. Observers can be coarsely divided into two broad classes: first principles or phenomenological estimators and empirical estimators. The phenomenological estimators can be also subdivided into classical observers and asymptotic observers. Classical observers include extended Kalman filter (EKF), extended Luenberger observer, high gain observer, nonlinear observers, and full horizon observer. In this class of estimators, a detailed knowledge of the reaction kinetics and associated transport phenomena are required to represent the balance equations. Modeling the biological kinetics reactions is a difficult and time-consuming task, and therefore the model used by the estimators could differ significantly from reality. This is the main disadvantage of these phenomenological estimators, i.e., their efficiency strongly relies on the model quality. Asymptotic observers are based on the idea that uncertainty in bioprocess models lies in the process kinetics models. The design of these observers is based on a state transformation performed to provide a model which is independent of the kinetics. A potential drawback of the asymptotic observers is that the rate of convergence is completely determined by the operating conditions, i.e., the rate of convergence can be very slow or the observer may not converge. Empirical estimators are based on constructing appropriate nonlinear models of biotechnological processes exclusively from the process input–output data without considering the functional or phenomenological relations between the bioprocess variables. However, the conventional empirical modeling approach is based on the knowledge of the structure (functional form) of the data-fitting model (in advance). This is a difficult task since it involves the heuristic selection of an appropriate nonlinear model structure from numerous alternatives.