Design of interval observers for an E. coli fed-batch fermentation with uncertain inputs

Abstract

In bioreactors, the measurement of variables that play a key role in the quality and productivity of fermentations, is of major importance. However, their direct measurement is often expensive or even impossible considering the current sensor technology. Therefore, on-line estimation of unmeasured variables in bioreactors can be an interesting approach. The objective of this work is to introduce an alternative solution for the state observation of bioprocesses in cases where the kinetic model is unclear and the concentration of the influent substrates is badly known, a situation that is common in many practical applications. The high-cell density fed-batch fermentation of Escherichia coli is studied in terms of applicability of a simple interval observer for the estimation of relevant variables of the process, when uncertainties of the process inputs exist. The simple interval observer is designed on the basis of the cooperativity properties of the observer error dynamics (Rapaport and Dochain, 2005). Further assumptions are the knowledge of the (lower and upper) bounds of the influent substrate concentration. Furthermore, an appropriate state transformation and conditions that guarantee system cooperativity have been introduced for that purpose. The performance of the interval observer is illustrated through numerical simulation.