Estimation of biomass concentration using interval observers in an E. coli fed-batch fermentation

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 observation of biomass concentration in E. coli fed-batch fermentations, in cases where the kinetic model is unclear and several variables, like the concentration of the influent substrates and the initial values of the state variables are badly known, a situation that is common in many practical applications. The simple interval observer is designed on the basis of the cooperativity properties of the observer error dynamics (Rapaport and Dochain, 2005). The performance of the interval observer is illustrated through numerical simulation and it was found that the observer deal well with uncertainties up to 50% and with white noise in the variables measured on-line. The interval obtained for the biomass estimation is also quite narrow, indicating that it is possible to accurately predict biomass concentration under the presence of uncertainties.