On-Line Estimation of the Reaction Rates in Bioreactors from Multirate Sampled Outputs with Multiple Delays

Abstract

This paper provides a simple high gain continuous-discrete time observer to handle the estimation problem of the reaction rates in bioreactors using delayed sampled measurements of the component concentrations in the context of multirate sampling of the outputs each one of which is affected by a constant delay. The rational behind the proposed observer design consists in the consideration of an appropriate corrective term provided by a linear Delay Differential Equation (DDE), which accounts for different sampling periods associated to the outputs as well as the underlying delays. The convergence analysis is performed thanks to a comprehensive Lyapunov approach under a well-defined condition on the sum of the maximum value of the sampling periods and of the output delays. The exponential convergence to zero of the underlying convergence error is established in the case of constant reaction rates. In the case where these rates are time-varying, the asymptotic estimation error admits an ultimate bound which can be made as small as desired by choosing appropriate values of the observer design parameters. The performance of the proposed observer and its main properties are highlighted through a fermentation process dealing with ethanol production.