Specific growth rate estimation in (fed-)batch bioreactors using second-order sliding observers

Abstract

This paper addresses the estimation of specific growth rate of microorganisms in bioreactors using sliding observers. In particular, a second-order sliding observer based on biomass concentration measurement is proposed. Differing from other proposals that only guarantee bounded errors, the proposed observer provides a smooth estimate that converges in finite time to the time-varying parameter. Stability is proved using a Lyapunov approach. The observer exhibits also robustness to process uncertainties since no model of the reaction is used for its design. In addition, the off-surface coordinate of the sliding observer is useful to determine the convergence time as well as to identify sensor faults and unexpected behaviors. Because of the structure of the output error injection, chattering phenomena of conventional sliding mode algorithms are substantially reduced. The features of the proposed observer are assessed by numerical and experimental data.