Smooth sliding-mode observers for specific growth rate and substrate from biomass measurement

This paper addresses the estimation of specific growth rate and substrate concentration from biomass measurements in fermentation processes. Specifically, sliding-mode observers are proposed, for which finite-time global convergence is demonstrated using Lyapunov stability theory and concepts of variable structure systems. Two observers are developed for specific growth rate estimation, one producing a discontinuous estimation which is used afterwards for substrate estimation, and the other one – based on high-gain observers – that generates a smooth estimation with first-order dynamics and finite-time bounded convergence error. In the case of substrate estimation, an observer that increases the convergence rate to a vicinity of the real substrate concentration while achieving asymptotic convergence despite kinetic model uncertainties in properly excited processes is designed. This observer also exhibits first-order dynamics.