Nonlinear PI control of fed-batch processes for growth rate regulation

Abstract

This paper deals with the regulation of the biomass specific growth rate, which is an important goal in many fed-batch fermentation processes. The proposed control system is based on the minimal model paradigm, requiring only biomass and volume measurement along with some bounds on the reaction rate. The controller has the structure of a partial state feed-back with adjustable gain. An integral-proportional control algorithm is designed to adjust this gain. It is inspired in concepts of invariant control and system immersion. First, a nonlinear integral action that makes invariant a goal manifold defined by a reference model dynamics is developed. Then, a proportional output error feed-back is incorporated to the control law with the aim of fastening convergence. Stability is investigated in detail using Lyapunov functions. To implement the control law, an estimation of the growth rate is required like any other PI-like controller. Because of its strong convergence properties, a sliding observer that requires the same process information as the controller is used for this task, although conventional continuous observers can alternatively be used provided they are fast enough to preserve stability. Simulation results showing the transient response and robustness features of the controller under nominal and perturbed scenarios are presented.