A closed loop exponential feeding law: Invariance and global stability analysis

This article addresses the computation of invariant control laws [A. Fradkov, I. Miroshnik, V. Nikiforov, Nonlinear and Adaptive Control of Complex Systems, Kluwer, 1999] for fed-batch fermenters represented by two standard models. It will be shown how to derive partial state feedbacks that, assuming ideal conditions and perfect model, keep the specific growth rate μ constant provided the initial conditions are adequate. The invariant control law is the closed loop version of the exponential feeding already suggested in several references as shown later. The paper presents an analysis of invariance and a study of global stability within the framework of partial stability. That is, stability with respect to some of the state variables. This enables us to treat the case with Haldane-like or non-monotonous kinetics.