Constant-yield control of the chemostat

—The present work addresses the problem of chemostat stabilization around an optimal steady state, in the sense of enlargement of its stability region. The need for stabilization becomes imperative under conditions where the growth of biomass is subject to substrate inhibition, and the primary concern is to prevent washout of the biomass in the presence of disturbances. Inspired by the empirical concept of constant-yield control, a nonlinear state feedback control law is derived, and the stability basin of resulting closed-loop system is estimated using a Lyapunov function approach. Our analysis extends previous results in the sense that it accounts for biomass decay and endogenous metabolism and, moreover, it covers the case where the product is soluble in the effluent stream.