Global stabilization of a continuous tank reactor with Monod kinetics and amplitude-velocity bounded control

Abstract

The problem of globally asymptotically stabilizing (GAS) a single-input two-state bioreactor, affine in the control and with Monod growth rate, by means of amplitude-derivative bounded nonlinear state feedback (SF) control is addressed within a control Lyapunov function (CLF) framework which exploits the dynamical characteristics of the open-loop (OL) reactor. The combination of notions and tools from CLF, dissipativeness, and chemical reactor engineering leads to a constrained damping-like controller with: (i) CLF constructed on the basis of the geometry of the OL dynamics, (ii) explicit formula representation, and (iii) assurance of closed-loop (CL) global robust (structurally stable) monostability, and control bounds as design degree of freedom.