GLOBAL STABILIZATION OF A BIOLOGICAL REACTOR BY LINEAR FEEDBACK CONTROL

A classical substrate inhibition model for biological reactors with PI controllers is subjected to a rigorous nonlinear analysis. The operating conditions and control settings that ensure global stability of the set-point are derived from bifurcation studies of the solution branches with the controller gains as the bifurcation parameters. The global stability of the set-point can be destroyed by co-existing extraneous attracting states, both steady and time-dependent, which may be introduced by the controllers that are designed to stabilize the set-point locally.