Non-linear Analysis of Feedback Controlled Aerobic Cultures

Abstract

In the present work, the results of a complete dynamical analysis of open- and closed-loop continuous bioreactor for cultures of substrate inhibited aerobic microorganisms were presented. In the closed loop system the dissolved oxygen concentration was controlled at a pre-set value by means of a proportional-integral feedback control scheme manipulating the inlet substrate concentration. A mathematical model was developed coupling the mass balance equation for the substrates (carbon-source and oxygen) and the controller. Solutions of both open- and closed-loop systems were assessed by means of parametric continuation technique and bifurcational analysis tools. The dynamics behavior was studied by changing the main operating parameters – dilution rate and gas-liquid mass transfer rate - and the controller parameters - gain and set-point – in a wide intervals. We have found that the regimes strongly depend on the operating conditions. In particular, the open-loop unstable steady state may be stabilized in closed-loop system, provided the proper choice of both the gain and the reset time for the selected set-point value of oxygen concentration.