Nonlinear analysis of substrate-inhibited continuous cultures operated with feedback control on dissolved oxygen

The dynamic behavior of open- and closed-loop continuous bioreactors for cultures of substrate-inhibited aerobic microorganisms was studied. A proportional-integral feedback control scheme was adopted to stabilize the dissolved oxygen concentration by manipulating the dilution rate: the bioreactor operated as an oxystat. The effects of operating parameters (inlet substrate concentration and gas-liquid mass transfer rate) and of controller parameters (gain, reset time, and set-point) on solutions of mathematical models of both open- and closed-loop systems were characterized by means of parametric continuation technique and bifurcational analysis tools. The open-loop unstable steady state characterized by inhibiting levels of substrate in the bioreactor may be stabilized at any dissolved oxygen concentration by adopting a PI feedback controller. The bifurcation analysis provided useful guidelines to tune the control parameters. Stable periodic and multiperiodic regimes may appear through Hopf and Flip bifurcations, respectively, if gain and reset time are not properly set. Ranges of parameter values characterized by no solution were also assessed. Bifurcation maps of the gain vs the set-point value of oxygen concentration were proposed for different representative cases of gas-liquid mass transfer rate and inlet substrate concentration.