Maximization of steady-state bacterial production in a chemostat with pH and substrate control

This analytical study deals with the steady-state behavior and control of microbial growth in continuous cultures. A second order Haldane-Monod model of continuous cultures is used as a basis for study of the effects of the adjustment of pH by the addition of acidic (or basic) materials. The treatment of a hydrogen ion concentration, in addition to substrate and microbial concentrations as state variables, results in a third order system of equations describing the process. The analysis of the system in equilibrium yields several admissible steady states, that is, steady states which satisfy all constraints. An optimal control problem is formulated and subsequently solved to maximize steady-state microbial production.