A set membership approach to oxygen transport modeling with unmodeled dynamics

Dissolved oxygen concentration in a cultivation broth is an important variable for bioprocesses operation. The oxygen transfer from air to liquid is determined by the oxygen transfer coefficient, usually regulated by the air flow rate and agitation speed. However, many microscopic phenomena are involved in the oxygen transfer. In this paper, a deterministic estimation method for the oxygen transfer coefficient of a bioreactor is proposed. The inclusion of probe dynamics and assumptions of deterministic undermodeling errors improve estimation results when compared to classic least squares methods. The approach is based on Set Membership techniques, it allows the user to fix hard bounds on the effect of unmodeled dynamics and provides feasible coefficient intervals by means of convex optimization problems. Results from a laboratory-scale bioreactor show the effectiveness of the proposed scheme and its advantages over a least-squares solution.