Adaptive extremum-seeking control applied to bioreactors

Adaptive extremum-seeking controllers are used to handle uncertainties in the modelling of industrial processes. Although these controllers are capable to handle uncertain parameters, an additional persistence of excitation condition is necessary to prove the convergence of these unknown parameters to their true values. If complex non-linear models are used it is not dear how this condition can be fulfilled. In this report the persistence of excitation condition for non-linear models is investigated further. The excitation condition is transformed to a rank condition. The rank condition can be used to compute an input signal that guarantees the fulfillment of the excitation condition. This new strategy is applied to an adaptive extremum-seeking controller for a bioreactor with Haldane kinetics. Simulation results are provided to show the effectiveness of the proposed approach. In the second part initial results of the application of an adaptive extremum-seeking controller to a fed-batch bioreactor are given and discussed.