A critical appraisal of the ΠΠ-criterion through continuation/optimization

Periodic forcing may improve bioreactor performances with respect to stationary operating conditions. An analytical procedure based on the so-called ππ-criterion was used by Parulekar [(1998). Analysis of forced periodic operations of continuous bioprocesses—single input variations. Chemical Engineering Science, 53(14), 2481–2502] to assess whether periodic forcing is beneficial, and, when this is the case, the criterion also gives an indication of the optimal forcing frequency. Such procedure is exact only in the limit of infinitesimal amplitude of the periodic forcing. In this work the applicability of the ππ-criterion to nonlinear models is investigated. The analysis is carried out by comparing the analytical predictions of the criterion with numerical predictions obtained with a continuation/optimization algorithm. As an example, two different reaction schemes are considered. The continuation/optimization procedure gives information on optimal forcing frequency and also on optimal forcing amplitude.