ABSTRACT
The rich dynamics exhibited by the different models studied in previous chapters were all uncovered when the chemostat was operated under time-invariant conditions. In this chapter, we investigate the dynamic charcteristics of an unstructed model of the chemostat when it is periodically forced. The dynamics of continuous bioreactors subject to periodic forcing of one or more bioreactor feed conditions were studied both theoretically and experimentally by a number of authors [4, 194, 272, 273, 281, 306, 339]. These studies showed that suitable periodic variations in one of the bioreactor inputs, e.g., dilution rate and feed concentration can, in a number of cases, improve the time-average performance of the continuous bioprocess vis-a´-vis its operation at a stable nontrivial steady state. In the aforementioned studies, the periodic forcing was carried out around a stable steady state, i.e., a point attractor for which the periodic operation of the bioreactor can only yield periodic behavior. In this chapter a different situation is examined for which the chosen center of forcing is itself a stable limit cycle. The bioreactor model selected for this investigation consists of the classical unstructured model for which the yield coefficient is linearly proportional to the substrate. This model was studied in Chapter 4 and was shown to predict oscillatory behavior for a wide range of model kinetic and operating parameters. The objectives of this chapter are twofold. The first objective is to examine the different nonlinear patterns that arise in the bioreactor when the substrate feed concentration is periodically varied around a limit cycle. The results of the investigation illustrate the interactions between the feed inputs, i.e., substrate feed concentration and the nonlinearities of the bioreactor. These results also show the impredictibility of the behavior of the bioreactor resulting from these parametric perturbations. Dramatic changes can be expected in the nature of the emerging dynamic behavior of the forced process [20].
