Alternate control-structures and plant-model mismatch for fed-batch bioreactors

Optimal feedback control of a fed-batch bioreactor may be implemented by regulating the feed rate or the feed concentration and either may be used to optimize the same performance index. The latter approach, however, offers several advantages. In two bioreactors operating to maximize the instantaneous product formation rate, one with feed rate and the other with feed concentration control, the same amount of nutrients are fed to both fermenters. At the end of fermentation the fermenter with feed concentration control produces higher antibiotic concentration in a lesser volume than the other. The feed rate strategy, however, is more tolerant of the errors in the model than its counterpart. Such robustness is because of the complex volume effects which are absent with feed concentration (the feed rate is constant). The feed concentration strategy uses more information described in the model and hence is more sensitive to the errors. When the volume dependence is removed by implementing the control in the mass variable forms instead of the commonly used concentration forms, the feed concentration strategy becomes more robust and consequently less sensitive to the modeling errors. An ability to implement the feed concentration structure in either the mass or the concentration forms allows for a choice between sensitivity and robustness. Higher sensitivity would be desirable during system identification studies where parameters are estimated from data, whereas higher robustness would be preferred during plant operation.