Geometric invariance and reference conditioning ideas for control of overflow metabolism

In many biotechnological processes, the optimal productivity corresponds to operating at critical substrate concentration. The problem, then, consists in finding the feeding rate compatible with the critical constraint which gives a specific growth rate as close as possible to the desired one, so as to avoid overflow metabolism. This value may be unknown and may change from experiment to experiment and from strain to strain, and even in the same experiment due to changing environmental and/or process conditions. Particularly, in the fed-batch fermentation of the industrial strain Saccharomyces cerevisiae a small amount of ethanol is allowed to be present in the culture, and the control problem is one of regulating the ethanol concentration at a given low reference value. In this paper, an approach based on geometric invariance via sliding mode reference conditioning is proposed to achieve the closest specific growth rate to the desired reference which is compatible with system constraints (e.g. ethanol concentration lower than a given threshold). It is shown how this approach is robust with respect to uncertainties in the process dynamics and with respect to unknown perturbations affecting the critical point.