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Minimal time control of fed-batch bioreactor with product inhibition

Térence Bayen 1, 2 Francis Mairet 3 
2 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
CRISAM - Inria Sophia Antipolis - Méditerranée , MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 Anlysis and Mathematical Modeling, Valparaiso
Departamento de Matematica [Valparaiso]
Abstract : This paper is devoted to the minimal time control problem for fed-batch bioreactors, in presence of an inhibitory product, which is released by the biomass proportionally to its growth. We first consider a growth rate with substrate saturation and product inhibition, and we prove that the optimal strategy is fill and wait (bang-bang). We then investigate the case of the Jin growth rate which takes into account substrate and product inhibition. For this type of growth function, we can prove the existence of singular arc paths defining singular strategies. Several configurations are addressed depending on the parameter set. For each case, we provide an optimal feedback control of the problem (of type bang-bang or bang-singular-bang). These results are obtained gathering the initial system into a planar one by using conservation laws. Thanks to Pontryagin maximum principle, Green's theorem, and properties of the switching function, we obtain the optimal synthesis. A methodology is also proposed in order to implement the optimal feeding strategies.
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Submitted on : Friday, September 21, 2012 - 10:18:15 AM
Last modification on : Wednesday, September 28, 2022 - 3:08:44 PM
Long-term archiving on: : Friday, December 16, 2016 - 3:05:44 PM

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Térence Bayen, Francis Mairet. Minimal time control of fed-batch bioreactor with product inhibition. Bioprocess and Biosystems Engineering, Springer Verlag, 2013, 36 (10), pp.1485-1496. ⟨10.1007/s00449-013-0911-9⟩. ⟨hal-00734225⟩

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