Optimizing the anaerobic digestion of microalgae in a coupled process

Térence Bayen 1 Francis Mairet 2 Pierre Martinon 3, 4 Matthieu Sebbah 5
2 Anlysis and Mathematical Modeling, Valparaiso
Departamento de Matematica [Valparaiso]
3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
5 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
Abstract : This work is devoted to maximizing the production of methane in a bioreactor coupling an anaerobic digester and a culture of micro-algae limited by light. The decision parameter is the dilution rate which is chosen as a control, and we enforce periodic constraints in order to repeat the same operation every day. The system is gathered into a three-dimensional system taking into account a day-night model of the light in the culture of micro-algae. Applying Pontryagin maximum principle, the necessary conditions on optimal trajectories indicate that the control consists of bang and/or singular arcs. We provide numerical simulations by both direct and indirect methods, which show the link between the light model and the structure of optimal solutions.
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Térence Bayen, Francis Mairet, Pierre Martinon, Matthieu Sebbah. Optimizing the anaerobic digestion of microalgae in a coupled process. 13th European Control Conference, Jul 2013, Zurich, Switzerland. pp.6. ⟨hal-00754971⟩

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