Periodic optimal control for biomass productivity maximization in a photobioreactor using natural light

Frédéric Grognard 1, * Andrei Akhmetzhanov 2 Olivier Bernard 1
* Auteur correspondant
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
Abstract : We address the question of optimization of the microalgal biomass long term productivity in the framework of production in photobioreactors under the influence of day/night cycles. For that, we propose a simple bioreactor model accounting for light attenuation in the reactor due to biomass density and obtain the control law that optimizes productivity over a single day through the application of Pontryagin's maximum principle, with the dilution rate being the main control. An important constraint on the obtained solution is that the biomass in the reactor should be at the same level at the beginning and at the end of the day so that the same control can be applied everyday and optimizes some form of long term productivity. Several scenarios are possible depending on the microalgae's strain parameters and the maximal admissible value of the dilution rate: bang-bang or bang-singular-bang control or, if the growth rate of the algae is very strong in the presence of light, constant maximal dilution. A bifurcation diagram is presented to illustrate for which values of the parameters these different behaviors occur. Finally, a simple sub-optimal bang-bang strategy is proposed that numerically achieves productivity levels that almost match those of the optimal strategy.
Type de document :
Rapport
[Research Report] RR-7929, INRIA. 2012, pp.28
Liste complète des métadonnées

Littérature citée [24 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00687322
Contributeur : Frédéric Grognard <>
Soumis le : jeudi 12 avril 2012 - 22:37:16
Dernière modification le : mardi 29 mai 2018 - 12:50:54
Document(s) archivé(s) le : mercredi 14 décembre 2016 - 22:41:56

Fichiers

RR-7929.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00687322, version 1
  • ARXIV : 1204.2906

Citation

Frédéric Grognard, Andrei Akhmetzhanov, Olivier Bernard. Periodic optimal control for biomass productivity maximization in a photobioreactor using natural light. [Research Report] RR-7929, INRIA. 2012, pp.28. 〈hal-00687322〉

Partager

Métriques

Consultations de la notice

755

Téléchargements de fichiers

194