Optimal control of filtration and back wash under membrane clogging

Nesrine Kalbussi (1) , Alain Rapaport (2) , Térence Bayen (3) , Nihel Benamar (1) , Fatma Ellouze (1) , Jérôme Harmand (4)

1 UTM - Université de Tunis El Manar
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier
4 LBE - Laboratoire de Biotechnologie de l'Environnement [Narbonne]

This paper presents an optimal control strategy allowing the maximization of the total production of a membrane filtration system over a finite time horizon. A simple mathematical model of membrane fouling is used to capture the dynamic behavior of the process which consists in the attachment of matter onto the membrane during the filtration period and the detachment of matter during the cleaning period. The control variable is the sequence of filtration/relaxation cycles over the time. Based on the Pontryaguin's Maximum Principle, we establish an optimal control strategy involving a singular arc and a switching curve.

Mots clés: optimal control; singular arc; membrane fouling; maximization of water production; MBR; relaxation

Domaines: Optimisation et contrôle [math.OC]

Nesrine Kalbussi, Alain Rapaport, Térence Bayen, Nihel Benamar, Fatma Ellouze, et al.. Optimal control of filtration and back wash under membrane clogging. 2016. ⟨hal-01393233v2⟩