Separating two species of microalgae in photobioreactors in minimal time. (March 2020) - Djema, Walid; Bernard, Olivier; Giraldi, Laetitia
Highlights: An optimal control strategy separating two species of microalgae in minimal time is provided. Microalgae dynamics are described by the Droop's model, taking into account the internal quota storage of the cells. Using Pontryagin's principle, a dilution-based control strategy is developed, leading to the most efficient species separation in minimal time. A numerical optimal synthesis based on direct methods is performed in order to determine the structure of the optimal feedback-control law, which is bang-singular. A turnpike-like behavior characterizing the optimal solution is highlighted. Abstract: This paper proposes a strategy to separate two strains of microalgae in minimal time. The control is the dilution rate of the continuous photobioreactor. The microalgae dynamics is described by the Droop's model, taking into account the internal quota storage of the cells. Using Pontryagin's principle, we develop a dilution-based control strategy that leads to the most efficient species separation in minimal time. A numerical optimal synthesis –based on direct optimization methods– is performed throughout the paper, in order to determine the structure of the optimal feedback-control law, which is bang-singular . Our numerical study reveals that singular arcs play a key role in the optimization problem since they allow the optimal solution to be close to an associated static optimal control problem. A resulting turnpike -like behavior, which characterizes the optimal solution, is highlighted throughout this work.