Separating two species of microalgae in photobioreactors in minimal time |
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| Affiliation: | 1. University Côte d’Azur (UCA), Inria Sophia Antipolis, France;2. Laboratoire d''oceanographie de Villefranche (LOV), Sorbonne Universite, CNRS, Observatoire Oceanologique, Villefranche-sur-Mer, France;1. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China;2. Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Ministry of Education, China;3. Universitat Politècnica de Catalunya, Institut de Robòtica i Informàtica Industrial (CSIC, UPC), C/. Llorens i Artigas 4-6, Barcelona 08028, Spain;4. College of Automation, Harbin Engineering University, No.145 Nantong Street, Nangang District, Harbin 150001, China;5. Massachusetts Institute of Technology, Cambridge MA 02139, USA |
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| 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. |
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