Maximizing biogas production from the anaerobic digestion |
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| Affiliation: | 1. Université de Tlemcen, Laboratoire d’Automatique, B.P 119 Tlemcen, Algeria;2. Irstea, UMR Itap, 361 rue Jean-François Breton, 34196 Montpellier, France;3. INRA, UR0050 LBE, Avenue des Etangs, 11100 Narbonne, France;4. INRA-INRIA, EPI MODEMIC, UMR MISTEA, 2 P. Viala, 34060 Montpellier, France;5. Université de Haute Alsace, 4 rue des Frères Lumière, 68093 Mulhouse, France;1. Institute of Biochemistry and Biophysics, University of Tehran, Tehran, Iran;2. Center of Excellence in Biothermodynamics, University of Tehran, Tehran, Iran;3. Department of Ophthalmology and Visual Sciences and McPherson Eye Research Institute, School of Medicine and Public Health, University of Wisconsin, Madison, WI, USA;1. Department of Electrical and Computer Engineering, University of Sharjah, Sharjah, United Arab Emirates;2. Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Doha, Qatar;3. Department of Chemical Engineering, Texas A&M University at Qatar, Doha, Qatar;4. Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA;1. Department of Electrical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar, 382355, Gujarat, India;2. Department of Chemical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar, 382355, Gujarat, India;1. Univ Lyon, INSA-Lyon, DEEP Laboratory – Wastes Water Environment Pollutions, EA 7429, 9 rue de la physique, F-69621 Villeurbanne Cedex, France;2. Arkolia Energies, 16 rue des vergers, F-34130 Mudaison, France |
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| Abstract: | This paper presents an optimal control law policy for maximizing biogas production of anaerobic digesters. In particular, using a simple model of the anaerobic digestion process, we derive a control law to maximize the biogas production over a period T using the dilution rate as the control variable. Depending on initial conditions and constraints on the actuator (the dilution rate D(·)), the search for a solution to the optimal control problem reveals very different levels of difficulty. In the present paper, we consider that there are no severe constraints on the actuator. In particular, the interval in which the input flow rate lives includes the value which allows the biogas to be maximized at equilibrium. For this case, we solve the optimal control problem using classical tools of differential equations analysis. Numerical simulations illustrate the robustness of the control law with respect to several parameters, notably with respect to initial conditions. We use these results to show that the heuristic control law proposed by Steyer et al., 1999 20] is optimal in a certain sense. The optimal trajectories are then compared with those given by a purely numerical optimal control solver (i.e. the “BOCOP” toolkit) which is an open-source toolbox for solving optimal control problems. When the exact analytical solution to the optimal control problem cannot be found, we suggest that such numerical tool can be used to intuiter optimal solutions. |
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| Keywords: | Optimal control Bioreactor Maximization Biogas Anaerobic digestion |
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