- 14 dec 2015: PhD defense of Amel Ghouali (Univ. Tlemcen and Univ. Montpellier II) SupAgro Montpellier, room 302, Build. 9, 14h: Optimal control and analysis of anaerobic digestion bioreactor.
Abstract: This thesis focuses on the optimal control of an anaerobic digestor for maximizing its biogas production. In particular, using a simple model of the anaerobic digestion process, we derive a control law to maximize the biogas production over a period of time using the dilution rate D(.) as the control variable. Depending on initial conditions and constraints on the actuator, the search for a solution to the optimal control problem reveals very different levels of difficulty. In the first part, 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, named WDAC (Well Dimensioned Actuator 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 an heuristic control law proposed in the literature 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. In the second part, the problem of maximizing the biogas production is treated when the actuator is under (-over) dimensioned. These are the cases UDAC (Under Dimensioned Actuator Cases) and ODAC (Over Dimensioned Actuator Cases). Then we solve these optimal problems using the Maximum Principle of Pontryagin.
Committee: Nahla ABDELLATIF, LAMSIN Tunis, Terence BAYEN, Univ. Montpellier II, Brahim CHERKI, Univ. Tlemcen, Frédéric JEAN, ENSTA Paris (referee), Jérôme HARMAND, INRA LBE Narbonne (co-director), Mustapha LAKRIB, Univ. Sidi Bel Abbes (referee), Claude LOBRY, Univ. Nice, Ali MOUSSAOUI, Univ. Tlemcen (co-director), Alain RAPAPORT, INRA MISTEA Montpellier.
- 1 – 3 dec 2015: Venue of Prof. Sten Madec, LMPTC, Univ. Tours
- 9 – 13 nov 2015: Venue of Prof. Pedro Gajardo, UTFSM, Valparaiso, Chile
- 15 sept-13 nov 2015: Venue of Pascale Cuevas (Univ. Santiago, Chile) as an internship for developing a simulation software for heterogeneous landfill.
- 27 july-11 september 2015: Venue of Aymen Abdelhamid (Polytech Nice) as an internhship about modelling over-yielding in microbial communities.
- 24 july 2015: the research project MicroSoil3D, whose Modemic is a partner, is selected by the ANR for the 2015 edition.
- 22 june-18 september 2015: Venue of Dr. Matthieu Sebbah (Math. Dept. UFSM, Valparaiso, Chile)
- 12-16 june 2015: Venue of Prof. Hector Ramirez (DIM & CMM, Univ. Chile, Santiago de Chile).
- 8-12 june 2015: Venue of Prof. Tomas Caraballo (Dep. de Ecuaciones Diferenciales y Analisis Numerico, Univ. de Sevilla, Spain) and Prof. Peter Kloeden (Goethe-Universitat, Frankfurt am Main, Germany).
- 25-27 may 2015: Venue of Prof. Piernicola Bettiol, Math. Dept, Univ. Brest, France, that will give a talk at ACSIOM seminar on Tuesday 26 at 10:00am.
- 4-5 may 2015: Jean-Raynald de Dreuzy (GéoSciences Rennes) and Alain Rapaport have given a mini lecture on Modelling and analyze of underground transfers at CMM (Center of mathematical Modelling), U. Chile (see also here)
- 27 april – 26 juin 2015: Venue of Maha Hmissi (PhD, Tunisia) as internship within the TREASURE network.
- 20-21 april 2015: Venue of Soledad Aronna (IMPA, Rio de Janeiro, Brazil)
- Annoucement of a research school on “resources/consumers models” (in french) organized by the team, to be held in September 2015 at Montpellier.
- 30-31 mar. 2015: Venue of Prof. Roger Arditi, Dept. of Biology, Univ. of Fribourg, Switzerland.
- 25-27 fev. 2015: venue of Prof. Philippe Bogaerts, 3BIO, Ecole Polytechnique de Bruxelles (Belgium) and Prof. Alain VandeWouver, Automatic Control Laboratory, University of Mons (Belgium).
- 26 fev. 2015: PhD defense of Guilherme Pimentel (Univ. of Mons and Univ. Montpellier II) SupAgro Montpellier, Amphi 2, Build. 2bis, 14h: Nonlinear Modeling, Identification and Control of Membrane Bioreactors
Abstract: This thesis proposes a simple submerged membrane bioreactor (sMBR) dynamic model that comprises physical and biological process behaviors. Filtration (physical aspect) is represented by a resistance-in-series model composed of a reversible resistance, linked to the sludge cake formation (that can be detached by air scouring) and an irreversible fouling resistance. The biological process is described by a simple chemostat model. The model asymptotic behavior, observability, controllability and fast and slow dynamics are analyzed. The latter analysis, based on Tikhonov’s theorem, reveals the possibility decouple the dynamics in three time-scales, i.e. long-term fouling evolution (slow dynamic), biological degradation (fast dynamic) and fouling cake formation (ultrafast dynamic).Therefore, a parameter identification is organized in three steps corresponding to the three time-scales obtained from the analytical analysis. The parameter identification is implemented using a weighted least-squares cost function and a lower bound on the covariance matrix of the parameter estimates, which is used to obtain the parameters confidence intervals, is computed by the inverse of the Fisher Information Matrix (FIM). The model capacity to predict trans-membrane pressure and biological degradation is proved by model identification and cross-validation results. As sMBR processes are relativity new, experimental process data are scarce. Thus, a lab-scale recirculating aquaculture system with an sMBR is designed, built and automated. Process online measurements, such as temperature, total suspended solids (TSS), ammonia and nitrate effluent concentrations, air cross- and effluent flow rates and trans-membrane pressure, are gathered in order to validate the proposed model. In addition, experimental data from a pilot plant located in Spain are also used to further analyze and validate the model. Concerning the process control theoretical study of two different approaches are presented: a nonlinear model predictive control (NMPC) is implemented in order to optimize the effluent production rate and maximize the period between two chemical cleaning procedures and a partial-linearizing feedback Lyapunov controller is designed in order to stabilize the fouling by actuating in the air cross- and effluent flows. The results included in this thesis show the importance of analytical model studies in order to gain process insight and deduce model simplification. Another important point is the simple dynamic model structure with a small number of parameters, which is adequate to implement advanced control strategies on sMBR processes and, similarly, to predict biological degradation and fouling build-up dynamics
Committee: M. Philippe BOGAERTS, Univ. Bruxelles (referee), Mrs Anne-Lise HANTSON, Univ. Mons, M. Jérôme Harmand, INRA LBE Narbonne, M. Marc Heran, Univ. Montpellier II, Mrs Isabelle QUEINNEC, LAAS-CNRS Toulouse (referee), M. Alain RAPAPORT, INRA MISTEA Montpellier (co-director), M. Alain Vande Wouver, Univ. Mons (co-director), M. Jean-Luc VASEL, Univ. Liège.
- 20 fev 2015: Inria-SAM center newsletter (in french): Quand le numerique invente une agriculture durable
- 16-20 fev 2015: venue of Maria Crespo from MOMAT, Departamento de Matematica Aplicada, Universidad Complutense de Madrid (Spain).
- 9-12 feb. 2015: workshop Persistence of population models in temporally fluctuating environments in the scope of the semester The role of mathematics and computer science in ecological theory, CIB, EPFL, Lausanne (Switzerland)
- 5 fevr 2015: Thematic day SAMI (System, Analysis, Modeling, Informatics) at LBE (Narbonne).
- 19 – 23 janv 2015: venue of Pierre Alexandre Bliman (Inria, Rocquencourt, France and Fundação Getulio Vargas, Rio de Janeiro, Brazil) and Abderrahman Iggidr (Inria Lorraine)
Pierre Alexandre will visit several teams at Montpellier and will give a talk at Modemic seminar.
- 15 janv – 13 mars 2005: MsC Internship of Camila Romero (Univ. de Chile)
Subject: Study of the minimum crisis time for the Lotka-Volterra prey-predator model. Supervising: T. Bayen and A. Rapaport
- 12 jan-12 feb 2015: venue of Nihel Ben Amar, Institut national des sciences appliquées et de technologie, Tunis.
Nihel is working on membrane modelling within the TREASURE network. She will give a seminar on the 5th february at the LBE (INRA Narbonne).
- 5-9 jan. 2015: venue of Matthew Wade and Robert Pattinson, School of Civil Engineering and Geosciences, Newcastle University.
- 19 dec. 2014: PhD defense of Amine Charfi (Univ. de Carthage, Tunisia): Study of a membrane bioreactor for the treatment of wastewaters : effect of biotic and abiotic parameters on membrane fouling
Abstract: This thesis has focused on the definition of a simulation tool for clarification operation by porous membranes to identify the dominant mechanisms membrane fouling during operations defined quantify the dynamics of clogging and optimize working conditions (filtration conditions and regeneration conditions in line). The work is particularly interested in BioReactor Anaerobic Membrane (BRMAn) is a technology that has been proven in the treatment of municipal and industrial water. It combines (i) biological treatment anaerobic allowing almost complete treatment of organic pollutants with a production of a source of energy (methane) and (ii) the membrane treatment ensuring total separation of the solid phase (biomass) and the liquid phase (water treated), for obtaining a high purity water.
Committee: Mrs Narjes BATIS, INSAT, Tunis (president), Mrs Nihel BEN AMAR, INSAT, Tunis (director), M. Hamza EL FIL, CERTE, Soliman (referee), M. Jérôme Harmand, INRA (co-director, excused because of geopolitical constraints), M. Hatem KSIBI, IPEIS, Sfax, M. Sami SAYADI, CBS, Sfax (referee).
- 15-19 dec. 2014: seminar week on Microbial ecology and mathematical modelling, EPFL, Lausanne (Switzerland)
In the framework of the semester The role of mathematics and computer science in ecological theory – 01 July to 31 December 2014, the team is organizing at CIB (Centre Interfacultaire Bernoulli) a week dedicated to mathematical models in microbial ecology.
- 8 dec. 2014: PhD defense of Coralie Fritsch (Univ. Montpellier II, Math. Dept. 14h): Probabilistic and numerical approaches of indivual_based models of the chemostat
Abstract : In the first part, we propose a new chemostat model in which the bacterial population is mass structured and individual-based and the substrate dynamics are modelized by an ordinary differential equation. We obtain a Markov process which we describe as random measures. We determine, under a certain normalization of the process, a result of convergence in distribution towards the solution of a system of integro-differential equations. In the second part, we are interested in adaptive dynamic models of the chemostat. We add a mutation mechanism to the individual-based model which was studied in the first part. Under rare mutations and large population size hypotheses, the asymptotical result of the first part allows us to reduce the study of the mutant population to a growth-fragmentation-washout model in a constant environment. We study the extinction probability of this mutant population. We also describe the deterministic model related to the hybrid individual-based model with mutations and we compare these two approaches (stochastic and deterministic). In particular we prove that the two approaches lead to the same invasion criteria of a mutant population in a resident population. We present numeric simulations in order to illustrate the mathematical results.
Committee: Michel Bénaïm, Université de Neuchâtel (president), Fabien Campillo, Inria (director), Nicolas Champagnat (Inria), Jean-François Delmas, École des Ponts ParisTech (referee), Benoîte De Saporta, Université Montpellier II, Jérôme Harmand, INRA (co-director), Catherine Larédo, INRA, Michèle Thieullen, Université Paris 6 (referee).
- 1 dec. 2014: arrival of Anne Bisson as a PhD candidate.
Anne is preparing a PhD on the subject “Probabilistic modelling of ecosystems functioning as communuties assembling”. She will be part time in the team, part time at UMR Eco&Sols, under the co-supervision of B. Jaillard (Eco&Sols) and A. Rapaport (Modemic).