About modeling and control strategies for scheduling crop irrigation

International audienceWe propose a new simplified crop irrigation model and study the optimal control which consists in maximizing the biomass production at harvesting time, under a constraint on the total amount of water used. Under water scarcity, we show that a strategy with a singular arc can be better than a simple bang-bang control as commonly used. The gain is illustrated on numerical simulations. This result is a promising first step towards the application of control theory to the problem of optimal irrigation scheduling

Optimal control of membrane filtration systems

International audienceThis paper studies an optimal control problem related to membrane filtration processes. A generic mathematical model of membrane fouling is used to capture the dynamic behavior of the filtration process which consists in the attachment of matter onto the membrane during the filtration period and the detachment of matter during the cleaning period. We consider the maximization of the net water production of a membrane filtration system (i.e. the filtrate) over a finite time horizon, where the control variable is the sequence of filtration/backwashing cycles over the operation time of process. Based on the Pontryagin Maximum Principle, we characterize the optimal control strategy and show that it exhibits a singular arc. Moreover we prove the existence of an additional switching curve before reaching the terminal state, and also the possibility of having a dispersal curve as a locus where two different strategies are both optimal

Integrated membrane bioreactors modelling: A review on new comprehensive modelling framework

Integrated Membrane Bioreactor (MBR) models, combination of biological and physical models, have been representing powerful tools for the accomplishment of high environmental sustainability. This paper, produced by the International Water Association (IWA) Task Group on Membrane Modelling and Control, reviews the state-of-the-art, identifying gaps for future researches, and proposes a new integrated MBR modelling framework. In particular, the framework aims to guide researchers and managers in pursuing good performances of MBRs in terms of effluent quality, operating costs (such as membrane fouling, energy consumption due to aeration) and mitigation of greenhouse gas emissions

Détection précoce et contrôle de colmatage d'une membrane de filtration

This work focuses on the development of a tool for anticipating and controlling the fouling of membrane filtration. Fouling is the major disadvantage that hinders the expansion of membrane processes, leading to a decrease in their performance and additional operating costs. This PhD work has therefore focused on the deve- lopment of an optimal control strategy to optimize the physical cleaning protocol and maximize the net production of a membrane filtration system. Firstly, an ex- perimental work was conducted to study the fouling mechanisms involved in the microfiltration and ultrafiltration of two types of suspensions whose filtration is of industrial interest. The analysis of the experimental results led to the conclusion that under the considered conditions the formation of a cake on the surface of the membrane is the predominant fouling mechanism. In the second part of this thesis, we are interested in optimizing the production of membrane filtration systems operating at constant transmembrane pressure. To do this, we started by choosing from the literature a simple mathematical model that describing the dynamics of different membrane filtration systems. The optimization problem was then solved by two di_erent approaches : a numerical approach and an analytical approach. For the numerical approach, we use Global Search and Pattern Search solvers programmed on MATLAB, based on the model chosen to anticipate and predict the production of the system. This approach is simple to implement and has made it possible to improve the production of a filtration process. However, it has some limitations such as the problem of local optimums. To overcome the limitations of the numerical approach, the problem of optimizing the cleaning strategy has been solved by an analytical approach based on the application of the Pontryagin Maximum Principle (PMP). The optimal solution obtained highlights the existence of a singular arc. The value of this arc is very important information that informs the ratio of the time between filtration periods and cleaning periods. To be applicable to a process, an approach allowing to approximate this singular arc by a succession of filtration / cleaning sequences has been presented by making sure that the determined ratio is well respected. The optimal strategy applied to a numerical case study significantly improves the net production of the filtration system compared to a strategy used in industry.Ce travail de thèse porte sur le développement d’un outil d’anticipation et de contrôle de colmatage des membranes de filtration. Le colmatage est l’inconvénient majeur qui handicape l’expansion des procédés de filtration membranaire, induisant une baisse de leurs performances et des sur-coûts d'exploitation. La limitation du colmatage est rendue possible soit en appliquant des cycles de lavages périodiques physiques ou chimiques de la membrane, induisant des arrêts de fonctionnement, soit en provoquant en continue des turbulences aux voisinages de la membrane (aération de la membrane). Toutefois, ces stratégies de lavage sont coûteuses et parfois inefficaces car elles ne tiennent pas compte des spécificités du procédé. Elles sont plutôt basées sur les recommandations des fournisseurs de la membrane et/ou l'expérience de l'opérateur. Ce travail de thèse a donc été axé sur le développement d'une stratégie de contrôle optimal permettant d'optimiser le protocole de lavage physique d’une membrane de filtration et de maximiser ainsi la production nette d’un système de filtration membranaire. Dans la première partie de cette thèse, nous menons un travail expérimental dans le but d’étudier et de comprendre les mécanismes de colmatage intervenant lors de la microfiltration et l’ultrafiltration de deux types de suspensions dont la filtration est d’intérêt industriel. Le dépouillement des résultats expérimentaux a permis de conclure que pour les conditions considérées la formation d’un gâteau à la surface de la membrane est le mécanisme prédominant dans le colmatage des membranes en microfiltration et ultrafiltration. Dans la deuxième partie de cette thèse, nous intéressons à l’optimisation de la production des systèmes de filtration membranaire fonctionnant à pression transmembranaire constante. Pour ce faire, nous avons commencé par choisir de la littérature un modèle mathématique simple et capable de décrire les dynamiques de différents systèmes de filtration membranaire. Après avoir choisi un modèle, nous résolvons le problème d’optimisation par deux approches différentes : une approche numérique et une approche analytique. Pour ce qui est de l’approche numérique, nous utilisons des solveurs d’optimisation (Global Search et Pattern Search) programmés sur MATLAB. Cette approche est simple à mettre en œuvre mais elle présente quelques limitations telles que le problème des optimums locaux. Pour pallier aux limitations de l'approche numérique, nous traitons le problème d'optimisation de la stratégie de lavage par une approche analytique qui se base sur l'application du principe du Maximum de Pontryagin (PMP). L’avantage principal de l’approche analytique est qu’elle n’est pas basée sur un modèle spécifique, mais plutôt sur des hypothèses décrivant les propriétés qualitatives des dynamiques d'une classe des systèmes de filtration. En procédant ainsi, la structure générale de la solution optimale pour toute une classe de procédés de MF/UF vérifiant les hypothèses définies est obtenue. L'analyse analytique met en évidence l'existence d'un arc singulier. La valeur de cet arc est une information très importante qui renseigne sur le rapport du temps entre périodes de filtration et périodes de lavage. La solution analytique telle qu’elle ne peut pas être appliquée en pratique notamment à cause de l’existence d’un arc singulier. Pour être applicable sur un procédé, nous présentons une approche permettant d’approximer cet arc singulier par une succession de séquences de filtrations/lavage en faisant en sorte que le ratio déterminé soit bien respecté.L'application de la stratégie optimale à un cas d’étude numérique améliore significativement la production nette du système de filtration par rapport à la stratégie « classique » utilisée couramment en industrie

Optimization of a membrane filtration system

Journée organisée conjointement par l'objet thématique SAMI (Système, Analyse, Modélisation, Informatique) de l'UR LBE Narbonne et l'UMR MISTEA MontpellierIn this work, we show the benefits of the optimal control theory compared to the numerical optimization in maximizing the total net water production of a membrane filtration system . A simple mathematical model of membrane fouling is used to capture the dynamic behavior of the process. The control variable is the sequence of filtration/membrane physical cleaning over the time

Modelling MBRs for optimizing water reuse in agriculture

International audienc

Firik, bulgur en tarhana:Voedselbereiding in heden en verleden

International audienceWe study theoretically on a simple crop model the problem of optimizing the crop biomass at harvesting date, choosing the temporal distribution of water under the constraint of a total water volume available for the season.We show with the tools of the optimal control theory that the optimal solution may present a singular arc, under a lower water availability, which leads to a bang-singular-bang solution.This differs from the usual irrigation policies under water scarcity, which are bang-bang

Modelling MBRs for optimizing water reuse in agriculture

International audienc

Model-Based Approach for Treated Wastewater Reuse Strategies Focusing on Water and Its Nitrogen Content “A Case Study for Olive Growing Farms in Peri-Urban Areas of Sousse, Tunisia”

One of Tunisia’s main challenges is to conserve and protect water resources for current and future generations. Using non-conventional water in agriculture, such as treated wastewater, can be a sustainable water-saving solution. Therefore, the objectives of this study are (i) to analyze the value chain of treated wastewater for olive growing farms production and (ii) to apply mathematical modeling to maximize the olive production in optimizing irrigation distribution and nitrogen amendment in olive growing farms. The work is carried out in a peri-urban irrigated perimeter of Msaken, Sousse, which is mainly occupied by olive trees and irrigated by treated wastewater. A SWOT analysis is also applied to identify the strengths and weaknesses of reuse in this study area. Moreover, mathematical models are used to determine the optimal schedule for fertigation with treated wastewater. In this process, data on rainfall, soil, water quality and olive production were collected from local farmers, local decision makers, field and laboratory experiments. SWOT results determine farmers’ perceptions of reusing treated wastewater for irrigation. The viability analysis, in terms of soil humidity and nitrogen, shows that the nitrogen stress is not a limiting factor for olive biomass production, but water stress is. This analysis provides numerical values for the maximum irrigation rate and total amount of irrigation water to ensure maximum olive production. It was found that the maximum irrigation could be 5.77 m3/day/ha and the total annual water requirement is 1240 m3/ha. Modeling appears to be an important tool to help local decision makers and to support and encourage local farmers to reuse treated wastewater under safe conditions and without environmental risks

Optimal control of a crop irrigation model under water scarcity

We consider a simple crop irrigation model and study the optimal control which consists of maximizing thebiomass production at harvesting time. A specificity of this work is to impose a quota on the water used forirrigation, in a context of limited resources. The model is written as a 2d non-autonomous dynamical systemwith a state constraint, and a non-smooth right member given by threshold-based soil and crop water stressfunctions. We show that when the water quota is below the threshold giving the largest possible production,the optimal strategy consists of irrigating once. We then show that the optimal solution can have one or severalsingular arcs, and therefore be better than simple bang-bang controls, as commonly used. The gains over thebest bang-bang controls are illustrated on numerical simulations. These new feedback controls that we obtainare a promising first step towards the concrete application of control theory to the problem of optimal irrigationscheduling under water scarcity