Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model

Serhani, Mustapha; Raïssi, Nadia; Cartigny, Pierre

doi:10.1051/mmnp/20094509

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…Part of the sludge inside the aerator is recycled to promote oxidation. The topic of waste water treatment has also been studied from many points of view, such as complex observation [20,21] and control [22,23], although the anaerobic component is considered in the majority of situations [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative

2021

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In this paper, the wastewater treatment model is investigated by means of one of the most robust fractional derivatives, namely, the Caputo fractional derivative. The growth rate is assumed to obey the Contois model, which is often used to model the growth of biomass in wastewaters. The characteristics of the model under consideration are derived and evaluated, such as equilibrium, stability analysis, and steady-state solutions. Further, important characteristics of the fractional wastewater model allow us to understand the dynamics of the model in detail. To this end, we discuss several important analyses of the fractional variant of the model under consideration. To observe the efficiency of the non-local fractional differential operator of Caputo over its counter-classical version, we perform numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of Oxygen Uptake Rate in Continuous Process under Caputo Derivative

2021

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“…Part of the sludge is recycled into the aerator to stimulate the oxidation. The wastewater treatment problem was often investigated under several points of view: dynamic [1,2,17], observation [9,15], control [6,12,13,16]. But in most cases, the anaerobic aspect is considered, [1,2,10,16,17].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity and Strong Controllability of a Nonlinear Chemostat Model

2015

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Abstract. We investigate the sensitivity behaviour and the controllability for an aerobic wastewater model. The problem is formulated as a nonlinear dynamical system. Using the tools of nonsmooth analysis, we firstly analyse the positivity and dissipation of the model. On the other hand, through the Gronwell's inequality, we prove a sensitivity property of the model, quantified by the control parameters and initial conditions. This sensitivity leads to an error estimation between two trajectories. The strong controllability is investigated in a new setting: we assume that the recycle rate R, the residence time τ and the dissolved oxygen saturation concentration Cs are measurable time varying control functions. Hence, we reformulate the system as a nonlinear control problem. In this context and without linearising, we provide a strong controllability result with respect to the perturbations on initial conditions. As a consequence, we prove that an equilibrium point (when it exists) is locally controllable. Finally, we give some simulations illustrating our results.Résumé. Dans ce travail, nousétudions la sensibilité et la contrôlabilité forte d'un modèle aérobie de traitement des eaux usées. Le problème est formulé sous forme d'un système dynamique non linéaire. En utilisant les outils d'analyse non lisse, nous nous intéressons, dans un premier temps,à l'analyse de la positivité et de la dissipation du modèle, puisà travers l'inégalité de Gronwall, nous mettons enévidence la sensibilité du modèle par rapport aux paramètres, (susceptibles d'être des outils de contrôle), et les conditions initiales. Cette sensibilité conduità une estimation de l'erreur entre deux trajectoires. La contrôlabilité forte estétudiée dans un nouveau contexte: nous supposons que le taux de recyclage R, le temps de séjour τ et le taux de saturation d'oxygène dissous Cs sont des fonctions du temps mesurables. Dans cette optique, nous formulons le système comme un problème de contrôle non linéaire et nous fournissons un résultat de contrôlabilité forte, par rapport aux perturbations des conditions initiales. Par conséquent, nous démontrons qu'un point d'équilibre (s'il existe) est localement contrôlable. Finalement, nous donnons quelques simulations illustrant nos résultats. .

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