Optimal control of a membrane filtration system

Kalboussi, Nesrine; Rapaport, Alain; Bayen, Térence; Amar, N.; Ellouze, Fatma; Harmand, J

doi:10.1016/j.ifacol.2017.08.1554

Cited by 7 publications

(7 citation statements)

References 7 publications

(6 reference statements)

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“…where U denotes the set of measurable functions over [0, T ] taking values in [−1, 1]. The question of practical applicability of a control that takes values different to −1 and 1 relies on approximations with chattering controls [19] and is exposed in [11,12] (see also [2] in the context of fed-batch bioprocesses). Next, we consider the following hypotheses on the model.…”

Section: Model Description and Preliminary Resultsmentioning

confidence: 99%

“…For the practical implementation of the optimal control law (where only the values u = −1 and u = 1 can be applied) it is not possible to stay exactly on the singular arc m = m. But an approximation by a sequence of filtration/backwashing can be applied to stay on the vicinity of the singular arc. This sequence can be chosen so that the average value of m is m, which provides a good approximation of the optimal value as it has been tested in [11,12]. One may argue that the optimal control problem could be reformulated as a discrete time problem where the time step is the smallest period of switching between filtration and backwashing that could be applied in practice.…”

Section: Discussionmentioning

confidence: 99%

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Optimal Control of Membrane-Filtration Systems

Kalboussi

Rapaport

Bayen

et al. 2019

IEEE Trans. Automat. Contr.

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This paper studies an optimal control problem related to membrane filtration processes. A simple 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 production of a membrane filtration system (i.e. the filtrate) over a finite time horizon, where 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 presents 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.

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Section: Model Description and Preliminary Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Optimal Control of Membrane-Filtration Systems

Kalboussi

Rapaport

Bayen

et al. 2019

IEEE Trans. Automat. Contr.

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“…The common chemical treatment procedures for removal of heavy metal ions from aqueous solution such as ion exchange [5], flotation [6], membrane filtration [7] and electrochemical treatment [8] are efficient in reducing metal ions in water but are expensive to operate. Hence, these methods do not likely satisfy the requirement of industrial wastewater treatment industries which hope for inexpensive, cleaner and greener technology.…”

Section: Introductionmentioning

confidence: 99%

REMOVAL OF Pb(II) FROM AQUEOUS SOLUTION BY PINEAPPLE PLANT STEM

2019

MJAS

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The excessive release of lead (Pb) ions into water stream and large production of agricultural wastes cause water and land pollution. Adsorption is useful in eliminating Pb(II) from water environment. The potential use of agricultural waste, pineapple plant stem as adsorbent to reduce the amount of Pb(II) in aqueous solutions was investigated. The material was modified with oxalic acid (OA) to improve the adsorption efficiency of Pb(II). Adsorption isotherms and kinetics were determined for the adsorption of Pb(II) on natural pineapple plant stem (NPPS) and OA modified pineapple plant stem (OAPPS) from aqueous solution in batch studies. The adsorption capacity of Pb(II) on pineapple plant stem depends considerably on the solution pH, in which the amount of Pb(II) adsorbed increased with increasing solution pH, reached its maximal with 14.25 mg/g at pH 5 and 30.47 mg/g at pH 4 for NPPS and OAPPS, respectively. The adsorption performance of the adsorbents was also studied at different initial Pb(II) concentrations (50 -150 mg/L), it was observed to be less affected at higher initial Pb(II) concentration. The adsorption isotherm was then investigated and the equilibrium data were well fitted with the Langmuir isotherm model with 13.30 and 27.70 mg/g as the calculated maximum capacities for NPPS and OAPPS, respectively. The adsorption of Pb(II) onto NPPS and OAPPS reached equilibrium after 60 minutes at all concentrations studied. The kinetics data were found to follow the pseudo-second order model.

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“…In a previous work [17], we solved the problem of optimizing the total production of a membrane filtration process operating at constant TMP and including periodic relaxation between filtration cycles. The analytical solution to this optimization problem was given.…”

mentioning

confidence: 99%

“…As in [17], the present work is devoted to the study of an analogous optimal control problem. However, membrane unclogging is performed here by periodic cycles of backwash instead of membrane relaxation.…”

mentioning

confidence: 99%