Takagi–Sugeno fuzzy-based approach for modeling and control of an activated sludge process

Wastewater treatment systems have recently taken on new trends resulting from the growing awareness of health and environmental risks. New strategies aimed at the recovery of treated water are increasingly being proposed. Given its better performance, biological treatment via an activated sludge pro...

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Published in:	International journal of dynamics and control Vol. 12; no. 8; pp. 3123 - 3138
Main Authors:	Arifi, Ali, Bouallègue, Soufiene
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024 Springer Nature B.V
Subjects:	Activated sludge process Carbon Compensation Complexity Control Control algorithms Control and Systems Theory Control theory Controllers Design Dissolved oxygen Dynamical Systems Effluents Energy consumption Engineering Fuzzy sets Linear matrix inequalities Neural networks Nitrogen Objectives Optimization Robust control Simulation Sludge State space models Variables Vibration Wastewater treatment Activated sludge process Takagi–Sugeno fuzzy modeling Parallel distributed compensation Carbon removal Wastewater treatment systems Static output feedback control
ISSN:	2195-268X, 2195-2698
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Abstract	Wastewater treatment systems have recently taken on new trends resulting from the growing awareness of health and environmental risks. New strategies aimed at the recovery of treated water are increasingly being proposed. Given its better performance, biological treatment via an activated sludge process (ASP) represents the key phase in the overall treatment chain. In this work, a Takagi–Sugeno (TS) fuzzy-based modeling and control approach of an ASP is proposed and successfully carried out for the carbon removal. Using the formalism of linear parameter-varying state-space representation and convex polytopic transformation, a TS fuzzy model of the studied ASP is firstly established. Such a fuzzy model is then used to design advanced control laws that maintain the considered state variables, i.e., volume of the effluent and concentrations of the heterotrophic biomass, biodegradable substrate and dissolved oxygen, at the set-point values. Two stabilization control approaches, namely parallel distributed compensation and static output parallel distributed compensation, are proposed and successfully applied. All these control problems are reformulated as Lyapunov quadratic stability conditions and linear matrix inequality constraints. Demonstrative results are carried out and compared to show the effectiveness and superiority of the proposed TS fuzzy-based control approach of such complex and nonlinear biochemical processes.
AbstractList	Wastewater treatment systems have recently taken on new trends resulting from the growing awareness of health and environmental risks. New strategies aimed at the recovery of treated water are increasingly being proposed. Given its better performance, biological treatment via an activated sludge process (ASP) represents the key phase in the overall treatment chain. In this work, a Takagi–Sugeno (TS) fuzzy-based modeling and control approach of an ASP is proposed and successfully carried out for the carbon removal. Using the formalism of linear parameter-varying state-space representation and convex polytopic transformation, a TS fuzzy model of the studied ASP is firstly established. Such a fuzzy model is then used to design advanced control laws that maintain the considered state variables, i.e., volume of the effluent and concentrations of the heterotrophic biomass, biodegradable substrate and dissolved oxygen, at the set-point values. Two stabilization control approaches, namely parallel distributed compensation and static output parallel distributed compensation, are proposed and successfully applied. All these control problems are reformulated as Lyapunov quadratic stability conditions and linear matrix inequality constraints. Demonstrative results are carried out and compared to show the effectiveness and superiority of the proposed TS fuzzy-based control approach of such complex and nonlinear biochemical processes.
Author	Arifi, Ali Bouallègue, Soufiene
Author_xml	– sequence: 1 givenname: Ali surname: Arifi fullname: Arifi, Ali organization: Research Laboratory in Automatic Control, National Engineering School of Tunis, National Engineering School of Gabès, University of Gabès – sequence: 2 givenname: Soufiene orcidid: 0000-0003-3172-6333 surname: Bouallègue fullname: Bouallègue, Soufiene email: soufiene.bouallegue@issig.rnu.tn organization: Research Laboratory in Automatic Control, National Engineering School of Tunis, High Institute of Industrial Systems of Gabès, University of Gabès
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Cites_doi	10.1007/s40435-023-01360-w 10.1201/b16637 10.3390/app7080813 10.1016/j.oceaneng.2022.113014 10.1109/CarpathianCC.2019.8766060 10.3390/su12030768 10.1016/j.asoc.2022.109636 10.1016/S0165-0114(98)00121-3 10.1201/9780203968567 10.3390/w12113220 10.1109/ICSMC.2000.886553 10.2166/wst.1999.0039 10.1109/STA56120.2022.10019005 10.1109/CDC.2002.1184510 10.3390/app8020261 10.1002/(SICI)1099-1239(199911)9:13<949::AID-RNC445>3.0.CO;2-G 10.1007/s40435-023-01285-4 10.1137/1.9781611970777 10.1016/j.neucom.2014.01.025 10.1021/ie8017687 10.3390/w13081037 10.1177/0142331220969056 10.1177/01423312211039048 10.1007/s40435-023-01368-2 10.1016/j.ifacol.2018.06.136 10.1016/j.envsoft.2003.03.005 10.1002/0471224596 10.23919/ChiCC.2019.8866516 10.1016/j.jprocont.2011.05.001 10.7717/peerj-cs.458 10.1007/s11431-021-1960-7 10.3390/math9222968
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IAWQ, London, UK XieYBWangDQiaoJFDynamic multi-objective intelligent optimal control toward wastewater treatment processesSci China Technol Sci20226556958010.1007/s11431-021-1960-7 FreitasJBSMarquezanLde Oliveira EvaldPJDPeñalozaEAGHernandez CelyMMA fuzzy-based predictive PID for DC motor speed controlInt J Dyn Control202410.1007/s40435-023-01368-2 TaghiehAZhangCAlattasKABouteraaYRathinasamySMohammadzadehAA predictive type-3 fuzzy control for under- actuated surface vehiclesOcean Eng2022266411301410.1016/j.oceaneng.2022.113014 CritesRWMiddlebrooksJBastianRKReedSCNatural wastewater treatment systems2014New YorkCRC Press10.1201/b16637 Rizwan AzharMEmadadeenAAdvanced control strategy for wastewater treatment process: a parametric studyInt J Chem Eng Appl20145335341 A Taghieh (1398_CR28) 2022; 266 S Revollar (1398_CR21) 2017; 7 A Taghieh (1398_CR35) 2021; 9 PG Georgieva (1398_CR16) 1999; 9 JBS Freitas (1398_CR29) 2024 S Boyd (1398_CR34) 1994 YB Xie (1398_CR23) 2022; 65 1398_CR41 1398_CR42 S Abdul Gaffar (1398_CR32) 2021 N Ballhysa (1398_CR4) 2020; 9 AM Nagy (1398_CR39) 2010; 49 L Debel Hansen (1398_CR18) 2021; 13 1398_CR43 1398_CR22 Y Qiao (1398_CR30) 2023 1398_CR9 S Revollar (1398_CR19) 2020; 12 RW Crites (1398_CR1) 2014 T Takagi (1398_CR24) 1985; 15 T Yang (1398_CR31) 2014; 136 W Gujer (1398_CR10) 1999; 39 K Tanaka (1398_CR25) 2001 A Khallouq (1398_CR37) 2021; 7 G Olsson (1398_CR2) 1999 AC Van Haandel (1398_CR3) 2012 W Wesley Eckenfelder (1398_CR8) 1998 KV Gernaey (1398_CR6) 2004; 19 SP Chakravarty (1398_CR17) 2022; 44 A Taghieh (1398_CR27) 2022; 129 L Matoug (1398_CR38) 2017; 46 1398_CR12 1398_CR11 M Rizwan Azhar (1398_CR13) 2014; 5 1398_CR33 J Yoneyama (1398_CR44) 2000; 111 N Sayadian (1398_CR26) 2024 AM Nagy (1398_CR40) 2011; 21 (1398_CR7) 2019 1398_CR14 A Taghieh (1398_CR36) 2021; 43 A Lahdhiri (1398_CR5) 2020 S Revollar (1398_CR20) 2018; 51 X Du (1398_CR15) 2018
References_xml	– reference: Debel HansenLVengMDurdevicPCompressor scheduling and pressure control for an alternating aeration activated sludge process: a simulation study validated on plant dataWater2021138103710.3390/w13081037 – reference: NagyAMMourotGMarxBRagotJSchutzGSystematic multi-modeling methodology applied to an activated sludge reactor modelInd Eng Chem Res2010492790279910.1021/ie8017687 – reference: CritesRWMiddlebrooksJBastianRKReedSCNatural wastewater treatment systems2014New YorkCRC Press10.1201/b16637 – reference: TakagiTSugenoMFuzzy identification of systems and its application to modeling and controlIEEE Trans Syst Man Cybern198515166172 – reference: LahdhiriALesageGHannachiAHeranVSteady-state methodology for activated sludge model 1 (ASM1) state variable calculation in MBRWater202010.3390/w12113220 – reference: YangTQiuWMaYChadliMZhangLFuzzy model-based predictive control of dissolved oxygen in activated sludge processesNeurocomputing2014136889510.1016/j.neucom.2014.01.025 – reference: ChakravartySPRoyARoyPControl of activated sludge treatment process using pre-compensated multi-variable quantitative feedback theory-based controllerTrans Inst Measur Control20224450652210.1177/01423312211039048 – reference: OlssonGNewellBWastewater treatment systems: modelling, diagnosis and control1999LondonIWA Publishing – reference: Petre E, Selișteanu D, Șulea-Iorgulescu C, Mehedințeanu S (2019) Mathematical modeling and control for an activated sludge process in a wastewater treatment plant. In: 20th International Carpathian control conference, Krakow-Wieliczka, Poland, 26–29 May 2019, pp 1–6 – reference: Dhouibi S, Jarray R, Bouallègue S (2023) Modelling and control of wastewater treatment systems: Case of activated sludge processes. In: 9th international conference on green energy and environmental engineering, Sousse, Tunisia, April 28–30, 2023 – reference: Henze M, Leslie Grady CP, Gujer W, Marais GR, Matsuo T (1987) Activated sludge model no.1, Technical Report. IAWQ, London, UK – reference: Wesley EckenfelderWGrauPActivated sludge process design and control: theory and practice1998New YorkCRC Press10.1201/9780203968567 – reference: Weijers S (2000) Modelling, identification and control of activated sludge plants for nitrogen removal. PhD dissertation, Technische Universiteit Eindhoven, Pays Bas – reference: Chadli M, Maquin D, Ragot J (2000) Relaxed stability conditions for Takagi-Sugeno fuzzy systems. In: IEEE international conference on systems, man and cybernetics, Nashville, TN, USA, 08–11 October 2000, pp 3514–3519 – reference: Dhouibi S, Bouallègue S (2022) Modeling and control design of an activated sludge process: A Multi-model approach. 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SubjectTerms	Activated sludge process Carbon Compensation Complexity Control Control algorithms Control and Systems Theory Control theory Controllers Design Dissolved oxygen Dynamical Systems Effluents Energy consumption Engineering Fuzzy sets Linear matrix inequalities Neural networks Nitrogen Objectives Optimization Robust control Simulation Sludge State space models Variables Vibration Wastewater treatment
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Title	Takagi–Sugeno fuzzy-based approach for modeling and control of an activated sludge process
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