{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T21:12:22Z","timestamp":1773436342301,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T00:00:00Z","timestamp":1660176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SaCoAV","award":["MINECO PID2020-114244RB-I00"],"award-info":[{"award-number":["MINECO PID2020-114244RB-I00"]}]},{"name":"SaCoAV","award":["001-P-001643"],"award-info":[{"award-number":["001-P-001643"]}]},{"name":"SaCoAV","award":["2017\/SGR\/482"],"award-info":[{"award-number":["2017\/SGR\/482"]}]},{"name":"ERDF Operational Program of Catalonia 2014\u20132020","award":["MINECO PID2020-114244RB-I00"],"award-info":[{"award-number":["MINECO PID2020-114244RB-I00"]}]},{"name":"ERDF Operational Program of Catalonia 2014\u20132020","award":["001-P-001643"],"award-info":[{"award-number":["001-P-001643"]}]},{"name":"ERDF Operational Program of Catalonia 2014\u20132020","award":["2017\/SGR\/482"],"award-info":[{"award-number":["2017\/SGR\/482"]}]},{"name":"DGR of Generalitat de Catalunya","award":["MINECO PID2020-114244RB-I00"],"award-info":[{"award-number":["MINECO PID2020-114244RB-I00"]}]},{"name":"DGR of Generalitat de Catalunya","award":["001-P-001643"],"award-info":[{"award-number":["001-P-001643"]}]},{"name":"DGR of Generalitat de Catalunya","award":["2017\/SGR\/482"],"award-info":[{"award-number":["2017\/SGR\/482"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This work proposes an economic model predictive control (EMPC) strategy in the linear parameter varying (LPV) framework for the control of dissolved oxygen concentrations in the aerated reactors of a wastewater treatment plant (WWTP). A reduced model of the complex nonlinear plant is represented in a quasi-linear parameter varying (qLPV) form to reduce computational burden, enabling the real-time operation. To facilitate the formulation of the time-varying parameters which are functions of system states, as well as for feedback control purposes, a moving horizon estimator (MHE) that uses the qLPV WWTP model is proposed. The control strategy is investigated and evaluated based on the ASM1 simulation benchmark for performance assessment. The obtained results applying the EMPC strategy for the control of the aeration system in the WWTP of Girona (Spain) show its effectiveness.<\/jats:p>","DOI":"10.3390\/s22166008","type":"journal-article","created":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T23:05:49Z","timestamp":1660259149000},"page":"6008","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Economic Linear Parameter Varying Model Predictive Control of the Aeration System of a Wastewater Treatment Plant"],"prefix":"10.3390","volume":"22","author":[{"given":"Fatiha","family":"Nejjari","sequence":"first","affiliation":[{"name":"Advanced Control Systems Group, Automatic Control Department, Edifici Gaia Campus de Terrassa, Universitat Polit\u00e8cnica de Catalunya, Rambla Sant Nebridi, 22, 08222 Terrassa, Spain"}]},{"given":"Boutrous","family":"Khoury","sequence":"additional","affiliation":[{"name":"Advanced Control Systems Group, Automatic Control Department, Edifici Gaia Campus de Terrassa, Universitat Polit\u00e8cnica de Catalunya, Rambla Sant Nebridi, 22, 08222 Terrassa, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6364-6429","authenticated-orcid":false,"given":"Vicen\u00e7","family":"Puig","sequence":"additional","affiliation":[{"name":"Advanced Control Systems Group, Automatic Control Department, Edifici Gaia Campus de Terrassa, Universitat Polit\u00e8cnica de Catalunya, Rambla Sant Nebridi, 22, 08222 Terrassa, Spain"},{"name":"Institut de Rob\u00f2tica i Inform\u00e0tica Industrial (CSIC-UPC), Llorens i Artigas, 4-6, 08028 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7827-2896","authenticated-orcid":false,"given":"Joseba","family":"Quevedo","sequence":"additional","affiliation":[{"name":"Advanced Control Systems Group, Automatic Control Department, Edifici Gaia Campus de Terrassa, Universitat Polit\u00e8cnica de Catalunya, Rambla Sant Nebridi, 22, 08222 Terrassa, Spain"}]},{"given":"Josep","family":"Pascual","sequence":"additional","affiliation":[{"name":"Advanced Control Systems Group, Automatic Control Department, Edifici Gaia Campus de Terrassa, Universitat Polit\u00e8cnica de Catalunya, Rambla Sant Nebridi, 22, 08222 Terrassa, Spain"}]},{"given":"Sergi","family":"de Campos","sequence":"additional","affiliation":[{"name":"ADASA Sistemas, S.A.U. C\/Ignasi Iglesias, 217, 08820 El Prat de Llobregat, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.cep.2004.08.002","article-title":"Long-term optimal aeration strategies for small-size alternating activated sludge treatment plants","volume":"44","author":"Chachuat","year":"2005","journal-title":"Chem. Eng. Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.conengprac.2003.07.001","article-title":"The cost benchmark simulation model current state and future perspective","volume":"12","author":"Jeppsson","year":"2004","journal-title":"Control Eng. Pract."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1016\/j.compchemeng.2007.06.008","article-title":"Dissolved oxygen control of the activated sludge wastewater treatment process using model predictive control","volume":"32","author":"Holenda","year":"2008","journal-title":"Comput. Chem. Eng."},{"key":"ref_4","first-page":"2763","article-title":"Fuzzy control and model predictive control configurations for effluent violations removal in wastewater treatment plants","volume":"54","author":"Santin","year":"2015","journal-title":"Control Eng. Pract."},{"key":"ref_5","unstructured":"Maciejowski, J.M. (2002). Predictive Control: With Constraints, Pearson Education."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2763","DOI":"10.1016\/j.compchemeng.2014.03.027","article-title":"Integration of set point optimization techniques into nonlinear MPC for improving the operation of WWTPs","volume":"68","author":"Vega","year":"2014","journal-title":"Comput. Chem. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2469","DOI":"10.1016\/j.compchemeng.2011.03.031","article-title":"Cost reduction of the wastewater treatment plant operation by MPC based on modified ASM1 with two-step nitrification\/denitrification model","volume":"35","author":"Ostace","year":"2011","journal-title":"Comput. Chem. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.compchemeng.2015.07.003","article-title":"Model predictive control for the self-optimized operation in wastewater treatment plants: Analysis of dynamic issues","volume":"82","author":"Francisco","year":"2015","journal-title":"Comput. Chem. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rawlings, J., Angeli, D., and Bates, C. (2012, January 10\u201313). Fundamentals of economic model predictive control. Proceedings of the 51st IEEE Conference on Decision and Control, Maui, HI, USA.","DOI":"10.1109\/CDC.2012.6425822"},{"key":"ref_10","first-page":"1579","article-title":"Economic Model Predictive Control of Aeration Systems in a Full Scale Biological Wastewater Treatment Plant","volume":"Volume 40","author":"Nejjari","year":"2017","journal-title":"Computer Aided Chemical Engineering (Proceedings of the 27th European Symposium on Computer Aided Process Engineering)"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.arcontrol.2020.04.016","article-title":"Model predictive control design for linear parameter varying systems: A survey","volume":"49","author":"Morato","year":"2020","journal-title":"Annu. Rev. Control"},{"key":"ref_12","unstructured":"Olsson, G., and Newell, B. (1999). Wastewater Treatment Systems: Modeling, Diagnosis and Control, IWA Publishing."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"173","DOI":"10.2166\/wst.1993.0657","article-title":"Reduced Order Models for On-Line Parameter Identification of the Activated Sludge Process","volume":"28","author":"Jeppsson","year":"1993","journal-title":"Water Sci. Technol."},{"key":"ref_14","first-page":"5","article-title":"R\u00e9duction du mod\u00e8le ASM 1 pour la commande optimale des petites stations d\u2019\u00e9puration \u00e0 boues activ\u00e9es","volume":"16","author":"Chachuat","year":"2003","journal-title":"Rev. Des Sci. de l\u2019eau"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Revollar, S., Vega, P., Vilanova, R., and Francisco, M. (2017). Optimal Control of Wastewater Treatment Plants Using Economic-Oriented Model Predictive Dynamic Strategies. Appl. Sci., 7.","DOI":"10.3390\/app7080813"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1016\/j.jprocont.2009.07.017","article-title":"A nonlinear observer for an activated sludge wastewater treatment process","volume":"19","author":"Boulkroune","year":"2009","journal-title":"J. Process Control"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Harja, G., Vlad, G., and Nascu, I. (2016, January 19\u201321). MPC advanced control of dissolved oxygen in an activated sludge wastewater treatment plant. Proceedings of the 2016 IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR), Cluj-Napoca, Romania.","DOI":"10.1109\/AQTR.2016.7501329"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"256","DOI":"10.2514\/3.20997","article-title":"Gain-Scheduled Missile Autopilot Design using Linear Parameter Varying Transformation","volume":"16","author":"Shamma","year":"1993","journal-title":"J. Guid. Control Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"596","DOI":"10.3182\/20050703-6-CZ-1902.00100","article-title":"Parameter reduction for LPV systems via principle components analysis","volume":"38","author":"Kwiatkowski","year":"2005","journal-title":"IFAC Proc. Vol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"14507","DOI":"10.3182\/20110828-6-IT-1002.00415","article-title":"Tuning of Predictive Controllers for Drinking Water Networked Systems","volume":"44","author":"Toro","year":"2011","journal-title":"IFAC Proc. Vol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ocampo-Martinez, C., Toro, R., Puig, V., Van Impe, J., and Logist, F. (2022). Multi-Objective-Based Tuning of Economic Model Predictive Control of Drinking Water Transport Networks. Water, 14.","DOI":"10.3390\/w14081222"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1061\/(ASCE)HY.1943-7900.0000702","article-title":"A preliminary numerical approach for the study of compressed air injection in inverted siphons","volume":"139","author":"Oliveira","year":"2013","journal-title":"J. Hydraul. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:07:24Z","timestamp":1760141244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,11]]},"references-count":22,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22166008"],"URL":"https:\/\/doi.org\/10.3390\/s22166008","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,11]]}}}