{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T07:08:06Z","timestamp":1783926486301,"version":"3.55.0"},"reference-count":52,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T00:00:00Z","timestamp":1783555200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002347","name":"Bundesministerium fur Forschung Technologie und Raumfahrt Informationstechnikzentrum Bund","doi-asserted-by":"publisher","award":["03ZU1115EC"],"award-info":[{"award-number":["03ZU1115EC"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers &amp; Chemical Engineering"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.compchemeng.2026.109791","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T20:00:26Z","timestamp":1783627226000},"page":"109791","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Two-stage model predictive stack control for PEM fuel cell systems"],"prefix":"10.1016","volume":"214","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1626-7639","authenticated-orcid":false,"given":"Nikolai","family":"Weber","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3041-7515","authenticated-orcid":false,"given":"Daniel","family":"Sallach","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3249-8496","authenticated-orcid":false,"given":"Alexandre","family":"Ennen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2191-6635","authenticated-orcid":false,"given":"Maximilian","family":"Basler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0222-3457","authenticated-orcid":false,"given":"Stefan","family":"Pischinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0305-398X","authenticated-orcid":false,"given":"Heike","family":"Vallery","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.compchemeng.2026.109791_b1","series-title":"Nonlinear Model Predictive Control of Combustion Engines: From Fundamentals to Applications","author":"Albin Rajasingham","year":"2021"},{"key":"10.1016\/j.compchemeng.2026.109791_b2","article-title":"A Condensing Algorithm for Nonlinear MPC with a Quadratic Runtime in Horizon Length","author":"Andersson","year":"2017","journal-title":"Optim. Online"},{"issue":"1","key":"10.1016\/j.compchemeng.2026.109791_b3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12532-018-0139-4","article-title":"CasADi: a software framework for nonlinear optimization and optimal control","volume":"11","author":"Andersson","year":"2019","journal-title":"Math. Program. Comput."},{"key":"10.1016\/j.compchemeng.2026.109791_b4","series-title":"Electrochemical Methods: Fundamentals and Applications","author":"Bard","year":"2001"},{"key":"10.1016\/j.compchemeng.2026.109791_b5","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1016\/j.ijhydene.2024.03.061","article-title":"State-of-Health observer for PEM fuel cells\u2014A novel approach for real-time online analysis","volume":"95","author":"Bartlechner","year":"2024","journal-title":"Int. J. Hydrog. Energy"},{"key":"10.1016\/j.compchemeng.2026.109791_b6","doi-asserted-by":"crossref","DOI":"10.1155\/2023\/8516622","article-title":"Urban Air Pollution and Greenness in Relation to Public Health","volume":"2023","author":"Bikis","year":"2023","journal-title":"J. Environ. Public Health"},{"key":"10.1016\/j.compchemeng.2026.109791_b7","series-title":"Transport Phenomena","author":"Bird","year":"2006"},{"key":"10.1016\/j.compchemeng.2026.109791_b8","series-title":"Numerical Treatment of Inverse Problems in Differential and Integral Equations: Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 \u2014 September 3, 1982","first-page":"95","article-title":"Recent Advances in Parameteridentification Techniques for O.D.E.","author":"Bock","year":"1983"},{"issue":"2","key":"10.1016\/j.compchemeng.2026.109791_b9","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1016\/S1474-6670(17)61205-9","article-title":"A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems*","volume":"17","author":"Bock","year":"1984","journal-title":"IFAC Proc. Vol."},{"key":"10.1016\/j.compchemeng.2026.109791_b10","series-title":"GHG Emissions of All World Countries","author":"Crippa","year":"2024"},{"key":"10.1016\/j.compchemeng.2026.109791_b11","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.renene.2017.06.027","article-title":"PEM fuel cell system control: A review","volume":"113","author":"Daud","year":"2017","journal-title":"Renew. Energy"},{"key":"10.1016\/j.compchemeng.2026.109791_b12","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.ijhydene.2024.01.351","article-title":"Performance-oriented model learning and model predictive control for PEMFC air supply system","volume":"64","author":"Deng","year":"2024","journal-title":"Int. J. Hydrog. Energy"},{"issue":"4","key":"10.1016\/j.compchemeng.2026.109791_b13","doi-asserted-by":"crossref","first-page":"F221","DOI":"10.1149\/2.0361904jes","article-title":"The Butler-Volmer Equation for Polymer Electrolyte Membrane Fuel Cell (PEMFC) Electrode Kinetics: A Critical Discussion","volume":"166","author":"Dickinson","year":"2019","journal-title":"J. Electrochem. Soc."},{"issue":"5","key":"10.1016\/j.compchemeng.2026.109791_b14","doi-asserted-by":"crossref","first-page":"1714","DOI":"10.1137\/S0363012902400713","article-title":"A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control","volume":"43","author":"Diehl","year":"2005","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/j.compchemeng.2026.109791_b15","series-title":"The Development of a Simulation Tool for Monitoring Heavy-Duty Vehicle CO 2 Emissions and Fuel Consumption in Europe","author":"Fontaras","year":"2013"},{"key":"10.1016\/j.compchemeng.2026.109791_b16","doi-asserted-by":"crossref","DOI":"10.1016\/j.jpowsour.2020.227996","article-title":"Degradation-conscious control for enhanced lifetime of automotive polymer electrolyte membrane fuel cells","volume":"457","author":"Goshtasbi","year":"2020","journal-title":"J. Power Sources"},{"issue":"2","key":"10.1016\/j.compchemeng.2026.109791_b17","doi-asserted-by":"crossref","DOI":"10.1149\/1945-7111\/ab6dd1","article-title":"A Mathematical Model toward Real-Time Monitoring of Automotive PEM Fuel Cells","volume":"167","author":"Goshtasbi","year":"2020","journal-title":"J. Electrochem. Soc."},{"issue":"1","key":"10.1016\/j.compchemeng.2026.109791_b18","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1080\/00207179.2016.1222553","article-title":"From linear to nonlinear MPC: bridging the gap via the real-time iteration","volume":"93","author":"Gros","year":"2016","journal-title":"Internat. J. Control"},{"issue":"17","key":"10.1016\/j.compchemeng.2026.109791_b19","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2024.107227","article-title":"Oxygen-sensor-based 2-DOF PI air-flow controller of fuel cell system","volume":"361","author":"Haddad","year":"2024","journal-title":"J. Franklin Inst."},{"key":"10.1016\/j.compchemeng.2026.109791_b20","doi-asserted-by":"crossref","DOI":"10.1016\/j.energy.2023.128459","article-title":"Fused multi-model predictive control with adaptive compensation for proton exchange membrane fuel cell air supply system","volume":"284","author":"Hu","year":"2023","journal-title":"Energy"},{"issue":"4","key":"10.1016\/j.compchemeng.2026.109791_b21","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1007\/s12239-024-00064-0","article-title":"Analysis of Power Consumption on BOP System in a Fuel Cell Electric Bus According to the Fuel Cell Load Range","volume":"25","author":"Kim","year":"2024","journal-title":"Int. J. Automot. Technol."},{"key":"10.1016\/j.compchemeng.2026.109791_b22","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1016\/j.ijhydene.2024.05.199","article-title":"Adaptive extended kalman filter for PEMFC membrane water content estimation","volume":"71","author":"Lance","year":"2024","journal-title":"Int. J. Hydrog. Energy"},{"key":"10.1016\/j.compchemeng.2026.109791_b23","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.jpowsour.2013.04.067","article-title":"Control of proton exchange membrane fuel cell system breathing based on maximum net power control strategy","volume":"241","author":"Li","year":"2013","journal-title":"J. Power Sources"},{"key":"10.1016\/j.compchemeng.2026.109791_b24","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.jpowsour.2016.08.019","article-title":"Nonlinear predictive control for durability enhancement and efficiency improvement in a fuel cell power system","volume":"328","author":"Luna","year":"2016","journal-title":"J. Power Sources"},{"key":"10.1016\/j.compchemeng.2026.109791_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.egyai.2024.100406","article-title":"A review of control strategies for proton exchange membrane (PEM) fuel cells and water electrolysers: From automation to autonomy","volume":"17","author":"Mao","year":"2024","journal-title":"Energy AI"},{"key":"10.1016\/j.compchemeng.2026.109791_b26","series-title":"Model Predictive Control Toolbox Version: 24.2 (R2024b)","author":"MathWorksInc.","year":"2024"},{"key":"10.1016\/j.compchemeng.2026.109791_b27","series-title":"Optimization Toolbox Version: 24.2 (R2024b)","author":"MathWorksInc.","year":"2024"},{"issue":"8","key":"10.1016\/j.compchemeng.2026.109791_b28","doi-asserted-by":"crossref","first-page":"A1633","DOI":"10.1149\/1.1940747","article-title":"A Generalized Phenomenological Model and Database for the Transport of Water and Current in Polymer Electrolyte Membranes","volume":"152","author":"Mazumder","year":"2005","journal-title":"J. Electrochem. Soc."},{"issue":"75","key":"10.1016\/j.compchemeng.2026.109791_b29","doi-asserted-by":"crossref","first-page":"29295","DOI":"10.1016\/j.ijhydene.2023.03.398","article-title":"Nonlinear model predictive control for efficient and robust airpath management in fuel cell vehicles","volume":"48","author":"Mele","year":"2023","journal-title":"Int. J. Hydrog. Energy"},{"key":"10.1016\/j.compchemeng.2026.109791_b30","article-title":"S32N7 Vehicle Super-Integration Processor","author":"NXP Semiconductors","year":"2024","journal-title":"S32N7 Super-Integr. Process. Softw.-Defin. Veh."},{"key":"10.1016\/j.compchemeng.2026.109791_b31","series-title":"Numerical Heat Transfer and Fluid Flow","author":"Patankar","year":"1980"},{"issue":"1","key":"10.1016\/j.compchemeng.2026.109791_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.enrev.2022.100002","article-title":"Progress in the proton exchange membrane fuel cells (PEMFCs) water\/thermal management: From theory to the current challenges and real-time fault diagnosis methods","volume":"1","author":"Pourrahmani","year":"2022","journal-title":"Energy Rev."},{"key":"10.1016\/j.compchemeng.2026.109791_b33","series-title":"Control of Fuel Cell Power Systems","author":"Pukrushpan","year":"2004"},{"key":"10.1016\/j.compchemeng.2026.109791_b34","series-title":"Model Predictive Control: Theory, Computation, and Design","author":"Rawlings","year":"2009"},{"issue":"12","key":"10.1016\/j.compchemeng.2026.109791_b35","doi-asserted-by":"crossref","first-page":"3148","DOI":"10.3390\/en13123148","article-title":"A Real-Time Dynamic Fuel Cell System Simulation for Model-Based Diagnostics and Control: Validation on Real Driving Data","volume":"13","author":"Ritzberger","year":"2020","journal-title":"Energies"},{"issue":"9","key":"10.1016\/j.compchemeng.2026.109791_b36","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/0098-1354(94)E0001-4","article-title":"Quadratic programming methods for reduced hessian SQP","volume":"18","author":"Schmid","year":"1994","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2026.109791_b37","series-title":"2023 31st Mediterranean Conference on Control and Automation","first-page":"89","article-title":"Nonlinear MPC for Fuel Cell Air Path Control with Experimental Validation","author":"Schmitt","year":"2023"},{"key":"10.1016\/j.compchemeng.2026.109791_b38","series-title":"Optimal State Estimation","first-page":"393","article-title":"Nonlinear Kalman filtering","author":"Simon","year":"2006"},{"issue":"8","key":"10.1016\/j.compchemeng.2026.109791_b39","doi-asserted-by":"crossref","first-page":"2334","DOI":"10.1149\/1.2085971","article-title":"Polymer Electrolyte Fuel Cell Model","volume":"138","author":"Springer","year":"1991","journal-title":"J. Electrochem. Soc."},{"key":"10.1016\/j.compchemeng.2026.109791_b40","series-title":"Fuel Cell Handbook, Fourth Edition","author":"Stauffer","year":"1998"},{"issue":"14","key":"10.1016\/j.compchemeng.2026.109791_b41","doi-asserted-by":"crossref","first-page":"90","DOI":"10.3182\/20090901-3-RO-4009.00012","article-title":"Model predictive control for automotive time-delay processes: An application to air-to-fuel ratio control*","volume":"42","author":"Trimboli","year":"2009","journal-title":"IFAC Proc. Vol."},{"key":"10.1016\/j.compchemeng.2026.109791_b42","doi-asserted-by":"crossref","DOI":"10.1016\/j.compchemeng.2024.108905","article-title":"Water and thermal management in PEM fuel cells using feasible humidity plots and model predictive controllers","volume":"192","author":"T\u00fcmer","year":"2025","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2026.109791_b43","series-title":"2020 SICE International Symposium on Control Systems","first-page":"77","article-title":"Efficient and life preserving power tracking control of a proton exchange membrane fuel cell using model predictive control","author":"Vrlic","year":"2020"},{"key":"10.1016\/j.compchemeng.2026.109791_b44","doi-asserted-by":"crossref","DOI":"10.1016\/j.enconman.2021.114851","article-title":"Simulation study on the PEMFC oxygen starvation based on the coupling algorithm of model predictive control and PID","volume":"249","author":"Wang","year":"2021","journal-title":"Energy Convers. Manage."},{"issue":"1","key":"10.1016\/j.compchemeng.2026.109791_b45","doi-asserted-by":"crossref","DOI":"10.1016\/j.enrev.2023.100054","article-title":"A systematic review of system modeling and control strategy of proton exchange membrane fuel cell","volume":"3","author":"Wang","year":"2024","journal-title":"Energy Rev."},{"issue":"7","key":"10.1016\/j.compchemeng.2026.109791_b46","doi-asserted-by":"crossref","first-page":"A1008","DOI":"10.1149\/1.1580822","article-title":"Transport in Polymer-Electrolyte Membranes: I. Physical Model","volume":"150","author":"Weber","year":"2003","journal-title":"J. Electrochem. Soc."},{"key":"10.1016\/j.compchemeng.2026.109791_b47","series-title":"Experimental Dataset: Two-Stage Model Predictive Stack Control for PEM Fuel Cell Systems","author":"Weber","year":"2026"},{"key":"10.1016\/j.compchemeng.2026.109791_b48","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1016\/j.ijhydene.2025.02.080","article-title":"Review of control strategies for onboard fuel cells: Insights from degradation mechanisms under variable load conditions","volume":"110","author":"Wu","year":"2024","journal-title":"Int. J. Hydrog. Energy"},{"key":"10.1016\/j.compchemeng.2026.109791_b49","doi-asserted-by":"crossref","DOI":"10.1016\/j.rser.2021.111908","article-title":"Progress and perspectives of integrated thermal management systems in PEM fuel cell vehicles: A review","volume":"155","author":"Xu","year":"2022","journal-title":"Renew. Sustain. Energy Rev."},{"issue":"3","key":"10.1016\/j.compchemeng.2026.109791_b50","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0013-4686(94)00277-8","article-title":"The water content dependence of electro-osmotic drag in proton-conducting polymer electrolytes","volume":"40","author":"Zawodzinski","year":"1995","journal-title":"Electrochim. Acta"},{"key":"10.1016\/j.compchemeng.2026.109791_b51","doi-asserted-by":"crossref","DOI":"10.1016\/j.icheatmasstransfer.2024.107376","article-title":"Advancements and insights in thermal and water management of proton exchange membrane fuel cells: Challenges and prospects","volume":"153","author":"Zhang","year":"2024","journal-title":"Int. Commun. Heat Mass Transfer"},{"key":"10.1016\/j.compchemeng.2026.109791_b52","doi-asserted-by":"crossref","DOI":"10.1016\/j.renene.2024.120992","article-title":"Innovative air supply management in fuel cells: An economic predictive control approach without pre-measured OER","volume":"232","author":"Zhu","year":"2024","journal-title":"Renew. Energy"}],"container-title":["Computers &amp; Chemical Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0098135426002449?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0098135426002449?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T06:28:21Z","timestamp":1783924101000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0098135426002449"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":52,"alternative-id":["S0098135426002449"],"URL":"https:\/\/doi.org\/10.1016\/j.compchemeng.2026.109791","relation":{"is-supplemented-by":[{"id-type":"uri","id":"https:\/\/data.mendeley.com\/preview\/mc46tw9t8m?a=12b7ebd4-5534-4574-b267-e2aab28f526f","asserted-by":"subject"}]},"ISSN":["0098-1354"],"issn-type":[{"value":"0098-1354","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Two-stage model predictive stack control for PEM fuel cell systems","name":"articletitle","label":"Article Title"},{"value":"Computers & Chemical Engineering","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.compchemeng.2026.109791","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"109791"}}