Integrated Modeling, Identification, and Neural Network Control of PEM Fuel Cells

Integrated Modeling, Identification, and Neural Network Control of PEM Fuel Cells | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Integrated Modeling, Identification, and Neural Network Control of PEM Fuel Cells Nuraddeen Magaji, Aliyu Tukur, ALiyu Usman, Muhammad Marwan sa,ad This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9324272/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Proton exchange membrane fuel cells (PEMFCs) are promising candidates for clean energy conversion in transportation, stationary, and distributed power applications. However, their nonlinear dynamics, coupled with water management and gas flow constraints, present significant challenges for real-time simulation and control. This work develops an integrated framework that combines physics-based modeling, data-driven identification, and neural network–based control for PEMFC systems. A dynamic five-state mass balance model is formulated to describe hydrogen, oxygen, and water mole inventories together with inlet valve dynamics. Synthetic datasets generated from the nonlinear plant are then used to train a long short-term memory (LSTM) network, enabling sequence-to-sequence prediction of PEMFC states. The LSTM surrogate achieves high fidelity with mean root mean square error (RMSE) below 1% on validation data, while reducing computation time by more than an order of magnitude compared to direct physics-based simulations. For control, an expert proportional–integral (PI) strategy is designed to regulate hydrogen and oxygen supply, and its operation is used to train a feedforward neural network (NN) controller via supervised learning. Quantitative evaluation shows that the NN closely reproduces the expert controller policy with RMSE of 0.52 mol/s for hydrogen and 0.47 mol/s for oxygen. Closed-loop validation demonstrates superior performance of the NN controller: under step input tracking, it achieves faster settling time (1.76 s vs. 2.64 s for PI) with negligible overshoot and zero steady-state error, while under disturbance rejection it reduces overshoot (2.03% vs. 3.71%) and halves settling time (0.30 s vs. 0.57 s). These results confirm that the NN controller’s faster response, reduced overshoot, and improved robustness, highlighting its suitability for real-time PEMFC energy management and automotive deployment. PEMFC LSTM neural network control system identification dynamic modeling surrogate model Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 12 May, 2026 Reviewers agreed at journal 28 Apr, 2026 Reviewers agreed at journal 27 Apr, 2026 Reviewers agreed at journal 24 Apr, 2026 Reviewers agreed at journal 23 Apr, 2026 Reviewers invited by journal 23 Apr, 2026 Editor invited by journal 22 Apr, 2026 Editor assigned by journal 13 Apr, 2026 Submission checks completed at journal 13 Apr, 2026 First submitted to journal 05 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9324272","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":633678282,"identity":"30b91cae-58c2-4985-8dd7-5e1d030f4e3f","order_by":0,"name":"Nuraddeen Magaji","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYNACHgk5NmbGxgcgJh+xWoz52ZsPG4CYbMTakziz51iaBIhFUIu52OHHL37IWDBuuJFjVvk1x06GjYH54aMbeLRYzk4zs+zhkWA2AGq5LbstGegwNmPjHDxaDG4nmBnw8EiwgbVIbmMGauFhk8avJf2b4R8eCR6QlmLJbfXEaMkxfgy0RUIS6H3Gj9sOE6WljFmGR8IAFMjSjNuO87AxE/RL+uaPb3vq6tuAUfnx57Zqe6Deh4/xaQECNgnGHgiLmQdM4lcOVvKB4QeExfiDsOpRMApGwSgYgQAAhCVE9bO6jFIAAAAASUVORK5CYII=","orcid":"","institution":"Bayero University Kano","correspondingAuthor":true,"prefix":"","firstName":"Nuraddeen","middleName":"","lastName":"Magaji","suffix":""},{"id":633678284,"identity":"7683abfa-958a-4068-93e6-352e037f8bf7","order_by":1,"name":"Aliyu Tukur","email":"","orcid":"","institution":"Bayero University Kano","correspondingAuthor":false,"prefix":"","firstName":"Aliyu","middleName":"","lastName":"Tukur","suffix":""},{"id":633678287,"identity":"91ea55c4-dbed-41a3-b663-5ff14471b0bf","order_by":2,"name":"ALiyu Usman","email":"","orcid":"","institution":"Bayero University Kano","correspondingAuthor":false,"prefix":"","firstName":"ALiyu","middleName":"","lastName":"Usman","suffix":""},{"id":633678288,"identity":"32289179-9f77-470b-928d-757b8edd268c","order_by":3,"name":"Muhammad Marwan sa,ad","email":"","orcid":"","institution":"Bayero University Kano","correspondingAuthor":false,"prefix":"","firstName":"ad","middleName":"Muhammad Marwan","lastName":"sa","suffix":""}],"badges":[],"createdAt":"2026-04-05 05:53:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9324272/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9324272/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108494195,"identity":"ebc13db4-e6b4-4e10-9fce-c8261fed46bd","added_by":"auto","created_at":"2026-05-05 10:03:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1038345,"visible":true,"origin":"","legend":"","description":"","filename":"PaperANN1DiscoverElectronics.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9324272/v1_covered_f2cf0020-4994-46d3-87b4-56e9f855cd45.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Integrated Modeling, Identification, and Neural Network Control of PEM Fuel Cells","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Electronics](https://www.springer.com/journal/44291)","snPcode":"44291","submissionUrl":"https://submission.nature.com/new-submission/44291","title":"Discover Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"PEMFC, LSTM, neural network control, system identification, dynamic modeling, surrogate model","lastPublishedDoi":"10.21203/rs.3.rs-9324272/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9324272/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eProton exchange membrane fuel cells (PEMFCs) are promising candidates for clean energy conversion in transportation, stationary, and distributed power applications. However, their nonlinear dynamics, coupled with water management and gas flow constraints, present significant challenges for real-time simulation and control. This work develops an integrated framework that combines physics-based modeling, data-driven identification, and neural network\u0026ndash;based control for PEMFC systems. A dynamic five-state mass balance model is formulated to describe hydrogen, oxygen, and water mole inventories together with inlet valve dynamics. Synthetic datasets generated from the nonlinear plant are then used to train a long short-term memory (LSTM) network, enabling sequence-to-sequence prediction of PEMFC states. The LSTM surrogate achieves high fidelity with mean root mean square error (RMSE) below 1% on validation data, while reducing computation time by more than an order of magnitude compared to direct physics-based simulations. For control, an expert proportional\u0026ndash;integral (PI) strategy is designed to regulate hydrogen and oxygen supply, and its operation is used to train a feedforward neural network (NN) controller via supervised learning. Quantitative evaluation shows that the NN closely reproduces the expert controller policy with RMSE of 0.52 mol/s for hydrogen and 0.47 mol/s for oxygen. Closed-loop validation demonstrates superior performance of the NN controller: under step input tracking, it achieves faster settling time (1.76 s vs. 2.64 s for PI) with negligible overshoot and zero steady-state error, while under disturbance rejection it reduces overshoot (2.03% vs. 3.71%) and halves settling time (0.30 s vs. 0.57 s). These results confirm that the NN controller\u0026rsquo;s faster response, reduced overshoot, and improved robustness, highlighting its suitability for real-time PEMFC energy management and automotive deployment.\u003c/p\u003e","manuscriptTitle":"Integrated Modeling, Identification, and Neural Network Control of PEM Fuel Cells","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-04 15:55:46","doi":"10.21203/rs.3.rs-9324272/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-13T01:51:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"326834078070034229425653585429582303639","date":"2026-04-28T20:50:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"125148165305037072074574390788506742363","date":"2026-04-27T20:09:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"319647347156569155974833285341542146070","date":"2026-04-24T22:32:27+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"183329912102508035314970066970904820596","date":"2026-04-24T03:35:15+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-23T17:03:11+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-04-22T06:19:30+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-13T08:02:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-13T08:02:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Electronics","date":"2026-04-05T05:48:50+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Electronics](https://www.springer.com/journal/44291)","snPcode":"44291","submissionUrl":"https://submission.nature.com/new-submission/44291","title":"Discover Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"623545e5-e95a-4512-936e-ffc98ad58672","owner":[],"postedDate":"May 4th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-13T01:51:43+00:00","index":36,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-04T15:55:46+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-04 15:55:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9324272","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9324272","identity":"rs-9324272","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}