FPGA-Based LQG Control of a Low-Speed Active Magnetic Bearing Joint: Implementation and Validation

FPGA-Based LQG Control of a Low-Speed Active Magnetic Bearing Joint: Implementation and Validation | 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 FPGA-Based LQG Control of a Low-Speed Active Magnetic Bearing Joint: Implementation and Validation Walter Torrestiana González, Leopoldo González González, Emmanuel González Mendoza, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7926101/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Active magnetic bearings (AMBs) enable contactless support and are attractive for precision mechanisms in particle-sensitive environments. This work presents a complete discrete-time linear-quadratic-Gaussian (LQG) control pipeline on a field-programmable gate array (FPGA) for a low-speed robotic joint using a three-degree-of-freedom active magnetic bearing (two radial axes and one axial levitator). A translational physics-based model explicitly captures bias currents and nominal air gaps, followed by equilibrium linearization and zero-order-hold discretization at 2 kHz. The estimator–controller ( linear–quadratic regulator , LQR, plus Kalman filter) is implemented in fixed-point logic with sub-200 \((\mu)\) s end-to-end latency. Experiments on a dedicated testbed compare the proposed LQG against a tuned proportional–integral–derivative (PID) controller and an observer-based pole-placement baseline under identical sensing and actuation. In the radial loop, LQG reduces startup settling time by approximately 44% and integrated absolute error by approximately 36.5%, with overshoot below 0.5% and actuator limits respected; recovery to a \((\pm 5%)\) band under external disturbances is about 13% faster. A nonlinear-plant robustness map indicates stable, non-overshooting behavior under \((\pm 20%)\) variations of magnetic and electrical parameters. Particle measurements during continuous operation remain below the International Organization for Standardization (ISO) Class 5 thresholds, supporting the suitability of the proposed joint for cleanroom robotics. Active magnetic bearing Linear quadratic Gaussian control FPGA implementation Discrete-time control Kalman filter Cleanroom robotics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 04 Dec, 2025 Reviews received at journal 03 Dec, 2025 Reviews received at journal 30 Nov, 2025 Reviews received at journal 17 Nov, 2025 Reviewers agreed at journal 07 Nov, 2025 Reviewers agreed at journal 02 Nov, 2025 Reviewers agreed at journal 02 Nov, 2025 Reviewers invited by journal 02 Nov, 2025 Editor assigned by journal 23 Oct, 2025 Submission checks completed at journal 23 Oct, 2025 First submitted to journal 22 Oct, 2025 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. We do this by developing innovative software and high quality services for the global research community. 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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-7926101","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":541736759,"identity":"08fe6770-6780-4e43-a0e2-df1cc5c15627","order_by":0,"name":"Walter Torrestiana González","email":"","orcid":"","institution":"National Autonomous University of Mexico (UNAM)","correspondingAuthor":false,"prefix":"","firstName":"Walter","middleName":"Torrestiana","lastName":"González","suffix":""},{"id":541736760,"identity":"3973d85e-5a78-4dab-990d-ccde11cc5372","order_by":1,"name":"Leopoldo González 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Validation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-control-automation-and-electrical-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcae","sideBox":"Learn more about [Journal of Control, Automation and Electrical Systems](https://link.springer.com/journal/40313)","snPcode":"40313","submissionUrl":"https://submission.springernature.com/new-submission/40313/3","title":"Journal of Control, Automation and Electrical Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Active magnetic bearing, Linear, quadratic, Gaussian control, FPGA implementation, Discrete-time control, Kalman filter, Cleanroom robotics","lastPublishedDoi":"10.21203/rs.3.rs-7926101/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7926101/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eActive magnetic bearings (AMBs) enable contactless support and are attractive for precision mechanisms in particle-sensitive environments. This work presents a complete discrete-time linear-quadratic-Gaussian (LQG) control pipeline on a field-programmable gate array (FPGA) for a low-speed robotic joint using a three-degree-of-freedom active magnetic bearing (two radial axes and one axial levitator). A translational physics-based model explicitly captures bias currents and nominal air gaps, followed by equilibrium linearization and zero-order-hold discretization at 2 kHz. The estimator\u0026ndash;controller (\u003cem\u003elinear\u0026ndash;quadratic regulator\u003c/em\u003e, LQR, plus Kalman filter) is implemented in fixed-point logic with sub-200 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\mu)\\)\u003c/span\u003e\u003c/span\u003es end-to-end latency. Experiments on a dedicated testbed compare the proposed LQG against a tuned proportional\u0026ndash;integral\u0026ndash;derivative (PID) controller and an observer-based pole-placement baseline under identical sensing and actuation. In the radial loop, LQG reduces startup settling time by approximately 44% and integrated absolute error by approximately 36.5%, with overshoot below 0.5% and actuator limits respected; recovery to a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\pm 5%)\\)\u003c/span\u003e\u003c/span\u003e band under external disturbances is about 13% faster. A nonlinear-plant robustness map indicates stable, non-overshooting behavior under \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\pm 20%)\\)\u003c/span\u003e\u003c/span\u003e variations of magnetic and electrical parameters. Particle measurements during continuous operation remain below the International Organization for Standardization (ISO) Class 5 thresholds, supporting the suitability of the proposed joint for cleanroom robotics.\u003c/p\u003e","manuscriptTitle":"FPGA-Based LQG Control of a Low-Speed Active Magnetic Bearing Joint: Implementation and Validation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-12 08:52:06","doi":"10.21203/rs.3.rs-7926101/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-04T13:30:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-04T03:20:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-30T15:27:50+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-18T01:59:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"260156117864045143026586948783948064564","date":"2025-11-07T20:49:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"39206472378034837721326283400963786930","date":"2025-11-02T22:38:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"126377381250179616311694991587844517489","date":"2025-11-02T20:47:14+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-02T20:08:37+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-23T14:36:19+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-23T14:35:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Control, Automation and Electrical Systems","date":"2025-10-22T18:24:41+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-control-automation-and-electrical-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcae","sideBox":"Learn more about [Journal of Control, Automation and Electrical Systems](https://link.springer.com/journal/40313)","snPcode":"40313","submissionUrl":"https://submission.springernature.com/new-submission/40313/3","title":"Journal of Control, Automation and Electrical Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"edb08a5b-e28b-4e21-88e9-914b48fdc648","owner":[],"postedDate":"November 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-24T10:04:28+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-12 08:52:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7926101","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7926101","identity":"rs-7926101","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}