Active disturbance rejection repetitive control for fractional-order time-delay systems with unknown disturbance†

Active disturbance rejection repetitive control for fractional-order time-delay systems with unknown disturbance† | 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 Article Active disturbance rejection repetitive control for fractional-order time-delay systems with unknown disturbance † Huihua Jian, Haizhen Wang, Jianhua Huang, Yong-Hong Lan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6697729/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, the problem of fractional-order active disturbance rejection repetitive control (FADRRC) for a class of fractional-order time-delay systems is investigated. First, a fractional-order extended state observer (FESO) is used to estimate the internal dynamics and the unknown external disturbances. Next, the linear bandwidth-parameterization method is applied to tune the gains of both the the observer and controlle. To reduce the impact of time-delay, a low-pass filter is added to the FESO. Then, the design problem of the FADRRC law is converted to the stability problem of the fractional-order system. Sufficient stability conditions are obtained by using the small gain theorem. Finally, numerical simulation results demonstrate the effectiveness of the proposed control method. Physical sciences/Engineering Physical sciences/Mathematics and computing Active disturbance rejection Repetitive control Extended state observer Fractional-order time-delay system Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6697729","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":467139280,"identity":"f4ae632f-a4a1-426f-b795-198dcca98104","order_by":0,"name":"Huihua Jian","email":"","orcid":"","institution":"Xinyu University","correspondingAuthor":false,"prefix":"","firstName":"Huihua","middleName":"","lastName":"Jian","suffix":""},{"id":467139281,"identity":"4610da69-1059-4dba-b376-021c835c1254","order_by":1,"name":"Haizhen Wang","email":"","orcid":"","institution":"Xinyu University","correspondingAuthor":false,"prefix":"","firstName":"Haizhen","middleName":"","lastName":"Wang","suffix":""},{"id":467139282,"identity":"92c79d1f-556a-4e5f-a34c-05fe71358f46","order_by":2,"name":"Jianhua Huang","email":"","orcid":"","institution":"Xinyu University","correspondingAuthor":false,"prefix":"","firstName":"Jianhua","middleName":"","lastName":"Huang","suffix":""},{"id":467139283,"identity":"e27e3e10-53ac-4d34-8f80-d567d6db65e6","order_by":3,"name":"Yong-Hong Lan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyklEQVRIiWNgGAWjYBACfvbG9g8JBv/k5NkbiNQi2XO4jeFDwQFjw54DRGoxuOHexjjjw4FEhhsJRGthbHvMY3AngXHm4403GGpsogk77HZjuzGPwbM8dum0YguGY2m5DYS08N052CDNY8BczDg7x0yCseEwYS0MNxLBWhIbbp4hUovAjcQ2yRkGhxMbbvAQqUWy52CzwQeDNGAgA/2SQIxf+NnbHz5I+GMDjMrDG298qLEhwi9IwEAigRTlEC2k6hgFo2AUjIKRAQADZEZWs79eZwAAAABJRU5ErkJggg==","orcid":"","institution":"Xiangtan University","correspondingAuthor":true,"prefix":"","firstName":"Yong-Hong","middleName":"","lastName":"Lan","suffix":""}],"badges":[],"createdAt":"2025-05-19 10:08:08","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6697729/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6697729/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85714919,"identity":"fbc40eed-aa8c-4943-9493-1156bbfab7f0","added_by":"auto","created_at":"2025-07-01 03:46:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":544066,"visible":true,"origin":"","legend":"","description":"","filename":"FADRRC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6697729/v1_covered_72925f90-797d-40d5-8bbf-21641d23c10e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eActive disturbance rejection repetitive control for fractional-order time-delay systems with unknown disturbance\u003csup\u003e†\u003c/sup\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Active disturbance rejection, Repetitive control, Extended state observer, Fractional-order time-delay system","lastPublishedDoi":"10.21203/rs.3.rs-6697729/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6697729/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, the problem of fractional-order active disturbance rejection repetitive control (FADRRC) for a class of fractional-order time-delay systems is investigated. First, a fractional-order extended state observer (FESO) is used to estimate the internal dynamics and the unknown external disturbances. Next, the linear bandwidth-parameterization method is applied to tune the gains of both the the observer and controlle. To reduce the impact of time-delay, a low-pass filter is added to the FESO. Then, the design problem of the FADRRC law is converted to the stability problem of the fractional-order system. Sufficient stability conditions are obtained by using the small gain theorem. 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