Design of a Finite-Time Sliding Mode Controller Algorithm for a Two-Axis Robotic Arm

Design of a Finite-Time Sliding Mode Controller Algorithm for a Two-Axis Robotic Arm | 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 Design of a Finite-Time Sliding Mode Controller Algorithm for a Two-Axis Robotic Arm Lei Zhang, Jianli Wang, Xiaodong Xie, Jintong Lu, Yuxi Zhang, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8278310/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Mar, 2026 Read the published version in Journal of Control, Automation and Electrical Systems → Version 1 posted 11 You are reading this latest preprint version Abstract This paper presents the design of a finite-time sliding mode control (FT-SMC) algorithm for a two-axis robotic arm, grounded in the principles of sliding mode control (SMC). SMC is a robust nonlinear control strategy known for its rapid response and has been extensively applied in robotic arm control. However, traditional SMC suffers from a convergence speed that is highly dependent on the initial system state; specifically, larger deviations from the sliding surface result in prolonged convergence times. To overcome this limitation, the FT-SMC approach introduces a novel sliding surface and a corresponding control law, enabling the system to reach the sliding surface within a predefined time frame and maintain motion along it thereafter. This study outlines a comprehensive methodology for designing a robotic arm controller based on FT-SMC. The dynamic model of the robotic arm is first derived using the Newton-Euler method, leading to the formulation of state-space equations that account for system uncertainties and external disturbances. A second-order differentiator based on SMC is then developed, with its parameters optimized for performance. A non-singular terminal sliding surface and an associated control law are subsequently constructed, and the Lyapunov stability theory is employed to ensure finite-time convergence to the sliding surface. Finally, the proposed FT-SMC algorithm is validated through comparative Simulink/SolidWorks simulation experiments against Second-Order Sliding Mode Control (SOSMC) and Proportional-Derivative (PD) control algorithms. The results demonstrate the algorithm’s superior effectiveness, achieving enhanced tracking accuracy and stability. Two-Axis Robotic Arm Sliding Mode Control Robustness Stability Finite-Time Convergence Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Mar, 2026 Read the published version in Journal of Control, Automation and Electrical Systems → Version 1 posted Editorial decision: Revision requested 29 Dec, 2025 Reviews received at journal 29 Dec, 2025 Reviews received at journal 22 Dec, 2025 Reviewers agreed at journal 22 Dec, 2025 Reviewers agreed at journal 21 Dec, 2025 Reviewers agreed at journal 21 Dec, 2025 Reviewers agreed at journal 10 Dec, 2025 Reviewers invited by journal 08 Dec, 2025 Editor assigned by journal 05 Dec, 2025 Submission checks completed at journal 05 Dec, 2025 First submitted to journal 04 Dec, 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. 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-8278310","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":557216502,"identity":"5b67f34d-710c-4370-bfb4-9f8e5587cf22","order_by":0,"name":"Lei Zhang","email":"","orcid":"","institution":"Henan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"Zhang","suffix":""},{"id":557216503,"identity":"c52f3dfa-c959-4f31-9e55-259a97edaf45","order_by":1,"name":"Jianli Wang","email":"","orcid":"","institution":"Henan University of 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Arm","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":"Two-Axis Robotic Arm, Sliding Mode Control, Robustness, Stability, Finite-Time Convergence","lastPublishedDoi":"10.21203/rs.3.rs-8278310/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8278310/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper presents the design of a finite-time sliding mode control (FT-SMC) algorithm for a two-axis robotic arm, grounded in the principles of sliding mode control (SMC). SMC is a robust nonlinear control strategy known for its rapid response and has been extensively applied in robotic arm control. However, traditional SMC suffers from a convergence speed that is highly dependent on the initial system state; specifically, larger deviations from the sliding surface result in prolonged convergence times. To overcome this limitation, the FT-SMC approach introduces a novel sliding surface and a corresponding control law, enabling the system to reach the sliding surface within a predefined time frame and maintain motion along it thereafter. This study outlines a comprehensive methodology for designing a robotic arm controller based on FT-SMC. The dynamic model of the robotic arm is first derived using the Newton-Euler method, leading to the formulation of state-space equations that account for system uncertainties and external disturbances. A second-order differentiator based on SMC is then developed, with its parameters optimized for performance. A non-singular terminal sliding surface and an associated control law are subsequently constructed, and the Lyapunov stability theory is employed to ensure finite-time convergence to the sliding surface. Finally, the proposed FT-SMC algorithm is validated through comparative Simulink/SolidWorks simulation experiments against Second-Order Sliding Mode Control (SOSMC) and Proportional-Derivative (PD) control algorithms. The results demonstrate the algorithm’s superior effectiveness, achieving enhanced tracking accuracy and stability.","manuscriptTitle":"Design of a Finite-Time Sliding Mode Controller Algorithm for a Two-Axis Robotic Arm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-10 23:25:13","doi":"10.21203/rs.3.rs-8278310/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-29T11:54:44+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-29T07:36:25+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-23T02:26:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"218610738812231878636326120099082023900","date":"2025-12-22T06:59:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"69111558706776417871400422594217673313","date":"2025-12-21T23:08:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"46093138385334746332323162315604904863","date":"2025-12-21T22:25:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"88811387510992019364834548976500676654","date":"2025-12-10T19:37:30+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-08T12:03:09+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-05T11:39:29+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-05T11:34:58+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Control, Automation and Electrical Systems","date":"2025-12-04T10:37:33+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":"487cb627-53a0-455d-b1b2-24bd042be599","owner":[],"postedDate":"December 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-09T16:10:27+00:00","versionOfRecord":{"articleIdentity":"rs-8278310","link":"https://doi.org/10.1007/s40313-026-01254-0","journal":{"identity":"journal-of-control-automation-and-electrical-systems","isVorOnly":false,"title":"Journal of Control, Automation and Electrical Systems"},"publishedOn":"2026-03-04 15:57:36","publishedOnDateReadable":"March 4th, 2026"},"versionCreatedAt":"2025-12-10 23:25:13","video":"","vorDoi":"10.1007/s40313-026-01254-0","vorDoiUrl":"https://doi.org/10.1007/s40313-026-01254-0","workflowStages":[]},"version":"v1","identity":"rs-8278310","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8278310","identity":"rs-8278310","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}