Optimizing interval type-2 fuzzy logic PID controller with an improved constraint differential evolution algorithm

Optimizing interval type-2 fuzzy logic PID controller with an improved constraint differential evolution algorithm | 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 Optimizing interval type-2 fuzzy logic PID controller with an improved constraint differential evolution algorithm Xin Chen, Haozhen Dong, Dong Li, Hanyu Li, Chen Shen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8016775/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract Compared to electric actuators, hydraulic actuators can deliver greater driving forces within limited spaces due to their high-power density characteristics, making them widely used in high-performance drive applications such as humanoid robots. However, these systems exhibit significant nonlinear dynamic properties, posing challenges for high-precision control of their output forces. To address the control challenges of hydraulic actuators for humanoid robots, this paper first establishes a system model integrating the hydraulic power source with nonlinear hydraulic cylinders. Subsequently, an improved constrained differential evolution with better and nearest option (ICBNDE) algorithm is proposed, featuring an efficient search mechanism and an approximate solution selection strategy. Then, an interval type-2 fuzzy logic PID controller (IT2FL-PID-C) optimized by ICBNDE is constructed for the closed-loop control of the hydraulic actuator system. To validate the proposed algorithm's performance, the convergence and feasibility analyses of ICBNDE are conducted on the CEC2006 constrained benchmark test. Subsequently, the designed controller is compared with a traditional PID controller, and ICBNDE is contrasted with several classical constrained optimization algorithms under identical architectures. Experimental results demonstrate that the ICBNDE based IT2FL-PID-C significantly outperforms traditional PID methods in both control accuracy and system stability. Furthermore, ICBNDE exhibits superior performance compared to other algorithms in controller parameter optimization, validating its effectiveness and superiority in controlling complex nonlinear hydraulic systems. Physical sciences/Engineering Physical sciences/Mathematics and computing interval type-2 fuzzy logic PID controller constraint differential evolution better and nearest option hydraulic actuator Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 25 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 21 Nov, 2025 Reviews received at journal 20 Nov, 2025 Reviews received at journal 12 Nov, 2025 Reviewers agreed at journal 12 Nov, 2025 Reviewers agreed at journal 11 Nov, 2025 Reviewers agreed at journal 11 Nov, 2025 Reviewers invited by journal 11 Nov, 2025 Editor assigned by journal 11 Nov, 2025 Editor invited by journal 11 Nov, 2025 Submission checks completed at journal 04 Nov, 2025 First submitted to journal 04 Nov, 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. 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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-8016775","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":548098879,"identity":"42611526-bd12-4bc6-83ed-ca33949f6405","order_by":0,"name":"Xin Chen","email":"","orcid":"","institution":"Wuhan Business University","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Chen","suffix":""},{"id":548098880,"identity":"154f8d79-f29c-41dd-aab4-6687cc3f3479","order_by":1,"name":"Haozhen Dong","email":"","orcid":"","institution":"CASIC Research Institute of Intelligent Decision 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algorithm","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"interval type-2 fuzzy logic PID controller, constraint differential evolution, better and nearest option, hydraulic actuator","lastPublishedDoi":"10.21203/rs.3.rs-8016775/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8016775/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCompared to electric actuators, hydraulic actuators can deliver greater driving forces within limited spaces due to their high-power density characteristics, making them widely used in high-performance drive applications such as humanoid robots. However, these systems exhibit significant nonlinear dynamic properties, posing challenges for high-precision control of their output forces. To address the control challenges of hydraulic actuators for humanoid robots, this paper first establishes a system model integrating the hydraulic power source with nonlinear hydraulic cylinders. Subsequently, an improved constrained differential evolution with better and nearest option (ICBNDE) algorithm is proposed, featuring an efficient search mechanism and an approximate solution selection strategy. Then, an interval type-2 fuzzy logic PID controller (IT2FL-PID-C) optimized by ICBNDE is constructed for the closed-loop control of the hydraulic actuator system. To validate the proposed algorithm's performance, the convergence and feasibility analyses of ICBNDE are conducted on the CEC2006 constrained benchmark test. Subsequently, the designed controller is compared with a traditional PID controller, and ICBNDE is contrasted with several classical constrained optimization algorithms under identical architectures. Experimental results demonstrate that the ICBNDE based IT2FL-PID-C significantly outperforms traditional PID methods in both control accuracy and system stability. Furthermore, ICBNDE exhibits superior performance compared to other algorithms in controller parameter optimization, validating its effectiveness and superiority in controlling complex nonlinear hydraulic systems.\u003c/p\u003e","manuscriptTitle":"Optimizing interval type-2 fuzzy logic PID controller with an improved constraint differential evolution algorithm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-22 01:31:38","doi":"10.21203/rs.3.rs-8016775/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-21T05:45:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-20T06:23:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-12T21:00:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"305716815877503676800053551108599557144","date":"2025-11-12T12:39:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"173212847967256267375485543892669314822","date":"2025-11-12T03:59:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"46093138385334746332323162315604904863","date":"2025-11-12T03:15:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-12T03:10:12+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-12T00:57:52+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-11-11T16:59:09+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-05T01:52:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-11-05T01:48:46+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"631362b6-c629-47dc-b056-206156f755fb","owner":[],"postedDate":"November 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":58317019,"name":"Physical sciences/Engineering"},{"id":58317020,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-03-02T16:05:56+00:00","versionOfRecord":{"articleIdentity":"rs-8016775","link":"https://doi.org/10.1038/s41598-026-41203-0","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-02-25 15:59:26","publishedOnDateReadable":"February 25th, 2026"},"versionCreatedAt":"2025-11-22 01:31:38","video":"","vorDoi":"10.1038/s41598-026-41203-0","vorDoiUrl":"https://doi.org/10.1038/s41598-026-41203-0","workflowStages":[]},"version":"v1","identity":"rs-8016775","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8016775","identity":"rs-8016775","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}