High-Order Hysteresis Derivative Bouc-Wen Model for Piezoelectric Actuators at High Frequencies and Its Control Compensation

High-Order Hysteresis Derivative Bouc-Wen Model for Piezoelectric Actuators at High Frequencies and Its Control Compensation | 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 High-Order Hysteresis Derivative Bouc-Wen Model for Piezoelectric Actuators at High Frequencies and Its Control Compensation Weisheng Chen, Qifei Xue This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8385717/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract The classical BOUC-WEN model(CBW) is applicable only to symmetric and rate-independent hysteresis phenomena, exhibiting comparatively low modelling accuracy under high-frequency conditions. This limitation restricts its application within piezoelectric actuator systems. To address this issue, this paper proposes a novel higher-order hysteretic derivative Bouc-Wen model (HODBW) for describing the asymmetry and velocity-dependent nonlinearity of piezoelectric actuators under high-frequency conditions. This model incorporates higher-order hysteresis derivatives to construct a dynamic representation capable of precisely describing complex hysteresis behaviour at high frequencies. Concurrently, to reduce model complexity, Principal Component Analysis (PCA) is employed to determine the minimal number of polynomial coefficients. Based on this, a polynomial fitting method is applied to accurately determine the specific form of the input voltage , thereby enhancing the model’s precision. Additionally, the Particle Swarm Optimisation (PSO) algorithm was employed to identify the unknown parameters within the HODBW model. For the proposed HODBW model, a customised feedforward-feedback composite control strategy has been designed. The feedfor-ward section employs an inverse model to establish a hysteresis observer, whilst the feedback section utilises an HOSMC strategy to achieve effective compensation for model errors. The results demonstrate that the HODBW model exhibits superior modelling accuracy compared to both the CBW model and conventional 1 modified models, whilst the proposed control strategy also delivers outstanding performance. This thereby validates its superiority and applicability under high-frequency conditions. Bouc-Wen (BW) model piezoelectric actuator hysteresis nonlinearity rate dependence high-frequency excitation Sliding mode control modeling and control Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 04 Feb, 2026 Reviews received at journal 03 Feb, 2026 Reviews received at journal 14 Jan, 2026 Reviewers agreed at journal 14 Jan, 2026 Reviewers agreed at journal 13 Jan, 2026 Reviewers invited by journal 13 Jan, 2026 Editor assigned by journal 26 Dec, 2025 Submission checks completed at journal 18 Dec, 2025 First submitted to journal 17 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. 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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-8385717","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":574743714,"identity":"ea4d184b-5901-4777-bb7c-7b7a33d235ae","order_by":0,"name":"Weisheng Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYFACHgZmICnHxt58gDQtxnw8xxJI05I4TyJHgTgNBufPHvxcUHEnvY0hh4HhR8U2IrTcyEuWnnHmWW4bw9kDjD1nbhPWYnaDx4yZt+1wbhtjXwIzYxsxWs6fAWr5dzidjZnHgEgtB3KAWhoOJ7CxEavF/kaOsTTPscOGbTxsCQeJ8otk/xnDzzw1h+Xl5z8++OBHBRFaUMABEtWPglEwCkbBKMAFAFYPOQooPFQrAAAAAElFTkSuQmCC","orcid":"","institution":"Xidian University","correspondingAuthor":true,"prefix":"","firstName":"Weisheng","middleName":"","lastName":"Chen","suffix":""},{"id":574743715,"identity":"fab0bfe2-a23f-4550-bd4d-ff16d18e4581","order_by":1,"name":"Qifei Xue","email":"","orcid":"","institution":"Xidian University","correspondingAuthor":false,"prefix":"","firstName":"Qifei","middleName":"","lastName":"Xue","suffix":""}],"badges":[],"createdAt":"2025-12-17 12:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8385717/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8385717/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100434095,"identity":"1d13bef9-121f-461c-9367-d6a728174719","added_by":"auto","created_at":"2026-01-16 15:18:03","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1655672,"visible":true,"origin":"","legend":"","description":"","filename":"HighOrderHysteresisDerivativeBoucWen.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8385717/v1/53c97dec1f82980903560770.pdf"},{"id":100434094,"identity":"e13faf8b-d1eb-4261-a581-a6541716f61b","added_by":"auto","created_at":"2026-01-16 15:18:03","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4266,"visible":true,"origin":"","legend":"","description":"","filename":"9f86aa309d244d54b911df4b48858013.json","url":"https://assets-eu.researchsquare.com/files/rs-8385717/v1/8dd50ddce6e0f27fefeb71ac.json"},{"id":100546785,"identity":"48aef3db-9d0a-4e69-9f16-11253da3eabf","added_by":"auto","created_at":"2026-01-19 08:12:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1138718,"visible":true,"origin":"","legend":"","description":"","filename":"HighOrderHysteresisDerivativeBoucWen.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8385717/v1_covered_14102726-deb6-4373-8a5a-b403eef844fb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"High-Order Hysteresis Derivative Bouc-Wen Model for Piezoelectric Actuators at High Frequencies and Its Control Compensation","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":"microsystem-technologies","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mite","sideBox":"Learn more about [Microsystem Technologies](http://link.springer.com/journal/542)","snPcode":"542","submissionUrl":"https://submission.nature.com/new-submission/542/3","title":"Microsystem Technologies","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Bouc-Wen (BW) model, piezoelectric actuator, hysteresis nonlinearity, rate dependence, high-frequency excitation, Sliding mode control, modeling and control","lastPublishedDoi":"10.21203/rs.3.rs-8385717/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8385717/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The classical BOUC-WEN model(CBW) is applicable only to symmetric and rate-independent hysteresis phenomena, exhibiting comparatively low modelling accuracy under high-frequency conditions. 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