Nonlinear effects of actuator rate and acceleration limits on closed-loop systems: a describing function approach

Nonlinear effects of actuator rate and acceleration limits on closed-loop systems: a describing function approach | 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 Nonlinear effects of actuator rate and acceleration limits on closed-loop systems: a describing function approach Luca Marino, Jurij Sodja This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7632329/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Apr, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted 4 You are reading this latest preprint version Abstract Actuator nonlinearities can significantly affect control systems, leading to performance degradation and even loss of stability. Physical constraints such as rate and acceleration limits are particularly detrimental in applications where rapid actuation is required, yet their combined effects remain largely unexplored. This paper investigates the nonlinear dynamic behaviour induced by rate and acceleration limits in closed-loop systems, focusing on their steady-state response to sinusoidal excitation. The saturation regimes induced by these actuator limits are fully characterized, and their analytical boundaries are represented in a two-dimensional parameter space defined by normalized rate and acceleration limits. Sinusoidal describing functions are derived for each regime, capturing the actuator dynamics in the frequency domain. These are used to analyse the effects of actuator nonlinearities on closed-loop performance, including the onset of nonlinear behaviour, phase lag and gain reduction. The conditions for the presence of jump resonance are analytically derived, along with the lowest frequency where multiple solutions appear, leading to potential abrupt changes in system response. The findings highlight how these nonlinear phenomena can severely degrade the performance and stability of closed loops, underlining the importance of accounting for actuator rate and acceleration limits in the analysis and design of feedback control systems. Actuator nonlinearities Feedback control systems Saturation regimes Jump resonance Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Apr, 2026 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Revision requested 01 Oct, 2025 Editor assigned by journal 22 Sep, 2025 Submission checks completed at journal 17 Sep, 2025 First submitted to journal 16 Sep, 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-7632329","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":523547465,"identity":"30b51878-7515-456b-bdd1-7c356c000d87","order_by":0,"name":"Luca Marino","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3UlEQVRIiWNgGAWjYBACPjBpAMTMzAcYGNgYZNgbgJwHeLSwwbWwsyU2ALk8PMeAnASCWkCAn8eQWC3ciZ8rCu7IMTDzfH/MU2bDwyPfwPYAvxbezZJnDJ4ZMzDzbmzmOZfGw8PGwG5AQMsGyQaDw4n7DwO18LYd5rFnY2CTIGTLT5CWBmaeh0At/0G2ENSyTRKqhRGo5QARWph5t1kCtQD9wmY4c865ZKCWxDa8WvjZezffbPhzWI6B//CDD2/K7OR4mA8fk/iARwsDM6YQYwM+DaNgFIyCUTAKiAAALgY9ANzWNBkAAAAASUVORK5CYII=","orcid":"","institution":"Delft University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Luca","middleName":"","lastName":"Marino","suffix":""},{"id":523547466,"identity":"1a8b40bb-f8e9-42bc-a620-bd6162b8a597","order_by":1,"name":"Jurij Sodja","email":"","orcid":"","institution":"Delft University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Jurij","middleName":"","lastName":"Sodja","suffix":""}],"badges":[],"createdAt":"2025-09-16 15:53:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7632329/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7632329/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-026-12449-0","type":"published","date":"2026-04-20T15:56:53+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":107927658,"identity":"c0d12b03-272f-422e-b996-d4e862206c60","added_by":"auto","created_at":"2026-04-27 16:00:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3778490,"visible":true,"origin":"","legend":"","description":"","filename":"NonlineardynActuatorlimits.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7632329/v1_covered_acd505c0-abfe-4768-97d9-035e83b107c0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear effects of actuator rate and acceleration limits on closed-loop systems: a describing function approach","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":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Actuator nonlinearities, Feedback control systems, Saturation regimes, Jump resonance","lastPublishedDoi":"10.21203/rs.3.rs-7632329/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7632329/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Actuator nonlinearities can significantly affect control systems, leading to performance degradation and even loss of stability. 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