Tempered–Fractional GMV Self–Tuning Regulation for PV–Boost Converter

Tempered–Fractional GMV Self–Tuning Regulation for PV–Boost Converter | 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 Tempered–Fractional GMV Self–Tuning Regulation for PV–Boost Converter Tawfik Guesmi, Mourad Elloumi, Khalid Alqunun, Mansoor Alturki, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9527286/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract As PV penetration increases, DC - DC boost converters are expected to achieve high accuracy DC-link voltage regulation against random changes in solar irradiance, load, and system parameters. Although fractional models and controllers offer extra flexibility to describe memory effects, conventional fractional operators may over-emphasize long-term memory and reduce adaptivity under nonstationarities. This paper introduces a tempered--fractional generalized minimum-variance self-tuning regulator (TF--GMV--STR) for PV--boost converters, in which tempering exponentially attenuates the long-memory kernel to produce a semi-long memory, resulting in better numerical stability. A discrete-time tempered fractional predictor is given in an ARMAX-like form, based on a truncated tempered Gr\"unwald--Letnikov realization, allowing for online prediction and innovation calculations. An explicit TF--GMV control law is formulated based on a tempered Diophantine equation, and incorporated into a self-tuning loop with recursive (forgetting) least-squares identification on the tempered basis. Digital realization issues are presented, such as fractional filters and low-order realizations for embedded implementation. Simulations versus the classical (integer order) GMV--STR show that the proposed TF--GMV--STR improves the speed and accuracy of voltage regulation with reduced oscillations and limited action of the duty cycle, while maintaining online accuracy for time-varying parameters. Mathematics Subject Classification: 93C40, 93D09, 93D15. Physical sciences/Engineering Physical sciences/Mathematics and computing Photovoltaic systems boost converter tempered fractional calculus generalized minimum variance control (GMV) self-tuning regulator (STR) ARMAX prediction recursive least squares estimator digital fractional approximation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 08 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviewers invited by journal 05 May, 2026 Editor assigned by journal 05 May, 2026 Editor invited by journal 05 May, 2026 Submission checks completed at journal 30 Apr, 2026 First submitted to journal 30 Apr, 2026 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-9527286","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":638325390,"identity":"03b49138-ce8a-49df-a3d1-f98291107f6b","order_by":0,"name":"Tawfik Guesmi","email":"","orcid":"","institution":"University of Ha'il","correspondingAuthor":false,"prefix":"","firstName":"Tawfik","middleName":"","lastName":"Guesmi","suffix":""},{"id":638325391,"identity":"7c683e41-6930-4e34-971d-dfe00a9ac1c0","order_by":1,"name":"Mourad Elloumi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYNACNgYGPnYQw8CGgYGZWC1sYJUGaRAtB4jXwnAYIoBPi257j9mHH2UMcmzMzMekbhSclzNnZ3/A/HEHbi1mZ84Yz+w5x2DMxsyWJp1jcNvYspnHgOHgGTxabuQYM/C2MSS2MfOYgbQkbjjMw8BwsA2/Fsa/bQz1UC3n6jccZn9AUAsz0JYENoiWAwkGhxkM8Gs5c6yYWeachGEbM1uydY5BsiHQYQYHzuLTcrx5M+ObMht5fvbmg7dz/tjJG5w//vBBJR4tUCCByj1AUMMoGAWjYBSMArwAABTHRpx1pFdUAAAAAElFTkSuQmCC","orcid":"","institution":"University of Gafsa","correspondingAuthor":true,"prefix":"","firstName":"Mourad","middleName":"","lastName":"Elloumi","suffix":""},{"id":638325392,"identity":"e3ef5f37-ad96-4056-95fc-73a529df6049","order_by":2,"name":"Khalid Alqunun","email":"","orcid":"","institution":"University of Ha'il","correspondingAuthor":false,"prefix":"","firstName":"Khalid","middleName":"","lastName":"Alqunun","suffix":""},{"id":638325393,"identity":"4f98852c-e3c7-421b-9704-746e57ea150a","order_by":3,"name":"Mansoor Alturki","email":"","orcid":"","institution":"University of Ha'il","correspondingAuthor":false,"prefix":"","firstName":"Mansoor","middleName":"","lastName":"Alturki","suffix":""},{"id":638325394,"identity":"1d6a374f-9158-47fd-9282-27c71a64bd0c","order_by":4,"name":"Abdullah Albaker","email":"","orcid":"","institution":"University of Ha'il","correspondingAuthor":false,"prefix":"","firstName":"Abdullah","middleName":"","lastName":"Albaker","suffix":""},{"id":638325395,"identity":"150c776f-ef46-4b87-961a-735545993f09","order_by":5,"name":"Badr M. 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Although fractional models and controllers offer extra flexibility to describe memory effects, conventional fractional operators may over-emphasize long-term memory and reduce adaptivity under nonstationarities. This paper introduces a tempered--fractional generalized minimum-variance self-tuning regulator (TF--GMV--STR) for PV--boost converters, in which tempering exponentially attenuates the long-memory kernel to produce a semi-long memory, resulting in better numerical stability. A discrete-time tempered fractional predictor is given in an ARMAX-like form, based on a truncated tempered Gr\\\"unwald--Letnikov realization, allowing for online prediction and innovation calculations. An explicit TF--GMV control law is formulated based on a tempered Diophantine equation, and incorporated into a self-tuning loop with recursive (forgetting) least-squares identification on the tempered basis. 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