Nonlinear optimal control for VSI-fed six-phase PMSMs in the traction of electric vehicles

Nonlinear optimal control for VSI-fed six-phase PMSMs in the traction of electric vehicles | 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 optimal control for VSI-fed six-phase PMSMs in the traction of electric vehicles Gerasimos Rigatos, Masoud Abbaszadeh, Mohamed Assaad Hamida, Pierluigi Siano, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4228139/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The need for high power in electric vehicles has motivated the use of multi-phase electric motors in the associated traction systems. In this article, a nonlinear optimal control approach is developed for voltage-source inverter-fed six-phase Permanent Magnet Synchronous Motors which can be used in electric vehicles' traction. The dynamic model of the VSI-fed six-phase PMSM undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The differential flatness properties of the state-space model of the six-phase PMSM are also proven, thus allowing to solve the setpoints definition problem in the motor's functioning. To estimate non-measurable state variables and to implement sensorless control for the dynamic model of the six-phase PMSMs, the H-infinity Kalman Filter is used as a robust state estimator. It is shown that under the proposed control scheme fast and accurate tracking of reference setpoints is achieved with moderate variations of the control inputs. six-phase permanent magnet synchronous metors voltage source inverters nonlinear Hinfinity control Taylor series expansion Jacobian matrices Riccati equation differential flatness properties global stability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-4228139","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":288262477,"identity":"148fd9de-ef2e-42b7-a7de-22ac47620713","order_by":0,"name":"Gerasimos Rigatos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYFACxgYgYcNDqpaENJK0gEDCYRIUy0cfbn7x88d5GX725gMMH/fUEtZieC6xzbIn4TaPZM+xBMYZz44ToaWHsc2AB6jF4EaOATPPgWPEaTH8k3COx/7++w/EaZHnYWx+zJNwgMdAgocBqKWGsBYDHsY2Zpm0ZB6JM2kGB2ccOECELT3sjz++sbGz528//PDBhwN1RNhygIFNAsYBWkFEBMk3MDB/QOITYcsoGAWjYBSMOAAASI47DjInUMsAAAAASUVORK5CYII=","orcid":"","institution":"Industrial Systems Institute","correspondingAuthor":true,"prefix":"","firstName":"Gerasimos","middleName":"","lastName":"Rigatos","suffix":""},{"id":288262478,"identity":"3d1a8585-b4d6-480c-b6be-61688413ccd9","order_by":1,"name":"Masoud Abbaszadeh","email":"","orcid":"","institution":"Rensselaer Polytechnic Institute","correspondingAuthor":false,"prefix":"","firstName":"Masoud","middleName":"","lastName":"Abbaszadeh","suffix":""},{"id":288262479,"identity":"9b1f9ab8-d2cd-4e03-9fec-bbc54b71f98d","order_by":2,"name":"Mohamed Assaad Hamida","email":"","orcid":"","institution":"École Centrale de Nantes","correspondingAuthor":false,"prefix":"","firstName":"Mohamed","middleName":"Assaad","lastName":"Hamida","suffix":""},{"id":288262480,"identity":"5110e057-d256-45f8-82a7-d1878903cd67","order_by":3,"name":"Pierluigi Siano","email":"","orcid":"","institution":"University of Salerno","correspondingAuthor":false,"prefix":"","firstName":"Pierluigi","middleName":"","lastName":"Siano","suffix":""},{"id":288262481,"identity":"600ebb59-3032-4653-98fd-d4973598996d","order_by":4,"name":"Tir Zoheir","email":"","orcid":"","institution":"University of El Oued","correspondingAuthor":false,"prefix":"","firstName":"Tir","middleName":"","lastName":"Zoheir","suffix":""}],"badges":[],"createdAt":"2024-04-06 15:44:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4228139/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4228139/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54274367,"identity":"0111b98b-858a-4d3c-a16b-cf6475541e11","added_by":"auto","created_at":"2024-04-08 07:30:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2936934,"visible":true,"origin":"","legend":"","description":"","filename":"NoptVSI6phasePMSMApr24LaTeX.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4228139/v1_covered_7a1b44b8-7177-4210-a1b1-e85e8d7a1365.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear optimal control for VSI-fed six-phase PMSMs in the traction of electric vehicles","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"six-phase permanent magnet synchronous metors, voltage source inverters, nonlinear Hinfinity control, Taylor series expansion, Jacobian matrices, Riccati equation, differential flatness properties, global stability","lastPublishedDoi":"10.21203/rs.3.rs-4228139/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4228139/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The need for high power in electric vehicles has motivated the use of multi-phase electric motors in the associated traction systems. In this article, a nonlinear optimal control approach is developed for voltage-source inverter-fed six-phase Permanent Magnet Synchronous Motors which can be used in electric vehicles' traction. The dynamic model of the VSI-fed six-phase PMSM undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The differential flatness properties of the state-space model of the six-phase PMSM are also proven, thus allowing to solve the setpoints definition problem in the motor's functioning. To estimate non-measurable state variables and to implement sensorless control for the dynamic model of the six-phase PMSMs, the H-infinity Kalman Filter is used as a robust state estimator. 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