Application of NMPC in the processing of Wolter-I grazing incident mirrors

Application of NMPC in the processing of Wolter-I grazing incident mirrors | 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 Application of NMPC in the processing of Wolter-I grazing incident mirrors Song Ding, Shuhai Yao, Liwei Sun, Jing Li, Hongyan Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9112718/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Wolter-I structures based on X-ray grazing incidence optics are often used in extreme ultraviolet (EUV) collection optical systems, especially in the application of discharge plasma (DPP) sources. With the development of computer technology, the computerized surface forming (CCOS) method can significantly improve the surface accuracy and meet the optical requirements of high precision when processing Wolter-I grazing incident mirrors. In this paper, the nonlinear model predictive control (NMPC) system is innovatively introduced into the traditional CCOS method instead of the PID control system, and the application of NMPC in the rough grinding and fine grinding stages of Wolter-I grazing incident mirrors is studied, and it is found that the processing process and processing efficiency are effectively optimized through the system. Firstly, a detailed geometric model of the mirror was established for the special geometry of the inner surface of the cylindrical surface of the Wolter-I grazing incident mirror. Secondly, in view of the complex and nonlinear characteristics of the Wolter-I grazing incident mirror, a nonlinear model of the machining process is established, and the influence of spindle feed rate, removal pressure, abrasive particle size and other factors on the machining accuracy is considered, and the simulation results show that when the spindle feed rate is 25mm/s, the removal pressure is 9 N, and the abrasive particle size is 10, the removal efficiency is the highest and the removal effect is the best. The experimental results show that the CCOS method combined with NMPC significantly improves the surface accuracy and effectively improves the processing efficiency and reduces the production cost when processing the Wolter-I grazing incident mirror. Physical sciences/Engineering Physical sciences/Optics and photonics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 06 May, 2026 Reviews received at journal 04 May, 2026 Reviews received at journal 03 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviewers agreed at journal 01 May, 2026 Reviewers invited by journal 30 Apr, 2026 Editor invited by journal 24 Mar, 2026 Editor assigned by journal 15 Mar, 2026 Submission checks completed at journal 15 Mar, 2026 First submitted to journal 13 Mar, 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. 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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-9112718","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":635439294,"identity":"9585312f-aca9-4b2b-9fb1-53ed84af25c6","order_by":0,"name":"Song Ding","email":"","orcid":"","institution":"Changchun Normal University","correspondingAuthor":false,"prefix":"","firstName":"Song","middleName":"","lastName":"Ding","suffix":""},{"id":635439295,"identity":"db797991-422b-4b4f-b436-edc574283406","order_by":1,"name":"Shuhai Yao","email":"","orcid":"","institution":"Changchun Normal University","correspondingAuthor":false,"prefix":"","firstName":"Shuhai","middleName":"","lastName":"Yao","suffix":""},{"id":635439296,"identity":"ffb2eaa6-4cc5-4d02-b6e4-f474ced6c38f","order_by":2,"name":"Liwei Sun","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3UlEQVRIie3QMQrCMBiG4ZSC049dI4q9QqTQSfQqKYVOVZzETUFor1Bv4eT8i0OX4Jy1uDooLk5q0lEk1s0hLzRkeeBrCLHZ/jMHOSHg6etCH9jA1KSzUjfRmOiDYVPiFxPEKhv2gvJwuuwz0m9L7txmBsLklGOUJRCKJKSKBB3J3W5hIjRlGO0OEEpoudeMRFvJWy4Yh9XkCUEBrh62/EqIrAkCo0D0MM6+ESbOijxioPpf8EgHG1Gtu8ZheTqo7mI09nL1Yjgf+u0y3t+Mw96i6nNWPwCbzWazfeoFoqRPzaW3Z08AAAAASUVORK5CYII=","orcid":"","institution":"Changchun Normal University","correspondingAuthor":true,"prefix":"","firstName":"Liwei","middleName":"","lastName":"Sun","suffix":""},{"id":635439297,"identity":"02340a4b-6d18-4483-8cdc-c4e6c3ec4b36","order_by":3,"name":"Jing Li","email":"","orcid":"","institution":"Changchun Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jing","middleName":"","lastName":"Li","suffix":""},{"id":635439298,"identity":"50f6706e-839e-4ec8-a823-7d4fe56921a4","order_by":4,"name":"Hongyan Zhou","email":"","orcid":"","institution":"Changchun Normal University","correspondingAuthor":false,"prefix":"","firstName":"Hongyan","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2026-03-13 09:09:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9112718/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9112718/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109067880,"identity":"879a73e0-69a5-4ace-9c5a-6127e63d4c42","added_by":"auto","created_at":"2026-05-12 10:02:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1165764,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9112718/v1_covered_3cd3d037-21c0-48f1-86e2-ba40b483b32a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of NMPC in the processing of Wolter-I grazing incident mirrors","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"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":"","lastPublishedDoi":"10.21203/rs.3.rs-9112718/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9112718/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWolter-I structures based on X-ray grazing incidence optics are often used in extreme ultraviolet (EUV) collection optical systems, especially in the application of discharge plasma (DPP) sources. With the development of computer technology, the computerized surface forming (CCOS) method can significantly improve the surface accuracy and meet the optical requirements of high precision when processing Wolter-I grazing incident mirrors. In this paper, the nonlinear model predictive control (NMPC) system is innovatively introduced into the traditional CCOS method instead of the PID control system, and the application of NMPC in the rough grinding and fine grinding stages of Wolter-I grazing incident mirrors is studied, and it is found that the processing process and processing efficiency are effectively optimized through the system. Firstly, a detailed geometric model of the mirror was established for the special geometry of the inner surface of the cylindrical surface of the Wolter-I grazing incident mirror. Secondly, in view of the complex and nonlinear characteristics of the Wolter-I grazing incident mirror, a nonlinear model of the machining process is established, and the influence of spindle feed rate, removal pressure, abrasive particle size and other factors on the machining accuracy is considered, and the simulation results show that when the spindle feed rate is 25mm/s, the removal pressure is 9 N, and the abrasive particle size is 10, the removal efficiency is the highest and the removal effect is the best. The experimental results show that the CCOS method combined with NMPC significantly improves the surface accuracy and effectively improves the processing efficiency and reduces the production cost when processing the Wolter-I grazing incident mirror.\u003c/p\u003e","manuscriptTitle":"Application of NMPC in the processing of Wolter-I grazing incident mirrors","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-11 13:51:27","doi":"10.21203/rs.3.rs-9112718/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-06T11:00:23+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-04T09:10:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T04:41:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"254898007185996512910028318874753196365","date":"2026-05-01T08:20:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"56044984257216043530033029148924466384","date":"2026-05-01T06:16:06+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-01T03:37:49+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-24T06:24:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-16T02:52:16+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-16T02:51:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-03-13T08:53:44+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":"c5fd28b0-2171-4075-a5dc-75e24cf3e49c","owner":[],"postedDate":"May 11th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-06T11:00:23+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-04T09:10:29+00:00","index":91,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-03T04:41:33+00:00","index":90,"fulltext":""},{"type":"reviewerAgreed","content":"254898007185996512910028318874753196365","date":"2026-05-01T08:20:17+00:00","index":89,"fulltext":""},{"type":"reviewerAgreed","content":"56044984257216043530033029148924466384","date":"2026-05-01T06:16:06+00:00","index":88,"fulltext":""},{"type":"reviewersInvited","content":"2","date":"2026-05-01T03:37:49+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":67627887,"name":"Physical sciences/Engineering"},{"id":67627888,"name":"Physical sciences/Optics and photonics"}],"tags":[],"updatedAt":"2026-05-18T12:53:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-11 13:51:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9112718","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9112718","identity":"rs-9112718","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}