Design and Analysis of a Hexadic Tank System: Classical and Advanced Control Algorithms

Design and Analysis of a Hexadic Tank System: Classical and Advanced Control Algorithms | 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 Design and Analysis of a Hexadic Tank System: Classical and Advanced Control Algorithms Sagnik Mitra, Ganti Suryanarayana Murthy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9335682/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 Hexadic tank system represents an extension of quadruple tank system for controlling non-growth-associated product dynamics in bioprocess industries, including two stage continuous fermentations, multiple distillation columns, pharmaceutical, and food processing applications. This study presents a comprehensive analysis encompassing theoretical foundations, simulation frameworks, hardware implementation, and experimental validation of three control algorithms: LQR, Linear MPC, and Robust MPC, evaluated under disturbance and non-disturbance conditions. Among the three control algorithms, Linear MPC with disturbances (LMPC \((_{\text{D}})\) ) achieves superior performance with the lowest mean error (1.67), maximum error (2.00), control variance (3.47), and overall sensitivity (2.52), with high settling times. RMPC \((_{\text{D}})\) shows the fastest minimum response (1.93 s) but exhibits higher mean error (2.5) and maximum error (5.0), and overall sensitivity (3.94). LQR controllers exhibit poor performance, with high sensitivity (94.08-226.47), large errors, and longer settling times (especially for LQR \((_{\text{D}})\) ), rendering them unsuitable for practical implementation. All controllers maintain zero steady-state error with stable eigenvalues ( \((-6.76\times10^{-3})\) to \((-4.34\times10^{-19})\) ). This confirms that the model predictive control strategies are optimal for tracking precision, disturbance rejection, and parameter insensitivity in bioprocess applications. Control Systems Process Control Hexadic Tank System Bioreactor Control Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryInformationSMV0R1.zip 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. 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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-9335682","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":622018380,"identity":"909152e1-02a2-40e9-ba0d-4b2aece5b09a","order_by":0,"name":"Sagnik Mitra","email":"","orcid":"","institution":"Indian Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Sagnik","middleName":"","lastName":"Mitra","suffix":""},{"id":622018382,"identity":"31d2c53b-2379-4efd-ad48-69f2b71dc558","order_by":1,"name":"Ganti Suryanarayana Murthy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7ElEQVRIiWNgGAWjYLCCBDDJw8DwwUCCgQ3MMcCrgbEBrIWNh4FxhoGEBHFaGKBamIEWSRB0k7z72eMPHjBsS9w+v/eYtE2BRR0fA/PDDwwFd3BqMTyTlwh02O3EOcf40qRzwA5jM5ZgMHiGW0tDjiFYyww2HjOoFgYzoF8O49bS/wZJiwVYC/s3vFrkJZBtYQBr4cFvi4HEG8MZCQa3jWew5Rhb9hhISLYx8xRLJOCzpT/H4OOPituyM5jPGN748aeOX769feOHD3/w2HIATILZLJA4YWaApQcctjQg2Mwf8CgcBaNgFIyCEQwAagRHCdu7KKYAAAAASUVORK5CYII=","orcid":"","institution":"Indian Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Ganti","middleName":"Suryanarayana","lastName":"Murthy","suffix":""}],"badges":[],"createdAt":"2026-04-06 16:08:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9335682/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9335682/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107480465,"identity":"2193d246-a437-4b8f-8067-f7fb67852866","added_by":"auto","created_at":"2026-04-22 02:10:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":709765,"visible":true,"origin":"","legend":"","description":"","filename":"DesignandAnalysisofaHexadicTankSystemClassicalandAdvancedControlAlgorithmsSMV0R1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9335682/v1_covered_f80dc9af-0e89-45c6-a670-5e3b8c2f7f2e.pdf"},{"id":107019077,"identity":"3c68a008-578d-4dbc-a2f1-39932b7e7bdd","added_by":"auto","created_at":"2026-04-15 20:48:43","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2814101,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformationSMV0R1.zip","url":"https://assets-eu.researchsquare.com/files/rs-9335682/v1/125d3bfab0e72c2c67471a1b.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Design and Analysis of a Hexadic Tank System: Classical and Advanced Control Algorithms","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Control Systems, Process Control, Hexadic Tank System, Bioreactor Control","lastPublishedDoi":"10.21203/rs.3.rs-9335682/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9335682/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHexadic tank system represents an extension of quadruple tank system for controlling non-growth-associated product dynamics in bioprocess industries, including two stage continuous fermentations, multiple distillation columns, pharmaceutical, and food processing applications. This study presents a comprehensive analysis encompassing theoretical foundations, simulation frameworks, hardware implementation, and experimental validation of three control algorithms: LQR, Linear MPC, and Robust MPC, evaluated under disturbance and non-disturbance conditions. Among the three control algorithms, Linear MPC with disturbances (LMPC\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((_{\\text{D}})\\)\u003c/span\u003e\u003c/span\u003e) achieves superior performance with the lowest mean error (1.67), maximum error (2.00), control variance (3.47), and overall sensitivity (2.52), with high settling times. RMPC\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((_{\\text{D}})\\)\u003c/span\u003e\u003c/span\u003e shows the fastest minimum response (1.93 s) but exhibits higher mean error (2.5) and maximum error (5.0), and overall sensitivity (3.94). LQR controllers exhibit poor performance, with high sensitivity (94.08-226.47), large errors, and longer settling times (especially for LQR\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((_{\\text{D}})\\)\u003c/span\u003e\u003c/span\u003e), rendering them unsuitable for practical implementation. All controllers maintain zero steady-state error with stable eigenvalues (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((-6.76\\times10^{-3})\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((-4.34\\times10^{-19})\\)\u003c/span\u003e\u003c/span\u003e). This confirms that the model predictive control strategies are optimal for tracking precision, disturbance rejection, and parameter insensitivity in bioprocess applications.\u003c/p\u003e","manuscriptTitle":"Design and Analysis of a Hexadic Tank System: Classical and Advanced Control Algorithms","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-15 20:48:39","doi":"10.21203/rs.3.rs-9335682/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"3f1bee1e-5faa-481a-bb3a-f53b4c783dbc","owner":[],"postedDate":"April 15th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-13T01:53:44+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-15 20:48:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9335682","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9335682","identity":"rs-9335682","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}