Experimental Comparison of Five MPC Variants for Hexadic Tank System Control: A Multi-Criteria Hardware Evaluation

Experimental Comparison of Five MPC Variants for Hexadic Tank System Control: A Multi-Criteria Hardware Evaluation | 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 Experimental Comparison of Five MPC Variants for Hexadic Tank System Control: A Multi-Criteria Hardware Evaluation Sagnik Mitra, Ganti Suryanarayana Murthy This is a preprint; it has not been peer reviewed by a journal.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-9526181/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 systems represent an advanced extension ofquadruple tank systems for controlling non-growth-associated productdynamics in bioprocess industries, including distillation columns,boiler processes, oil refineries, pharmaceutical, and food processingapplications. These systems present significant control challenges dueto their multivariable dynamics, coupling effects, and nonlinearbehaviours, making controller selection critical for industrialdeployment. This paper presents a comprehensive hardware-basedcomparison of five Model Predictive Control (MPC) variants---LQR,Linear MPC, Robust MPC, Event-driven MPC, and Scale-Free MPC - on ahexadic (six-tank) system testbed. Scale-Free MPC is a norm-basedpredictive control formulation that avoids explicit state-weight scalingby normalising the cost function with respect to state magnitudes,enabling consistent performance across a wide range of operatingconditions. Through 100 closed-loop experiments across 10 setpointsunder nominal and disturbed conditions, we evaluate controllerperformance using 15 metrics spanning speed, accuracy, stability,energy efficiency, and robustness. The multicriteria evaluationmethodology achieves 100% validation pass rate with 4.51% averageprediction error against hardware measurements, and demonstrates 23%performance improvement over the LQR naive baseline. Statisticalanalysis (one-way ANOVA, F (4, 95) = 9.52, p < 0.001) with TukeyHSD post-hoc testing confirmed significant performance differences amongcontrollers. Event-driven MPC achieved the highest composite score (0.7354 ± 0.016, 95% CI [0.705, 0.766]), demonstrating statistically significant superiority over LQR Control (∆ = 0.137, p < 0.01) and Robust MPC (∆ = 0.076, p < 0.05), whileperforming equivalently to Linear MPC (∆ = 0.031, p = 0.89) and Scale-Free MPC (∆ = 0.039, p = 0.71). Model Predictive Control Bioprocess Control Hexadic TankSystem Multi-criteria Evaluation Scale-Free MPC 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-9526181","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":631403719,"identity":"218bfbcb-4b38-48b7-81d8-c14b497217dc","order_by":0,"name":"Sagnik Mitra","email":"","orcid":"","institution":"IIT Indore","correspondingAuthor":false,"prefix":"","firstName":"Sagnik","middleName":"","lastName":"Mitra","suffix":""},{"id":631403720,"identity":"ce262a3b-0124-4c10-9d26-57b74b2c19a0","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":"IIT Indore","correspondingAuthor":true,"prefix":"","firstName":"Ganti","middleName":"Suryanarayana","lastName":"Murthy","suffix":""}],"badges":[],"createdAt":"2026-04-25 13:54:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9526181/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9526181/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109296067,"identity":"09aa5d38-dede-4b32-8786-a153133861b7","added_by":"auto","created_at":"2026-05-15 08:45:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1014735,"visible":true,"origin":"","legend":"","description":"","filename":"2ndPaperonControlV1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9526181/v1_covered_bc78e069-476f-4f4c-996b-8d1857b44b9c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Experimental Comparison of Five MPC Variants for Hexadic Tank\nSystem Control: A Multi-Criteria Hardware Evaluation","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":"Model Predictive Control, Bioprocess Control, Hexadic TankSystem, Multi-criteria Evaluation, Scale-Free MPC","lastPublishedDoi":"10.21203/rs.3.rs-9526181/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9526181/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHexadic tank systems represent an advanced extension ofquadruple tank systems for controlling non-growth-associated productdynamics in bioprocess industries, including distillation columns,boiler processes, oil refineries, pharmaceutical, and food processingapplications. These systems present significant control challenges dueto their multivariable dynamics, coupling effects, and nonlinearbehaviours, making controller selection critical for industrialdeployment. This paper presents a comprehensive hardware-basedcomparison of five Model Predictive Control (MPC) variants---LQR,Linear MPC, Robust MPC, Event-driven MPC, and Scale-Free MPC - on ahexadic (six-tank) system testbed. Scale-Free MPC is a norm-basedpredictive control formulation that avoids explicit state-weight scalingby normalising the cost function with respect to state magnitudes,enabling consistent performance across a wide range of operatingconditions. Through 100 closed-loop experiments across 10 setpointsunder nominal and disturbed conditions, we evaluate controllerperformance using 15 metrics spanning speed, accuracy, stability,energy efficiency, and robustness. The multicriteria evaluationmethodology achieves 100% validation pass rate with 4.51% averageprediction error against hardware measurements, and demonstrates 23%performance improvement over the LQR naive baseline. Statisticalanalysis (one-way ANOVA, F (4, 95) = 9.52, p \u0026lt; 0.001) with TukeyHSD post-hoc testing confirmed significant performance differences amongcontrollers. Event-driven MPC achieved the highest composite score (0.7354 ± 0.016, 95% CI [0.705, 0.766]), demonstrating statistically significant superiority over LQR Control (∆ = 0.137, p \u0026lt; 0.01) and Robust MPC (∆ = 0.076, p \u0026lt; 0.05), whileperforming equivalently to Linear MPC (∆ = 0.031, p = 0.89) and Scale-Free MPC (∆ = 0.039, p = 0.71).\u003c/p\u003e","manuscriptTitle":"Experimental Comparison of Five MPC Variants for Hexadic Tank\nSystem Control: A Multi-Criteria Hardware Evaluation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-14 14:50:30","doi":"10.21203/rs.3.rs-9526181/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":"May 14th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T14:50:30+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-14 14:50:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9526181","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9526181","identity":"rs-9526181","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}