PAPERmaking! Vol11 Nr1 2025

™™™Ǥƒ–—”‡Ǥ ‘Ȁ• ‹‡–‹ˆ‹ ”‡’‘”–•

Design and optimal tuning of fractional order PID controller for paper machine headbox using Œ‡ŽŽ›Ƥ•Š•‡ƒ” Š‘’–‹‹œ‡”ƒŽ‰‘”‹–Š Divya Nataraj ͷ & Manoharan Subramanian ͸ Š‹•ƒ—• ”‹’–’”‘’‘•‡•–Š‡ ‡ŽŽ›Ƥ•Š‡ƒ” Š’–‹‹œƒ–‹‘ȋ ȌƒŽ‰‘”‹–ŠǦ„ƒ•‡† ”ƒ –‹‘ƒŽ”†‡” ”‘’‘”–‹‘ƒŽǦ –‡‰”ƒŽǦ‡”‹˜ƒ–‹˜‡ȋ  Ȍ ‘–”‘ŽŽ‡”–—‹‰ˆ‘”ƒ’ƒ’‡”ƒ Š‹‡Š‡ƒ†„‘šǤŠ‡‘˜‡Ž–› ‘ˆ–Š‹•‡–Š‘†Ž‹‡•‹‹–‡‰”ƒ–‹‰–Š‡ –‡ Š‹“—‡ˆ‘”‘’–‹‹œ‹‰–Š‡’ƒ”ƒ‡–‡”•‘ˆ–Š‡   ‘–”‘ŽŽ‡”–‘‘‹–‘”ƒ† ‘–”‘ŽŠ‡ƒ†„‘š’”‡••—”‡ƒ†•–‘ Ž‡˜‡Ž‡ƥ ‹‡–Ž›ƒ†‡ơ‡ –‹˜‡Ž›ǤŠ‡  ƒŽ‰‘”‹–Š‡•—”‡•‘’–‹ƒŽ–—‹‰‘ˆ ‘–”‘ŽŽ‡”’ƒ”ƒ‡–‡”•„›‹‹‹œ‹‰‡””‘”‹†‹ ‡••— Šƒ• –‡‰”ƒŽ ‘ˆ“—ƒ”‡†””‘”ȋ Ȍǡ –‡‰”ƒŽ‘ˆ‹‡„•‘Ž—–‡””‘”ȋ Ȍǡƒ† –‡‰”ƒŽ‘ˆ„•‘Ž—–‡””‘”ȋ ȌǤ ‹—Žƒ–‹‘• ‘†— –‡†‘–Š‡Ȁ‹—Ž‹’Žƒ–ˆ‘”†‡‘•–”ƒ–‡–Šƒ––Š‡   ‘–”‘ŽŽ‡” –—‡†—•‹‰ ƒ Š‹‡˜‡••—’‡”‹‘”’‡”ˆ‘”ƒ ‡ ‘’ƒ”‡†–‘ ‘˜‡–‹‘ƒŽ ȋ”‘’‘”–‹‘ƒŽǦ –‡‰”ƒŽȌ ƒ† ȋ”‘’‘”–‹‘ƒŽǦ –‡‰”ƒŽǦ‡”‹˜ƒ–‹˜‡Ȍ ‘–”‘ŽŽ‡”•Ǥ’‡ ‹Ƥ ƒŽŽ›ǡ–Š‡ Ǧ–—‡†   ‘–”‘ŽŽ‡” ‡šŠ‹„‹–‡†ƒ͸ͻά”‡†— –‹‘‹”‹•‡–‹‡ǡƒ͹Ͷά‹’”‘˜‡‡–‹•‡––Ž‹‰–‹‡ǡƒ†ƒ͸Ͷά†‡ ”‡ƒ•‡ ‹‘˜‡”•Š‘‘–™Š‡ ‘’ƒ”‡†–‘–Š‡  ‘–”‘ŽŽ‡”Ǥ —”–Š‡”‘”‡ǡ ‘’ƒ”ƒ–‹˜‡ƒƒŽ›•‡•™‹–Š‘–Š‡” ‘’–‹‹œƒ–‹‘–‡ Š‹“—‡•ǡ‹ Ž—†‹‰‘–Š Žƒ‡’–‹‹œƒ–‹‘ȋ Ȍǡ–‹‘’–‹‹œƒ–‹‘ȋȌǡ ƒ†Ž‡’Šƒ– ‡”†‹‰’–‹‹œƒ–‹‘ȋ Ȍǡ”‡˜‡ƒŽ–Šƒ––Š‡ ƒŽ‰‘”‹–Š’”‘˜‹†‡•Š‹‰Š‡”ƒ —”ƒ ›ƒ† •–ƒ„‹Ž‹–›‹†‹˜‡”•‡‘’‡”ƒ–‹‰ ‘†‹–‹‘•ǤŠ‹••–—†›—†‡”• ‘”‡•–Š‡‡ƥ ƒ ›‘ˆ–Š‡ Ǧ–—‡†   ‘–”‘ŽŽ‡”ƒ•ƒ”‘„—•–•‘Ž—–‹‘ˆ‘” ‘’Ž‡š‹†—•–”‹ƒŽƒ’’Ž‹ ƒ–‹‘•ǡ•— Šƒ•’ƒ’‡”ƒ Š‹‡Š‡ƒ†„‘š •›•–‡•ǡƒ†Š‹‰ŠŽ‹‰Š–•‹–•’‘–‡–‹ƒŽ–‘‡Šƒ ‡’”‘ ‡••‡ƥ ‹‡ ›ƒ† ‘–”‘Ž’”‡ ‹•‹‘Ǥ Keywords FOPID controller, JSO, Paper machine head box, EHO, MFO and ALO The paper machine is used in the paper and pulp industry to produce paper material at higher speeds and in large quantities. The fourdrinier paper machine represents a modern evolution in papermaking technology 1 . A movable plain-woven mesh is used to produce paper web by creating a continuously moving wet mat and filtering the fibers held in a paper stock. Materials such as paper, fabric, cardboard, and plastic films are transformed into nets with a width up to 10 m and a speed of 40 m/s 2 . In paper production, a distribution element called headbox converts the flow of material in a tube into a continuous belt, which dries and becomes a continuous sheet. To ensure high-quality production, the width of the material belt in the Cross Direction (CD) must match the Machine Direction (MD) 3–5 subsequently. The size of the object and the base weight for each zone can be reliably calculated based on the amplitude of the beta radiation. In any case, web-based beta traffic cannot be measured on a case-by-case basis. It is customary to measure the weight of the foundation with a device that wipes the pieces running in front 6,7 . The estimated signal is divided into MD and CD segments. The main function of the paper machine is to create a sheet and then absorb water, squeeze it and evaporate 8 . The paper machine is divided into two basic parts; the wet and dry part 9–11 . The final thin film is designed by a continuous technical system (thread), which allows water to escape from the formed film. As the sheet passes through the wet press, excess water is removed, forcing the water-permeable structure against the paper 12,13 . The integration of Fractional Order PID (FOPID) controllers with Jellyfish Search Optimizer (JSO) offers a robust and efficient solution for controlling the headbox in paper production. Traditional PID controllers face significant limitations in handling the nonlinear and multivariable nature of the headbox dynamics, especially under varying operational conditions 14 . FOPID controllers provide enhanced flexibility and precision through fractional calculus, allowing for superior performance in such scenarios. The JSO algorithm, inspired by jellyfish movement, is adept at balancing exploration and exploitation during optimization, making it particularly ͷ ‡’ƒ”–‡–‘ˆǡ”‹ƒƒ”‹•Šƒ‰‹‡‡”‹‰‘ŽŽ‡‰‡ǡ‘‹„ƒ–‘”‡ǡƒ‹Žƒ†—ͼͺͷͶ͸͸ǡ †‹ƒǤ ͸ Department ‘ˆ ǡ  ‘ŽŽ‡‰‡ ‘ˆ ‰‹‡‡”‹‰ ƒ†‡ Š‘Ž‘‰›ǡ ‘‹„ƒ–‘”‡ǡƒ‹Ž ƒ†— ͼͺͷͷͶͻǡ †‹ƒǤ email: Ǥ†‹˜›ƒ•”‹͸Ͷ͸ͼ̻ ‰ƒ‹ŽǤ ‘

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