PAPERmaking! Vol11 Nr1 2025

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41. Saini, P., Kumar, R., Juneja, P. K. & Parashar, D. Robustness analysis of decoupled PID controller for paper machine headbox. In 2020 International Conference on Power Electronics & IoT Applications in Renewable Energy and its Control (PARC) 503–507 (IEEE, 2020). 42. Lv, J., Ju, X. & Wang, C. Neural network prescribed-time observer-based output-feedback control for uncertain pure-feedback nonlinear systems. Expert Syst. Appl. 264 , 125813 (2025). 43. Chou, J. S. & Truong, D. N. Multiobjective optimization inspired by behavior of jellyfish for solving structural design problems. Chaos Solitons Fractals 135 , 09738 (2020). 44. Mukhtar, A. & Mukhtar, F. Liquid Level Control Strategy Using Fractional Order PID Controller Based on Artificial Intelligence 1675–1680 (International Research Journal of Engineering and Technology (IRJET), 2020). 45. He, D. et al. Research on vertical vibration characteristics of rolling mill based on magnetorheological fluid damper absorber. Mech. Syst. Signal Process. 224 , 112203 (2025). 46. Abdulwahhab, O. W. Design of a complex fractional order PID controller for a first order plus time delay system. ISA Trans. 99 , 154–158 (2020). 47. Chou, J. S. & Truong, D. N. A novel metaheuristic optimizer inspired by behavior of jellyfish in ocean. Appl. Math. Comput. 389 , 125535 (2021).  ‘™Ž‡†‰‡‡–• Not Applicable. —–Š‘” ‘–”‹„—–‹‘• All the authors contributed to this research work in terms of concept creation, conduct of the research work, and manuscript preparation. —†‹‰ No funding received for this research work. Declarations Competing interests The authors declare no competing interests. –Š‹ •ƒ’’”‘˜ƒŽƒ† ‘•‡––‘’ƒ”–‹ ‹’ƒ–‡ Not applicable. Consent for publication Not applicable. ††‹–‹‘ƒŽ‹ˆ‘”ƒ–‹‘ Correspondence and requests for materials should be addressed to D.N. Reprints and permissions information is available at www.nature.com/reprints. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommo ns.org/licenses/by-nc-nd/4.0/. © The Author(s) 2025

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