{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:52:45Z","timestamp":1760241165596,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Eusko Jaurlaritza","doi-asserted-by":"publisher","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MCIU\/AEI\/FEDER, UE","award":["RTI2018-094902-B-C22"],"award-info":[{"award-number":["RTI2018-094902-B-C22"]}]},{"name":"MINECO\/FEDER, EU","award":["DPI2015-70075-R"],"award-info":[{"award-number":["DPI2015-70075-R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>At present, two main magnetic confinement fusion devices exist: tokamaks and stellarators. Moreover, stellarators have been demonstrated to be a good alternative to tokamaks, due to their ability to operate in continuous mode, which eventually translates into a higher commercial profitability. In stellarators, the magnetic confinement of the plasma is achieved exclusively by the coils, thus no electric current through the plasma is needed. In particular, this article presents the Columbia Non-Neutral Torus stellarator that is located in the Automatic Control Group of Euskal Herriko Unibertsitatea (EHU). This EHU stellarator maintains symmetry in its structure due to the topology of the mesh that is formed by its coils. A cornerstone of future fusion reactors is to obtain real-time control that enables a sustained reaction. In this article, a control-oriented model for the installed magnetic confinement coils is presented. The model is based on matrices that preserve symmetry, which is defined from physical principles and then validated by different sets of experimental data. Then, based on this model, a novel predictive control suited to this particular model with symmetric objective function is implemented in the numerical simulations, and its response is compared to that of traditional controllers. Finally, this control is implemented in a real plant and the satisfactory experiment results provide validation of both the numerical model and proposed controller.<\/jats:p>","DOI":"10.3390\/sym12010011","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:23:12Z","timestamp":1577071392000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Real-Time Control for the EHU Stellarator"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9801-4130","authenticated-orcid":false,"given":"Izaskun","family":"Garrido","sequence":"first","affiliation":[{"name":"Automatic Control Group\u2014ACG, Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, University of the Basque Country(UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javier","family":"Maseda","sequence":"additional","affiliation":[{"name":"Automatic Control Group\u2014ACG, Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, University of the Basque Country(UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Itziar","family":"Martija","sequence":"additional","affiliation":[{"name":"Automatic Control Group\u2014ACG, Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, University of the Basque Country(UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aitor J.","family":"Garrido","sequence":"additional","affiliation":[{"name":"Automatic Control Group\u2014ACG, Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, University of the Basque Country(UPV\/EHU), Po Rafael Moreno no3, 48013 Bilbao, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"ref_1","unstructured":"ITER Organization (2019, December 18). What is ITER?. Available online: https:\/\/www.iter.org\/proj\/inafewlines."},{"key":"ref_2","unstructured":"Wikimedia Foundation, Inc. (2019, December 18). Nuclear Fusion-Wikipedia. Available online: https:\/\/en.wikipedia.org\/wiki\/Nuclear_fusion."},{"key":"ref_3","unstructured":"ITER Organization (2019, December 18). What is a TOKAMAK?. Available online: https:\/\/www.iter.org\/mach\/Tokamak."},{"key":"ref_4","unstructured":"Wikimedia Foundation, Inc. (2019, December 18). Stellarator-Wikipedia. Available online: https:\/\/en.wikipedia.org\/wiki\/Stellarator."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"De la Sen, M., Garrido, A.J., Soto, J.C., Barambones, O., and Garrido, I. (2008). Suboptimal regulation of a class of bilinear interconnected systems with finite-time sliding planning horizons. Math. Probl. Eng., 817063.","DOI":"10.1155\/2008\/817063"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1016\/S1474-6670(17)52521-5","article-title":"Frequency Domain System Identification Toolbox for MATLAB","volume":"24","author":"Pintelon","year":"1991","journal-title":"IFAC Proc. Vol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Li, K., and Thompson, S. (2001, January 4\u20137). Fundamental grey-box modelling. Proceedings of the 2001 European Control Conference (ECC), Porto, Portugal.","DOI":"10.23919\/ECC.2001.7076500"},{"key":"ref_8","unstructured":"Garrido, I., Garrido, A.J., Sevillano, M.G., Romero, J.A., Amundarain, M., and Alberdi, M. (2008, January 4\u20137). Tokamak state-space control modeling. Proceedings of the Canadian Conference on Electrical and Computer Engineering, Niagara Falls, ON, Canada."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Garrido, A.J., Otaola, E., Garrido, I., Lekube, J., Maseda, F.J., Liria, P., and Mader, J. (2015). Mathematical Modeling of Oscillating Water Columns Wave-Structure Interaction in Ocean Energy Plants. Math. Probl. Eng., 727982.","DOI":"10.1155\/2015\/727982"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Heong Ang, K., Chong, G., and Li, Y. (2005). PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol., 13.","DOI":"10.1109\/TCST.2005.847331"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"De la Sen, M. (2019). On Cauchy\u2019s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls. Symmetry, 11.","DOI":"10.3390\/sym11050712"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.nahs.2015.12.004","article-title":"Output controllability of the discrete-time linear switched systems","volume":"2016","author":"Babiarz","year":"2016","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Garrido, A.J., Garrido, I., Barambones, O., Alkorta, P., and Maseda, F.J. (2008, January 14\u201317). Simple Linear Models for Plasma Control in Tokamak Reactors. Proceedings of the 2008 International Conference on Control, Automation and Systems, Seoul, Korea.","DOI":"10.1109\/ICCAS.2008.4694261"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.jprocont.2010.10.006","article-title":"Tuning rules for optimal PID and fractional-order PID controllers","volume":"21","author":"Padula","year":"2011","journal-title":"J. Process Control"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MIE.2013.2290138","article-title":"Model predictive control: A review of its applications in power electronics","volume":"8","author":"Vazquez","year":"2014","journal-title":"IEEE Ind. Electron. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4885","DOI":"10.1016\/j.jfranklin.2016.09.007","article-title":"Model predictive control of cash balance in a cash concentration and disbursements system","volume":"353","author":"Ibeas","year":"2016","journal-title":"J. Frankl. Inst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Garrido, I., Garrido, A.J., Romero, J.A., Carrascal, E., Sevillano-Berasategui, M.G., and Barambones, O. (2015). Low Effort Li Nuclear Fusion Plasma Control Using Model Predictive Control Laws. Math. Probl. Eng., 527420.","DOI":"10.1155\/2015\/527420"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sturzenegger, D., Morari, M., Semeraro, V., Gyalistras, D., and Smith, R.S. (2014, January 4\u20136). BRCM Matlab Toolbox: Model generation for model predictive building control. Proceedings of the American Control Conference (ACC), Portland, OR, USA.","DOI":"10.1109\/ACC.2014.6858967"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Garrido, A.J., Garrido, I., Alberdi, M., Amundarain, M., Barambones, O., and Romero, J.A. (2013, January 23\u201327). Robust Control of Oscillating Water Column (OWC) Devices: Power Generation Improvement. Proceedings of the 2013 MTS\/IEEE Oceans Conference-San Diego, San Diego, CA, USA.","DOI":"10.1109\/WCST.2013.6750399"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:43:39Z","timestamp":1760190219000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,19]]},"references-count":19,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["sym12010011"],"URL":"https:\/\/doi.org\/10.3390\/sym12010011","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,12,19]]}}}