{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:35:54Z","timestamp":1765546554000,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,26]],"date-time":"2020-02-26T00:00:00Z","timestamp":1582675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper proposes a fractional-order sliding mode controller (FOSMC) for the robust control of a nonlinear process subjected to unknown parametric disturbances. The controller aims to ensure optimal growth in photobioreactors of native microalgae involved in eutrophication of the Sinaloa rivers in Mexico. The controller design is based on the Caputo fractional integral-order derivative and on the convergence properties of a sliding surface. For nonlinear systems, the proposed FOSMC guarantees convergence to the sliding surface even in the presence of model disturbances. The proposed controller is compared to an Internal Model Control (IMC) through numerical simulations.<\/jats:p>","DOI":"10.3390\/a13030050","type":"journal-article","created":{"date-parts":[[2020,2,27]],"date-time":"2020-02-27T03:21:16Z","timestamp":1582773676000},"page":"50","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Fractional Sliding Mode Nonlinear Procedure for Robust Control of an Eutrophying Microalgae Photobioreactor"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0262-420X","authenticated-orcid":false,"given":"Abraham Efraim","family":"Rodr\u00edguez-Mata","sequence":"first","affiliation":[{"name":"Conacyt-Tecnol\u00f3gico Nacional de Mexico\\Instituto Tecnol\u00f3gico de Culiac\u00e1n, 80220 Culiac\u00e1n Rosales, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ricardo","family":"Luna","sequence":"additional","affiliation":[{"name":"Center for Research and Innovation (CRI), Vi\u00f1a Concha y Toro, 3550000 Pencahue, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1278-7782","authenticated-orcid":false,"given":"Jose Ricardo","family":"P\u00e9rez-Correa","sequence":"additional","affiliation":[{"name":"Chemical and Bioprocess Engineering Department, Pontificia Universidad Cat\u00f3lica de Chile, Vicu\u00f1a Mackenna 4860, Macul, Santiago, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alejandro","family":"Gonzalez-Huitr\u00f3n","sequence":"additional","affiliation":[{"name":"Conacyt-Tecnol\u00f3gico Nacional de Mexico\\Instituto Tecnol\u00f3gico de Culiac\u00e1n, 80220 Culiac\u00e1n Rosales, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9227-4505","authenticated-orcid":false,"given":"Rafael","family":"Castro-Linares","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Center for Research and Advanced Studies of the National Polytechnic Institute (Cinvestav), 07360 Ciudad de Mexico, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2367-4553","authenticated-orcid":false,"given":"Manuel A.","family":"Duarte-Mermoud","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Advanced Mining Technology Center (AMTC), University of Chile, Av. Tupper 2007, Santiago, Chile: <email>mduartem@ing.uchile.cl<\/email>"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,26]]},"reference":[{"key":"ref_1","first-page":"81","article-title":"Theoretical-practical study on the removal of contaminants in Los Remedios River (State of Mexico)","volume":"24","author":"Carmona","year":"2009","journal-title":"Ingenier\u00eda Hidr\u00e1ulica en M\u00e9xico"},{"key":"ref_2","first-page":"121","article-title":"Biomass production and nutrient budget in outdoor cultures of Scenedesmus obliquus(Chlorophyceae) in artificial wastewater, under the winter and summer conditions of Mazatlan, Sinaloa, Mexico","volume":"55","author":"Voltolina","year":"2005","journal-title":"Vie et milieu"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1016\/j.jprocont.2011.07.012","article-title":"Hurdles and challenges for modelling and control of microalgae for CO2 2 mitigation and biofuel production","volume":"21","author":"Bernard","year":"2011","journal-title":"J. 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