{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:43:00Z","timestamp":1760150580113,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T00:00:00Z","timestamp":1701993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer.<\/jats:p>","DOI":"10.3390\/axioms12121107","type":"journal-article","created":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T05:47:30Z","timestamp":1702014450000},"page":"1107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9681-9656","authenticated-orcid":false,"given":"Vicente","family":"Borja-Jaimes","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda Electr\u00f3nica, TecNM-Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico (CENIDET), Cuernavaca 62490, Morelos, Mexico"}]},{"given":"Manuel","family":"Adam-Medina","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Electr\u00f3nica, TecNM-Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico (CENIDET), Cuernavaca 62490, Morelos, Mexico"}]},{"given":"Jarniel","family":"Garc\u00eda-Morales","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Electr\u00f3nica, TecNM-Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico (CENIDET), Cuernavaca 62490, Morelos, Mexico"}]},{"given":"Alan","family":"Cruz-Rojas","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Computacionales e Ingenier\u00edas, Centro Universitario de los Valles, Universidad de Guadalajara, Ameca 46600, Jalisco, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6998-4074","authenticated-orcid":false,"given":"Alfredo","family":"Gil-Velasco","sequence":"additional","affiliation":[{"name":"Direcci\u00f3n Acad\u00e9mica de la Ingenier\u00eda en Tecnolog\u00edas de la Informaci\u00f3n y la Ingenier\u00eda en Electr\u00f3nica y Telecomunicaciones, Universidad Polit\u00e9cnica del Estado de Morelos, Jiutepec 62550, Morelos, Mexico"}]},{"given":"Antonio","family":"Coronel-Escamilla","sequence":"additional","affiliation":[{"name":"Divisi\u00f3n Acad\u00e9mica de Mec\u00e1nica Industrial, Universidad Tecnol\u00f3gica Emiliano Zapata del Estado de Morelos, Emiliano Zapata 62765, Morelos, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1016\/j.rser.2017.08.060","article-title":"A comprehensive review on single phase heat transfer enhancement techniques in heat exchanger applications","volume":"81","author":"Alam","year":"2018","journal-title":"Renew. 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