{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T14:46:57Z","timestamp":1769525217954,"version":"3.49.0"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:00:00Z","timestamp":1649203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this research, a proportional integral derivative regulator, a first-order sliding-mode regulator, and a second-order sliding-mode regulator are compared, for the regulation of two different types of mathematical model. A first-order sliding-mode regulator is a method where a sign-mapping checks that the error decays to zero after a convergence time; it has the problem of chattering in the output. A second-order sliding-mode regulator is a smooth method to counteract the chattering effect where the integral of the sign-mapping is used. A second-order sliding-mode regulator is presented as a new class of algorithm where the trajectory is asymptotic and stable; it is shown to greatly improve the convergence time in comparison with other regulators considered. Simulation and experimental results are described in which an electric oven is considered as a stable linear mathematical model, and an inverted pendulum is considered as an asymmetrical unstable non-linear mathematical model.<\/jats:p>","DOI":"10.3390\/sym14040759","type":"journal-article","created":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T22:23:23Z","timestamp":1649370203000},"page":"759","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["The Regulation of an Electric Oven and an Inverted Pendulum"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0384-8616","authenticated-orcid":false,"given":"Ricardo","family":"Balcazar","sequence":"first","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2005-5979","authenticated-orcid":false,"given":"Jos\u00e9 de Jes\u00fas","family":"Rubio","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"given":"Eduardo","family":"Orozco","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"given":"Daniel","family":"Andres Cordova","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6261-4081","authenticated-orcid":false,"given":"Genaro","family":"Ochoa","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2875-0500","authenticated-orcid":false,"given":"Enrique","family":"Garcia","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2377-1639","authenticated-orcid":false,"given":"Jaime","family":"Pacheco","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"given":"Guadalupe Juliana","family":"Gutierrez","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, ESIME Azcapotzalco, Instituto Polit\u00e9cnico Nacional, Av. de las Granjas no. 682, M\u00e9xico City 02250, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8665-4096","authenticated-orcid":false,"given":"Dante","family":"Mujica-Vargas","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Tecnol\u00f3gico Nacional de M\u00e9xico\/CENIDET, Interior Internado Palmira S\/N, Cuernavaca 62490, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3925-2435","authenticated-orcid":false,"given":"Carlos","family":"Aguilar-Iba\u00f1ez","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Av. Juan de Dios B\u00e1tiz S\/N, Col. San Pedro Zacatenco, M\u00e9xico City 07738, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Huba, M., Chamraz, S., Bistak, P., and Vrancic, D. (2021). Making the PIand PID Controller Tuning Inspired by Ziegler and Nichols Precise and Reliable. Sensors, 21.","DOI":"10.3390\/s21186157"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Vrancic, D., and Huba, M. (2021). High-Order Filtered PID Controller Tuning Based on Magnitude Optimum. Mathematics, 9.","DOI":"10.3390\/math9121340"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Huba, M., and Vrancic, D. (2021). Extending the Model-Based Controller Design to Higher-Order Plant Models and Measurement Noise. Symmetry, 13.","DOI":"10.3390\/sym13050798"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Huba, M., Bistak, P., Vrancic, D., and Zakova, K. (2021). 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