{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T14:56:10Z","timestamp":1763564170963,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T00:00:00Z","timestamp":1621814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes an online direct closed-loop identification method based on a new dynamic sliding mode technique for robotic applications. The estimated parameters are obtained by minimizing the prediction error with respect to the vector of unknown parameters. The estimation step requires knowledge of the actual input and output of the system, as well as the successive estimate of the output derivatives. Therefore, a special robust differentiator based on higher-order sliding modes with a dynamic gain is defined. A proof of convergence is given for the robust differentiator. The dynamic parameters are estimated using the recursive least squares algorithm by the solution of a system model that is obtained from sampled positions along the closed-loop trajectory. An experimental validation is given for a 2 Degrees Of Freedom (2-DOF) robot manipulator, where direct and cross-validations are carried out. A comparative analysis is detailed to evaluate the algorithm\u2019s effectiveness and reliability. Its performance is demonstrated by a better-quality torque prediction compared to other differentiators recently proposed in the literature. The experimental results highlight that the differentiator design strongly influences the online parametric identification and, thus, the prediction of system input variables.<\/jats:p>","DOI":"10.3390\/s21113653","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T23:35:05Z","timestamp":1621899305000},"page":"3653","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Software Sensor to Enhance Online Parametric Identification for Nonlinear Closed-Loop Systems for Robotic Applications"],"prefix":"10.3390","volume":"21","author":[{"given":"Lilia","family":"Sidhom","sequence":"first","affiliation":[{"name":"Laboratory of Energy Applications and Renewable Energy Efficiency (LAPER), El Manar University, Tunis 1068, Tunisia"},{"name":"National Engineering School of Bizerta, Carthage University, Tunis 7080, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ines","family":"Chihi","sequence":"additional","affiliation":[{"name":"Laboratory of Energy Applications and Renewable Energy Efficiency (LAPER), El Manar University, Tunis 1068, Tunisia"},{"name":"National Engineering School of Bizerta, Carthage University, Tunis 7080, Tunisia"},{"name":"D\u00e9partement Ing\u00e9nierie, Campus Kirchberg, Facult\u00e9 des Sciences, des Technologies et de M\u00e9decine, Universit\u00e9 du Luxembourg, 1359 Luxembourg, Luxembourg"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6846-2090","authenticated-orcid":false,"given":"Ernest Nlandu","family":"Kamavuako","sequence":"additional","affiliation":[{"name":"Department of Engineering, King\u2019s College London, London WC2R 2LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nelles, O. 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