{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:31:11Z","timestamp":1775539871609,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T00:00:00Z","timestamp":1617840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["No.62001115, 61903086"],"award-info":[{"award-number":["No.62001115, 61903086"]}]},{"name":"Fundamentals and Basic of Applications Research Foundation of Guangdong Province","award":["No.2019A1515110136"],"award-info":[{"award-number":["No.2019A1515110136"]}]},{"DOI":"10.13039\/501100010226","name":"Department of Education of Guangdong Province","doi-asserted-by":"publisher","award":["No.2019KTSCX193"],"award-info":[{"award-number":["No.2019KTSCX193"]}],"id":[{"id":"10.13039\/501100010226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Aiming at the problem of fault diagnosis in continuous time systems, a kind of fault diagnosis algorithm based on adaptive nonlinear proportional integral (PI) observer, which can realize the effective fault identification, is studied in this paper. Firstly, the stability and stability conditions of fault diagnosis method based on the PI observer are analyzed, and the upper bound of the fault estimation error is given. Secondly, the fault diagnosis algorithm based on adjustable nonlinear PI observer is designed and constructed, it is analyzed and we proved that the upper bound of fault estimation under this algorithm is better than that of the traditional method. Finally, the L-1011 unmanned aerial vehicle (UAV) is taken as the experimental object for numerical simulation, and the fault diagnosis method based on adaptive observer factor achieves faster response speed and more accurate fault identification results.<\/jats:p>","DOI":"10.3390\/a14040119","type":"journal-article","created":{"date-parts":[[2021,4,8]],"date-time":"2021-04-08T10:34:39Z","timestamp":1617878079000},"page":"119","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Fault Diagnosis Algorithm Based on Adjustable Nonlinear PI State Observer and Its Application in UAV Fault Diagnosis"],"prefix":"10.3390","volume":"14","author":[{"given":"Qing","family":"Miao","sequence":"first","affiliation":[{"name":"School of Mathematics and Big Data, Foshan University, Foshan 528225, China"}]},{"given":"Juhui","family":"Wei","sequence":"additional","affiliation":[{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Jiongqi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, Foshan University, Foshan 528225, China"},{"name":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Yuyun","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Big Data, Foshan University, Foshan 528225, China"},{"name":"Hi-Tech Research Institute, Hunan Institute of Traffic Engineering, Hengyang 421099, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s40032-021-00666-y","article-title":"A Review on Vibration-Based Fault Diagnosis Techniques for Wind Turbine Gearboxes Operating Under Nonstationary Conditions","volume":"102","author":"Sharma","year":"2021","journal-title":"J. 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