{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T22:09:53Z","timestamp":1777932593812,"version":"3.51.4"},"reference-count":12,"publisher":"SAGE Publications","issue":"9-10","license":[{"start":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T00:00:00Z","timestamp":1188604800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:p>The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.<\/jats:p>","DOI":"10.1177\/1077546307077499","type":"journal-article","created":{"date-parts":[[2007,9,27]],"date-time":"2007-09-27T08:03:13Z","timestamp":1190880193000},"page":"1407-1418","source":"Crossref","is-referenced-by-count":48,"title":["Performance of Fractional PID Algorithms Controlling Nonlinear Systems with Saturation and Backlash Phenomena"],"prefix":"10.1177","volume":"13","author":[{"given":"Ramiro S.","family":"Barbosa","sequence":"first","affiliation":[{"name":"Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal,"}]},{"given":"J.A.","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal"}]},{"given":"Alexandra M.","family":"Galhano","sequence":"additional","affiliation":[{"name":"Institute of Engineering of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2007,9,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1049\/el:19930253"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-004-3763-7"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2006.02.005"},{"key":"atypb4","volume-title":"Proceedings of the Fifth EURMECH Nonlinear Dynamics Conference (ENOC'05)","author":"Lanusse, P."},{"issue":"1","key":"atypb5","first-page":"47","volume":"4","author":"Machado, J.A.T.","year":"2001","journal-title":"Fractional Calculus & Applied Analysis"},{"issue":"3","key":"atypb6","first-page":"147","volume":"8","author":"Manabe, S.","year":"1963","journal-title":"ETJ of Japan"},{"key":"atypb7","volume-title":"Proceedings of the 19th Biennial Conference on Mechanical Vibration and Noise (VIB'03)","author":"Manabe, S."},{"key":"atypb8","volume-title":"Feedback Control Systems","author":"Phillips, C.","year":"1996"},{"key":"atypb9","volume-title":"Fractional Differential Equations","author":"Podlubny, I.","year":"1999"},{"key":"atypb10","volume-title":"Applied Nonlinear Control","author":"Slotine, J.E.","year":"1991"},{"key":"atypb11","volume-title":"Mathematical Modeling and Digital Simulation for Engineers and Scientists","author":"Smith, J.M.","year":"1987","edition":"2"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2003.08.001"}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307077499","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307077499","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T01:24:22Z","timestamp":1777685062000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546307077499"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":12,"journal-issue":{"issue":"9-10","published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1177\/1077546307077499"],"URL":"https:\/\/doi.org\/10.1177\/1077546307077499","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"value":"1077-5463","type":"print"},{"value":"1741-2986","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9]]}}}