{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T04:29:47Z","timestamp":1777523387118,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T00:00:00Z","timestamp":1583107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>This paper presents a new strategy for the control of large displacements in structures under earthquake excitation. Firstly, an improved fractional order proportional-derivative (FOPD) controller is proposed. Secondly, a decentralized strategy is designed by adding a regulator and fault self-regulation to a standard decentralized controller. A new control architecture is obtained by combining the improved FOPD and the decentralized strategy. The parameters of the control system are tuned using an intelligent optimization algorithm. Simulation results demonstrate the performance and reliability of the proposed method.<\/jats:p>","DOI":"10.3390\/math8030326","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T07:50:53Z","timestamp":1583135453000},"page":"326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Improved Decentralized Fractional PD Control of Structure Vibrations"],"prefix":"10.3390","volume":"8","author":[{"given":"Kang","family":"Xu","sequence":"first","affiliation":[{"name":"College of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8110-5378","authenticated-orcid":false,"given":"Liping","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5680-5199","authenticated-orcid":false,"given":"Minwu","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Civil Engineering, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"additional","affiliation":[{"name":"UISPA\u2013LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"J. A.","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal"}]},{"given":"Houzhen","family":"Zhai","sequence":"additional","affiliation":[{"name":"The 29th research Institute of CETC, Chengdu 610036, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2850","DOI":"10.1177\/1077546319861009","article-title":"Study and control of thermoelastic damping of in-plane vibration of the functionally graded nano-plate","volume":"25","author":"Rahimi","year":"2019","journal-title":"J. Vib. 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