{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T02:30:41Z","timestamp":1777084241165,"version":"3.51.4"},"reference-count":53,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,10,31]],"date-time":"2021-10-31T00:00:00Z","timestamp":1635638400000},"content-version":"vor","delay-in-days":303,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFB1307203"],"award-info":[{"award-number":["2018YFB1307203"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002822","name":"Central South University","doi-asserted-by":"publisher","award":["ZZYJKT2021-17"],"award-info":[{"award-number":["ZZYJKT2021-17"]}],"id":[{"id":"10.13039\/501100002822","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The dynamic characteristics of the mechanical arm with a rigid\u2010flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid\u2010flexible coupling. So, accurately positioning and controlling the rigid\u2010flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid\u2010flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high\u2010dimensional solution of the vibration equation of the rigid\u2010flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin\u2019s method, the system is simplified and the approximate solution is obtained through the interaction between high\u2010order and low\u2010order modes. The truncated finite mode is also used to construct a lowest\u2010order dynamic model on the basis of approximate inertia manifold. Given the reduced\u2010order rigid\u2010flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid\u2010flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.<\/jats:p>","DOI":"10.1155\/2021\/8290978","type":"journal-article","created":{"date-parts":[[2021,10,31]],"date-time":"2021-10-31T16:35:08Z","timestamp":1635698108000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Approximate Inertial Manifold\u2010Based Model Reduction and Vibration Suppression for Rigid\u2010Flexible Mechanical Arms"],"prefix":"10.1155","volume":"2021","author":[{"given":"Lisha","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hua","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chong","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3398-992X","authenticated-orcid":false,"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,10,31]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsmc.2018.2882734"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1177\/1077546315607694"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2017.05.022"},{"key":"e_1_2_10_4_2","first-page":"1","article-title":"Composite sliding mode control for a free-floating space rigid-flexible coupling mechanical arm system","volume":"124","author":"Congqing W.","year":"2013","journal-title":"International Journal of Advanced Robotic Systems"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/7333.918283"},{"key":"e_1_2_10_6_2","doi-asserted-by":"crossref","unstructured":"KumarR. 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