{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T15:22:45Z","timestamp":1777303365287,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T00:00:00Z","timestamp":1612310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Deanship of Scientific Research at King Saud University through research group number RG-1440-048","award":["RG-1440-048."],"award-info":[{"award-number":["RG-1440-048."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The nonlinear vibration control of a nonlinear dynamical system modeled as the well-known Duffing oscillators is investigated within this article. The conventional Positive Position Feedback (PPF) controller is proposed to mitigate the considered system nonlinear vibrations. The whole system mathematical model is analyzed by applying the multiple time scales perturbation method. The slow-flow modulation equations that govern the oscillation amplitudes of both the main system and controller are derived. The stability analysis is investigated based on Lyapunov\u2019s first method. The effects of the different control parameters on both the main system and controller are explored. The obtained analytical and numerical results illustrated that the PPF controller can eliminate the main system nonlinear vibrations once the controller natural frequency is tuned to be the same value as the external excitation frequency, otherwise, the controller adds excessive vibrational energy to the main system rather than suppressing it. In addition, the PPF controller can destabilize the main system motion when excited by strong excitation force. Therefore, a modified version of the PPF controller named the Adaptive Positive Position Feedback (APPF) controller is proposed to overcome the main drawbacks of the conventional PPF controller. The idea is to track the external excitation frequency using an adaptive frequency measurement technique to update continuously the PPF controller natural frequency to become the same value of the excitation frequency. Based on this strategy, the system mathematical model is analyzed again by making the controller\u2019s natural frequency equal to the external excitation frequency. The obtained analytical and numerical simulations showed that the adaptive positive position feedback controller can suppress the main system nonlinear vibration close to zero regardless of the excitation force amplitude and excitation frequency.<\/jats:p>","DOI":"10.3390\/sym13020255","type":"journal-article","created":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T20:31:51Z","timestamp":1612384311000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Adaptive versus Conventional Positive Position Feedback Controller to Suppress a Nonlinear System Vibrations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3275-2392","authenticated-orcid":false,"given":"N. A.","family":"Saeed","sequence":"first","affiliation":[{"name":"Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8115-4882","authenticated-orcid":false,"given":"Emad Mahrous","family":"Awwad","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia"},{"name":"Industrial Electronics and Control Engineering Department, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Talaat","family":"Abdelhamid","sequence":"additional","affiliation":[{"name":"Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt"},{"name":"Shenzhen Institutes of Advanced Technology, Chinese Academy of Science, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7967-4259","authenticated-orcid":false,"given":"Mohammed A.","family":"El-Meligy","sequence":"additional","affiliation":[{"name":"Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Sharaf","sequence":"additional","affiliation":[{"name":"Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1002\/(SICI)1099-1514(199604\/06)17:2<141::AID-OCA566>3.0.CO;2-D","article-title":"Short communications optimal vibration control with modal positive position feedback","volume":"17","author":"Baz","year":"1996","journal-title":"Optim. Control Appl. 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