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Shock and Vibration
Volume 14, Issue 1, Pages 1-14

Cubic Velocity Feedback Control of High-Amplitude Vibration of a Nonlinear Plant to a Primary Resonance Excitation

Li Jun, Shen Rongying, and Hua Hongxing

Vibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Received 16 May 2005; Revised 10 December 2005

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


High-amplitude response suppression of the primary resonance of a nonlinear plant under cubic velocity feedback control is investigated. By means of the multiple scales method, two equations on the amplitude and phase of the response of the nonlinear system are obtained and the force-response and frequency-response curves are shown. The stability analyses for the open- and closed-loop responses of the system are carried out and the performance of the control strategy is investigated. The instantaneous power requirement of the control law is also examined. It can be demonstrated that appropriate choice for the feedback gain can greatly reduce the response amplitude of the primary resonance and completely eliminate the multiple responses. Finally the perturbation solutions are verified with numerical simulations.