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Shock and Vibration
Volume 2014 (2014), Article ID 172570, 9 pages
Research Article

Experimental Verifications of Vibration Suppression for a Smart Cantilever Beam with a Modified Velocity Feedback Controller

1The State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China
2Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China

Received 5 August 2013; Accepted 21 January 2014; Published 27 February 2014

Academic Editor: Mohammad Elahinia

Copyright © 2014 Ting Zhang et al. 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.


This paper presents various experimental verifications for the theoretical analysis results of vibration suppression to a smart flexible beam bonded with a piezoelectric actuator by a velocity feedback controller and an extended state observer (ESO). During the state feedback control (SFC) design process for the smart flexible beam with the pole placement theory, in the state feedback gain matrix, the velocity feedback gain is much more than the displacement feedback gain. For the difference between the velocity feedback gain and the displacement feedback gain, a modified velocity feedback controller is applied based on a dynamical model with the Hamilton principle to the smart beam. In addition, the feedback velocity is attained with the extended state observer and the displacement is acquired by the foil gauge on the root of the smart flexible beam. The control voltage is calculated by the designed velocity feedback gain multiplied by the feedback velocity. Through some experiment verifications for simulation results, it is indicated that the suppressed amplitude of free vibration is up to 62.13% while the attenuated magnitude of its velocity is up to 61.31%. Therefore, it is demonstrated that the modified velocity feedback control with the extended state observer is feasible to reduce free vibration.