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Shock and Vibration
Volume 2014, Article ID 953694, 10 pages
Research Article

Active Vibration Suppression of a 3-DOF Flexible Parallel Manipulator Using Efficient Modal Control

State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 1 May 2014; Accepted 20 June 2014; Published 20 October 2014

Academic Editor: Jeong-Hoi Koo

Copyright © 2014 Quan 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 addresses the dynamic modeling and efficient modal control of a planar parallel manipulator (PPM) with three flexible linkages actuated by linear ultrasonic motors (LUSM). To achieve active vibration control, multiple lead zirconate titanate (PZT) transducers are mounted on the flexible links as vibration sensors and actuators. Based on Lagrange’s equations, the dynamic model of the flexible links is derived with the dynamics of PZT actuators incorporated. Using the assumed mode method (AMM), the elastic motion of the flexible links are discretized under the assumptions of pinned-free boundary conditions, and the assumed mode shapes are validated through experimental modal test. Efficient modal control (EMC), in which the feedback forces in different modes are determined according to the vibration amplitude or energy of their own, is employed to control the PZT actuators to realize active vibration suppression. Modal filters are developed to extract the modal displacements and velocities from the vibration sensors. Numerical simulation and vibration control experiments are conducted to verify the proposed dynamic model and controller. The results show that the EMC method has the capability of suppressing multimode vibration simultaneously, and both the structural and residual vibrations of the flexible links are effectively suppressed using EMC approach.