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Shock and Vibration
Volume 2016, Article ID 2689178, 14 pages
http://dx.doi.org/10.1155/2016/2689178
Research Article

Modelling and Composite Control of Single Flexible Manipulators with Piezoelectric Actuators

1School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China
2School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000, China

Received 11 July 2016; Accepted 23 August 2016

Academic Editor: Salvatore Russo

Copyright © 2016 En Lu 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.

Abstract

The piezoelectric actuators are used to investigate the active vibration control of flexible manipulators in this paper. Based on the assumed mode method, piezoelectric coupling model, and Hamilton’s principle, the dynamic equation of the single flexible manipulator (SFM) with surface bonded actuators is established. Then, a singular perturbation model consisted of a slow subsystem and a fast subsystem is formulated and used for designing the composite controller. The slow subsystem controller is designed by fuzzy sliding mode control method, and the linear quadratic regulator (LQR) optimal control method is used to design fast subsystem controller. Furthermore, the changing trends of natural frequencies along with the changes in the position of piezoelectric actuators are obtained through the ANSYS Workbench software, by which the optimal placement of actuators is determined. Finally, numerical simulations and experiments are presented. The results demonstrate that the method of optimal placement is feasible based on the maximal natural frequency, and the composite controller presented in this paper can not only realize the trajectory tracking of the SFM and has a good result on the vibration suppression.