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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 691464, 9 pages
http://dx.doi.org/10.1155/2014/691464
Research Article

Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

1Dalian University of Technology, Dalian 116024, China
2State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China

Received 16 October 2013; Revised 20 November 2013; Accepted 21 November 2013; Published 29 January 2014

Academic Editor: Rongni Yang

Copyright © 2014 Qingkai Han 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 nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.