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Shock and Vibration
Volume 2015, Article ID 769151, 9 pages
Research Article

Virtual Constraints Based Control Design of an Inclined Translational Oscillator with Rotational Actuator System

1School of Electrical Engineering, Southeast University, Nanjing 210096, China
2Jiangsu Key Laboratory of Smart Grid Technology and Equipment, Nanjing 210096, China
3School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

Received 16 April 2015; Revised 12 July 2015; Accepted 21 July 2015

Academic Editor: Georges Kouroussis

Copyright © 2015 Bingtuan Gao 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.


Translational oscillator with rotational actuator (TORA) system, whose translational and rotational movements occur in horizontal planes, is a benchmark of underactuated mechanical systems for studying of control techniques. Currently, the research work of the benchmark mainly focuses on stabilizing control of equilibrium points of the dynamical system. The problem of steering TORA to arbitrary points in its state space is rarely studied. In this paper, the movements of the TORA system are extended to inclined planes and dynamics of the inclined TORA system is presented firstly. Following that, a trajectory tracking control method based on virtual constraints is proposed to steer the oscillations of the inclined TORA system. A virtual constraints based method is presented to generate periodic trajectories which pass through desired point; and a Lyapunov based control design is proposed to track the generated trajectories. Finally, the performance and feasibility of the proposed control design methodology are illustrated and analyzed according to numerical simulations.