Journal of South China University of Technology (Natural Science Edition) ›› 2013, Vol. 41 ›› Issue (2): 24-29,43.doi: 10.3969/j.issn.1000-565X.2013.02.005

• Electronics, Communication & Automation Technology • Previous Articles     Next Articles

Vibration Control of Flexible Beam Based on Lyapunov Direct Method

Liu Yu1 Huang Hao-wei1 Wu Yi-lin2 Wu Xin-sheng1   

  1. 1. School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, Guangdong, China;2. Department of Computer Science, Guangdong University of Education, Guangzhou 510310, Guangdong, China
  • Received:2012-07-13 Revised:2012-11-09 Online:2013-02-25 Published:2013-01-05
  • Contact: 吴忻生(1961-),男,副教授,主要从事自动化技术和智能控制系统研究. E-mail:auxswu@scut.edu.cn
  • About author:刘屿(1977-),男,博士,助理研究员,主要从事分布参数系统控制研究.E-mail:auylau@scut.edu.cn
  • Supported by:

    国家自然科学基金资助项目(61203060);广东省自然科学基金资助项目(S2011040005707,S2012010008462);高等学校博士学科点专项科研基金资助项目(20120172120033);华南理工大学中央高校基本科研业务费专项资金资助项目(2011ZZ0020)

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Abstract:

In order to avoid control spillover and implement real-time control of the system, a proportional-deriva-tive (PD) boundary controller is proposed for the active vibration control of a flexible beam with unknown boundary disturbance and varying tension. The proposed controller, which is based on the infinite-dimensional distributed pa-rameter model of the flexible beam, employs the boundary control technique and Lyapunov's direct method to re-duce the beam vibration. With the proposed boundary control method, uniform boundary and exponential stabilityare both achieved under external disturbances. The proposed PD controller is simple and is independent of the pa-rameters of the flexible beam system. Moreover, it ensures the real-time and robust control of the system. Simula-tion results indicate that the proposed control method effectively suppresses the vibration of the beam and reduces the vibration amplitude as well.

Key words: flexible structures, vibration, boundary control, Lyapunov functions, stability