Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2767

Full Length Research Paper

The time delayed feedback control to suppress the vibration of the autoparametric dynamical system

Yasser A. Amer
  • Yasser A. Amer
  • Mathematics Department, Faculty of Science, Zagazig University, Egypt.
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Samira M. Soleman
  • Samira M. Soleman
  • Mathematics Department, Faculty of Science, EL-Zawya University, Libya.
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  •  Received: 13 March 2015
  •  Accepted: 15 July 2015
  •  Published: 15 August 2015

Abstract

The response of a dynamical system of two-degree-of-freedom with parametrically excited pendulum is solved and studied. The delayed feedback control is applied to suppress or stabilize the vibration of the system. The case of 1:2 sub-harmonic resonances between pendulum and primary system is studied; the method of multiple scales is applied to obtain second-order approximations of the response of the system. It is shown that the delayed feedback control can be used to suppress the vibration or stabilize the system when the saturation control is invalid, the vibration of the system can be suppressed by the delayed feedback control. The effect of delay on the suppression is discussed; the vibration of the system can be suppressed at some values of the delay.
 
Key words: Frequency response, delayed feedback control, multiple times scale, vibration suppression.