Control of Erosion of Safe Basins in a Softening Duffing Oscillator by Velocity Delayed Feedback

Huilin Shang

Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (5) : 54-58.

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PDF(1672 KB)
Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (5) : 54-58.
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Control of Erosion of Safe Basins in a Softening Duffing Oscillator by Velocity Delayed Feedback

  • Huilin Shang

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Abstract

Abstract: In order to apply delayed feedback controlling the erosion of safe basins in nonlinear systems, a softening Duffing oscillator is considered in the paper as an example, a linear delayed velocity feedback is induced to the system, and the effects of delayed velocity feedback on controlling the basin erosion are investigated. Firstly, the condition of fractal erosion of safe basin’s boundary of the delayed controlled system is obtained by the Melnikov method. Then considering time delay as a variable parameter and employing the 4th-order Runge-Kutta and the Monte-Carlo methods, the evolutions of boundaries and area of safe basins with the delay are presented. It is found that the delayed velocity feedback can greatly affect the safe basin, and the erosion of safe basin can be reduced by the increase of the delay effectively. It follows that the delayed velocity feedback can be used as a good approach to control the erosion of safe basins.

Key words

softening Duffing oscillator / erosion of safe basin / time delay / feedback / fractal

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Huilin Shang. Control of Erosion of Safe Basins in a Softening Duffing Oscillator by Velocity Delayed Feedback[J]. Journal of Vibration and Shock, 2011, 30(5): 54-58
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