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Prof. Abd Elrehim Mohamed Abdo Elnaggar :: Publications:

Title:
Control of the nonlinear oscillator bifurcation under a superharmonic resonance
Authors: A M Elnaggar; K M Khalil
Year: 2013
Keywords: Not Available
Journal: Journal of Applied Mechanics and Technical Physics
Volume: 54
Issue: 1
Pages: 34-43
Publisher: Not Available
Local/International: International
Paper Link:
Full paper Not Available
Supplementary materials Not Available
Abstract:

A weakly nonlinear oscillator is modeled by a differential equation. A superharmonic resonance system can have a saddle-node bifurcation, with a jumping transition from one state to another. To control the jumping phenomena and the unstable region of the nonlinear oscillator, a combination of feedback controllers is designed. Bifurcation control equations are derived by using the method of multiple scales. Furthermore, by performing numerical simulations and by comparing the responses of the uncontrolled system and the controlled system, we clarify that a good controller can be obtained by changing the feedback control gain. Also, it is found that the linear feedback gain can delay the occurrence of saddle-node bifurcations, while the nonlinear feedback gain can eliminate saddle-node bifurcations. Feasible ways of further research of saddle-node bifurcations are provided. Finally, we show that an appropriate nonlinear feedback control gain can suppress the amplitude of the steady-state response.

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