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Dr. Khalil Mohamed Khalil Mohamed :: Publications:

Title:
The response of nonlinear controlled system under an external excitation via time delay state feedback
Authors: A M Elnaggar; K M Khalil
Year: 2014
Keywords: Nonlinear system; Multiple scales method; Saddle-node bifurcation; Primary resonance; Superharmonic resonance; Subharmonic resonance
Journal: Journal of King Saud University-Engineering Sciences
Volume: Not Available
Issue: Not Available
Pages: Not Available
Publisher: Not Available
Local/International: International
Paper Link:
Full paper Khalil Mohamed Khalil Mohamed_1-s2.0-S101836391400004X-main_2.pdf
Supplementary materials Not Available
Abstract:

An analysis of primary, superharmonic of order five, and subharmonic of order one-three resonances for non-linear s.d.o.f. system with two distinct time-delays under an external excitation is investigated. The method of multiple scales is used to determine two first order ordinary differential equations which describe the modulation of the amplitudes and the phases. Steady-state solutions and their stabilities in each resonance are studied. Numerical results are obtained by using the Software of Mathematica, which presented in a group of figures. The effect of the feedback gains and time-delays on the non-linear response of the system is discussed and it is found that: an appropriate feedback can enhance the control performance. A suitable choice of the feedback gains and time-delays can enlarge the critical force amplitude, and reduce the peak amplitude of the response (or peak amplitude of the free oscillation term) for the case of primary resonance (superharmonic resonance). Furthermore, a proper feedback can eliminate saddle-node bifurcation, thereby eliminating jump and hysteresis phenomena taking place in the corresponding uncontrolled system. For subharmonic resonance, an adequate feedback can reduce the regions of subharmonic resonance response.

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