A method for time delay vibration control of the principal and fundamental resonances of two nonlinearly coupled van der Pol oscillators is investigated Using the asymptotic perturbation method, four slow-flow equations on the amplitude and phase of the oscillators are obtained. Their fixed points correspond to a two-period quasi-periodic phase-locked motion for the original system. In the system without control, stable periodic solutions (if any) exist only for fixed values of amplitude and phase and depend on the system parameters and excitation amplitude. In many cases, the amplitudes of these solutions do not correspond to the technical requirements. On the contrary, it is demonstrated that, if vibration control terms are added, stable two-period quasi-periodic solutions with arbitrarily chosen amplitudes can be accomplished. Therefore, an effective vibration control is possible if appropriate time delay and feedback gains are chosen.
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January 2011
Research Papers
Time Delay Control for Two van der Pol Oscillators
Attilio Maccari
Attilio Maccari
Via Alfredo Casella 3, 00013 Mentana, Rome, Italy
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Attilio Maccari
Via Alfredo Casella 3, 00013 Mentana, Rome, Italy
J. Comput. Nonlinear Dynam. Jan 2011, 6(1): 011016 (7 pages)
Published Online: October 7, 2010
Article history
Received:
October 20, 2009
Revised:
March 21, 2010
Online:
October 7, 2010
Published:
October 7, 2010
Citation
Maccari, A. (October 7, 2010). "Time Delay Control for Two van der Pol Oscillators." ASME. J. Comput. Nonlinear Dynam. January 2011; 6(1): 011016. https://doi.org/10.1115/1.4002390
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