Resonance behavior in coupled Van der Pol harmonic oscillators with controllers and delayed feedback

Abstract

It has been revealed in the proposed work that a pair of delay positive position feedback control can lessen the vibration response of double Van der Pol oscillators with external forces. We also studied the effects of both the control and the delayed feedback signal gains to illustrate the low vibration amplitudes. The averaging perturbation process has been used to consider the frequency-response equations of amplitudes and modulation phases at the primary resonance and one-to-one internal resonances. According to the perturbation solutions for the four-degrees-of-freedom system, we presented the frequency response curves that were periodic in the time delays. The stability analysis presented in this study has shown optimum stable ranges. If the time delays increase, the steady-state amplitudes of the oscillator’s system will periodically result in few stable regions and more unstable ones. The numerical simulation has been introduced to check the analytical approximation. It was also found to be almost identical after presenting the comparison of the results.