Analysis of Harmonically Forced Duffing Oscillator with Time Delay State Feedback by Incremental Harmonic Balance Method

Abstract

Periodic solutions of a harmonically forced Duffing oscillator with time-delay state feedback are investigated using the incremental harmonic balance method. In the process of solving, the explicit effect matrix of the time delay term was derived. The stability of the periodic solutions was determined by a method which combines the continuous time approximation and multivariable Floquet theory. On this basis, the frequency–amplitude response curve and stability characteristics of the primary resonance and the 1/3 subharmonic resonance were obtained. The stable results were compared with results obtained by the numerical method, which demonstrated the effectiveness and accuracy of the incremental harmonic balance method for the analysis of strongly nonlinear equations with time delays. The influence of the time delay and feedback control parameters on the primary and 1/3 subharmonic resonance is investigated. The periodicity of the effect of the time delay is also discussed.