Jumps phenomenon elimination of a Duffing oscillator using pole placement control method

This paper presents a numerical and analytical study in the time-frequency domain to control the bifurcation and instability in a forced Duffing oscillator by a linear state feedback control. The proposed method evolves minimizing computational expenses of analytical approaches by an approximate method to suppress the responses of the dynamical system based on pole placement theory. The instability frequency range of Duffing oscillator is identified by approximate analytical methods. Bifurcation and jump points of Duffing oscillator are identified in the frequency domain by perturbation and harmonic balance methods for average and strong nonlinearity of the system, respectively. The Caughey method is used to linearize Duffing oscillator to solve system in the state space form. A linear state feedback controller with pole placement is applied to system in the time domain. The observed controlling force is added to approximate solution equation in frequency domain which vanished bifurcation length. The results reveal that the proposed method can be beneficial in reducing dynamic responses and eliminating jump points of system with high accuracy.