Stability and time-delayed feedback control of a relative-rotation nonlinear dynamical system under quasic-periodic parametric excitation

Abstract

The dynamical equation of a relative-rotation nonlinear dynamic system, which contains quasi-periodic parametric excitation and time delays, is established. Bifurcation response equation of 1/2 subharmonic primary parametric resonance is obtained by the method of multiple scales, and the stability of the system is analyzed. By solving the steady state solutions of the uncontrolled system, the effect of quasi-periodic parametric excitation on system response is studied through discussing the dynamics of the system. Time-delay feedback control method is used to control the bifurcation and limit cycle(region). Numerical results show that the bifurcation and the stability of the limit cycle(region) are controlled effectively by changing the time-delay parameters.