Analysis and suppression of the nonlinear oscillations of a continuous rotating shaft using an active time-delayed control

Abstract

This paper deals with reduction of oscillations of a continuous spinning shaft using proportional-derivative time delay controller. The stable and unstable zones of the system are obtained using the Routh-Hurwitz criteria. For small values of proportional coefficients, the Hopf bifurcation occurs in the high values of time delays while in the higher values of proportional coefficients instability occurs in the lower values. Also, in small values of derivative coefficients the Hopf bifurcation happens in the lower values of time delays, while in the higher values of derivative coefficients mentioned bifurcation occurs in the higher values.

Keywords:

• Active control
• time delay
• spinning shaft
• Hopf bifurcation
• nonlinear oscillation
• resonance analysis