Time-delayed positive position feedback control of nonlinear vibrations of continuous rotating shafts

Abstract

The objective of the present study is to suppress the large amplitudes of a continuous spinning shaft under an active vibration control. For this purpose, the Positive Position Feedback (PPF) control with time-delays are applied to the system via Macro-Fiber-Composite (MFC) sensors and actuators. The nonlinear dynamics of the system is explored analytically utilizing the perturbation method in the primary and one-to-one internal resonances. The steady state solutions of the system and controller in the Cartesian and polar forms are obtained. The effects of the controller gains and time delays on the stability and loci of bifurcations of the system are investigated. The controller shows its feasibility in controlling the system vibrations. Also, it is demonstrated that by increasing the controller gain coefficients the minimum amplitude regions of the system are increased. Furthermore, the safe boundary of the loop delays is studied. The results of the analytical approach are in good agreement with the numerical results of the original system of equations.