Investigation of the time delay effect on the control of rotating blade vibrations

In this paper, a time-delayed positive position feedback (PPF) controller is applied to reduce the nonlinear oscillations of the dynamical system of a rotating blade. The main system is coupled to the controller whose natural frequency is approximately equal to the natural frequency of the main system. The main system has two oscillatory modes that are found to be powerfully linearly coupled. The approximate nonlinear dynamical behavior is studied and analyzed by applying the multiple time scales method. The effects of the time delay are investigated to indicate the safe region of operation. Time history and different curves are included to show the effectiveness of the controller. Eventually, validation curves are given to estimate the degree of closeness between the analytical and numerical solutions.