Time-delayed control to suppress the nonlinear vibrations of a horizontally suspended Jeffcott-rotor system

Time-delay is an unavoidable phenomenon in active control systems. Measuring of the system states, processing of the measured signals, executing the control laws, conditioning and enforcing the control actions are the main reasons of time-delayed systems. This paper studies the vibration control of a horizontally suspended Jeffcott-rotor system having cubic and quadratic nonlinearities via time-delayed position-velocity controller. The intervals of the time-delays (τ1 and  τ2) at which the system response is stable has been studied. The τ1 − τ2 plane is constructed to illustrate the area at which the system solutions are stable. The influences of the controller gains on the stable-solutions area in τ1 − τ2 plane are explored. The analysis revealed that the time-delay increases the vibration amplitudes and can destabilize the system solution in the case of negative position feedback control, while at positive position feedback control it improves the vibration suppression performance. The time-delays mechanism in stabilizing and destabilizing the dynamical systems is explained. Then, we proposed a simple and concrete method to determine the optimal value for time-delays that can improve the vibrations suppression efficiency. The acquired analytical results are confirmed numerically and the optimal working conditions of the system are concluded. Finally, a comparison with the papers that published previously is included.