Using the delayed feedback to control the vibration of the auto-parametric dynamical system

The delayed feedback control is applied to suppress the vibration of the primary system in an auto-parametric dynamical system. The multiple scale method is employed to obtain the range of the saturation control when the system is excited by the harmonic vibration. The delayed feedback control is used to control the vibration of the primary system when the system is in saturation control. The effects of the gain and delay on the vibration suppression of the primary system are analyzed. The results show that the vibration of the primary system can be suppressed at some values of the gain and delay. As the delay varies for a fixed gain, it is seen that the vibration of the primary system can be suppressed at some values of the delay. There is a maximum vibration suppression point at these values of delay, where the amplitude of the primary system can be suppressed to a minumum value. As the gain increases, the performance of the vibration suppression is improved at the maximum vibration suppression point. It implies that if the suitable delay and gain are achieved the vibration of the primary system almost could be suppressed to zero.