Noise- and delay-enhanced stability in a nonlinear isolation system

Abstract

In this paper, we present a detailed study of time-delayed feedback control of the nonlinear vibration isolation system driven by stochastic environmental fluctuations. We investigate the effects of time-delayed control force and nonlinear damping on the mean first passage time from the periodic attractors to reveal the complicated nonlinear stochastic dynamics of this system. Varying the intensities of noise sources, we find that the mean lifetime of the lower amplitude periodic attractor is characterized by nonmonotonic behavior as a function of the noise intensities. One remarkable behavior is the phenomenon of noise-enhanced stability has been carried out to evaluate the isolation performance of the controlled system. Moreover, the proper time delay value is obtained based on the consideration for the noise- and delay-enhanced stability. Finally, we observe that these transient properties are connected with the dynamics of time-delayed active control. Our analysis suggests that one form of the control force outperforms the other by many reasonable measures of control isolation effectiveness, which provides the guidance for optimizing time-delayed active control for stochastic fluctuations in engineering practices.