Time-Delayed Feedback Control Design and Its Application for Vibration Absorption

In this article, the vibration absorption performances of a vibration absorber with time-delayed feedback control for a low frequency primary system are studied. In order to extend the effective working frequency band of the time-delayed vibration absorber, its stiffness is designed as an adjustable parameter. The stiffness value of the beam-structure absorber can be tuned by a group of stoppers that can change the constraint condition of the beam. First, the mechanical model of the proposed delay-coupled system is established. Then, the stability boundaries of the proposed system are derived. Next, the analytical approximate solutions of the system are obtained to reveal the frequency response functions. Moreover, two parameter design principles for low-frequency nonlinear primary system are proposed based on the antiresonance frequency and optimum condition. The results show that, for the low-frequency nonlinear primary system, according to the design principles, the antiresonance frequency band can be tuned and the vibration amplitude can be reduced to zero due to the effect of time-delayed control. Relevant experimental prototype is constructed to verify the efficacy of the proposed vibration absorber with time-delayed control.