Nonlinear analysis of a quasi-zero-stiffness vibration isolator with time-delayed position-velocity feedback control

Feedback control methods have been developed to enhance the isolation performance of quasi-zero-stiffness vibration isolators (QZS-VIs). Although most such methods can effectively suppress vibrations within the resonant region, they degrade the isolation performance in the isolation region. Moreover, most feedback control methods are sensitive to time delay, and optimal control performance can only be achieved under specific delay values. To overcome the above dilemmas, a novel position-velocity feedback control method is proposed. First, a mathematical model of the controlled QZS-VI system is established. The steady-state solutions are obtained analytically by applying the averaging method, and their stability is thoroughly analyzed. Then, the effect of feedback parameters on the frequency response is revealed, and the phenomenon of frequency island is discovered. The basis for selecting feedback parameters is also provided. Finally, the force transmissibility of the proposed controlled QZS-VI system is analyzed and compared with those under classic feedback control methods. The control effects of the proposed feedback control are illustrated from the perspective of equivalent damping ratio. The results demonstrate that the proposed position-velocity feedback control can attenuate vibration in the resonant region or eliminate jump phenomenon without sacrificing isolation performance in the isolation region. When well-tuned feedback gains are adopted, the control performance of the controlled system is weakly sensitive to time delays within a certain range.