Hybrid Time-Delayed Feedforward and Feedback Control of Lever-Type Quasi-Zero-Stiffness Vibration Isolators

Quasi-zero-stiffness (QZS) vibration isolators can achieve a considerable vibration isolation performance in the low-frequency range. However, the vibration isolation performance and stability would become worse under complex excitation environments, such as large strokes, uncertain excitation amplitudes, etc. This work proposes a hybrid time-delayed feedforward and feedback controller (HTD-FFC) to improve the broadband vibration isolation performance and stability of lever-type QZS (L-QZS) vibration isolators. The nonlinear governing equation of L-QZS vibration isolators with HTD-FFC is established and the corresponding frequency response relationship is derived by applying the harmonic balance method. The stability criterion is established. The effects of the time delay and gains of the time-delayed feedback controller (TD-FBC) and HTD-FFC are numerically and experimentally analyzed. Compared to the TD-FBC, the HTD-FFC with different time delays can efficiently suppress and even eliminate the peak transmissibility without seriously affecting the performance in the isolation region. The HTD-FFC not only improves the vibration isolation performance but also eliminates the unstable and chaotic behaviors to strengthen the robustness and stability of L-QZS vibration isolators. This article provides a time-delayed hybrid control approach to improve the vibration performance and stability of QZS vibration isolators.