Dynamical analysis and design theory for active bistable vibration isolators considering delay effect

Bistable vibration isolators (BVIs), which can undergo intra- and inter-well motions, have recently gained much attention as different motions can lead to different low-frequency isolation properties. To fully exploit the strength of BVIs, feedback actuation is injected into a classic three-spring-two-link bistable structure, and the classic PD control is applied to tune system's stiffness and damping. Moreover, the effect of the inevitable loop delay on BVI performance is considered. Operable regions of control parameters to maintain bistable characteristics and robustness regions where active BVIs are operable regardless of delay perturbations are determined. Besides, bistable dynamics, complicated by the transcendentality caused by delay, are investigated. By taking the BVI as phase zero, the number of variables to be solved is reduced, and an efficient frequency-sweeping-based calculation procedure is proposed. The BVI is evaluated by force and displacement transmissibility, showing that both intra- and inter-well motions benefit vibration isolation. For the former, the BVI yields broadband vibration isolation similar to conventional high-static-low-dynamics-stiffness vibration isolators. For the latter, an isolation valley can occur, resulting in exclusive ultra-low-frequency vibration isolation. Furthermore, properly tuning feedback actuation enhances the vibration isolation performance in both cases, and the often-overlooked loop delay can play a very positive role. Finally, the mechanism of isolation valley is qualitatively elucidated. The presented theories, including control stability analysis, delay-coupled nonlinear dynamical analysis, and beneficial parameter tuning, establish a basic design framework for active BVIs.