准零刚度隔振系统吸引子迁移控制研究

Attractor migration control of a vibration isolation system with quasi zero stiffness

以准零刚度隔振系统为对象,建立动力学模型,画出分岔图研究吸引子共存现象,并利用点映射方法分析共存吸引子的吸引域。在共存吸引子的吸引域之间建立一条目标轨道,分别采用开环、闭环和开环加闭环控制方法使系统迁移至目标轨道,实现系统吸引子迁移控制。同时,对开环加闭环控制方法的稳定性和可行性进行了分析。仿真结果表明:该系统同时存在两个稳定的不同振幅的周期1吸引子,开环和闭环控制方法难以使系统迁移至目标轨道,无法实现吸引子迁移控制;开环加闭环控制可使系统沿着目标轨道在两个周期1吸引子的吸引域之间进行迁移,当其运行在较大振幅的周期1吸引子上时,可控制系统迁移至较小振幅的周期1吸引子上,从而实现减振降噪。该方法为提高非线性隔振系统的隔振效果提供了新的思路。

The dynamic model for a vibration isolation system with quasi zero stiffness was established. The phenomenon of attractor coexistence was studied by drawing a bifurcation diagram, and the corresponding attraction domains were also analysed. A target orbit was established between the coexisting attractors, and the open loop control, closed loop control, open plus closed loop control were adopted to migrate the system to the target orbit respectively, in order to achieve the attractor migration control. The stability and feasibility of the open plus closed loop control method was investigated. The simulation results show that： the system has two stable periodic 1 attractors with different amplitudes. The open loop control method and closed loop control method are difficult to migrate the system to the target orbit, while the open plus closed loop control can make the system migrate between the attractions of two periodic 1 attractors along the target orbit, so, the system can be migrated to the periodic 1 attractor with small amplitude when it operates on the periodic 1 attractor with large amplitude, and thus achieves the vibration and noise reduction. The method provides a new way to improve the vibration isolation effect of nonlinear vibration isolation systems.