机械振动系统混沌化控制

根据混沌的本质，对工程中一类在周期激励力作用下的振动问题，将其动力字方程进行无量纲化后，采用传统的跟踪控制的方法，使其跟踪一种During系统从而混沌化。根据出现混沌的必要条件（M6lnikov判据）设计控制参数，对共振频率下和最大转速情况进行仿真计算，实现了在一定的频率范围内对振动系统进行混沌化的过程。将无控制和经过混沌化控制2种情况进行比较发现：在共振频率下，无控制情况下输出振幅是混沌化后输出振幅的近60倍，说明了这种混沌化控制方法对控制共振的有效性。

Chaotification for a mechanical vibration system

According to the nature of chaos, the mechanical system under period excitation is guided to a chaotic system by a traditional control method. After the dynamic equation is changed to a dimensionless one, it tracks a kind of Duffing system when a controller is added. The control parameter is selected according to Melnikov criterion. The numerical simulations show the effects of the method both at the resonance frequency and at the maximum frequency. The chaotification of the vibration system is realized within a certain range of frequency, Comparison shows if the chaotification control method is not used, the output amplitude of vibration could be about 60 times of that had been used. So the method is useful for avoiding resonance.