一类对称碰撞系统的间歇混沌控制方法

An Intermittent Chaos Control Method for a Class of Symmetric Impact Systems

研究了对称碰撞系统的间歇混沌控制方法,将Hopf分岔控制思想应用于该系统上,对该类系统的混沌控制提供一个新的控制方法.这里以两自由度弹性双碰系统为探究对象,首先,建立两自由度弹性双碰系统的力学模型,并根据其运动特点将其分成4个阶段,建立了合适的Poincaré映射;然后,取定一个合适的定相位面,施加间歇线性控制律,并构建施加控制后的映射,根据映射的稳定性判据得到该系统混沌控制的显式条件;最后,分别对原系统和控制系统进行了数值模拟.计算结果表明,该控制方法能够很好地控制原系统的混沌运动,实现了预期目的,验证了该控制方法在弹性系统上的有效应用.该控制方法有利于提高系统的运行稳定性和使用寿命,具有一定的实际意义.

An intermittent chaos control method for symmetric impact systems was studied. The Hopf bifurcation control was applied to make a new control method for chaos control of such systems. The 2-DOF elastic double-impact system was considered. Firstly,the mechanical model for the 2-DOF system was built and its motion was divided into 4 stages according to the dynamic characteristics. Then,an appropriate Poincaré mapping was established; a suitable fixed phase plane was chosen,a linear controller was applied to the section to get the mapping with control,and the chaotic control explicit condition was obtained according to the stability criterion. Finally,numerical analyses of the original system and the controlled system were carried out respectively. The numerical results show that,the proposed method controls the chaos movement of the original system well,to achieve the desired goal and verify the correctness of the method. The method,with practical significance,is helpful to improve the stability,working efficiency and service life of the system.