开放系统中多步化学反应的混沌及控制

Chaos analysis and control of multi-step chemical reaction in open system

为了更好地控制化学系统中的混沌,以Willamowski-Rssler模型所对应的量纲一动力演化方程为研究对象,进行了复杂动力学特征分析,包括相轨迹图、Lyapunov指数和庞加莱映射图,这些特征都表明该三维动力系统含有混沌吸引子,同时也加深了对系统中复杂行为的认识。以LaSalle恒定性原理为基础,通过线性变换设计了一种只含1个控制项的控制器,理论推导和数值模拟都表明该控制器能够将Willamowski-Rssler系统的混沌态有效地消除,且稳定于一个平衡点,结果表明了化学工程中混沌的可控性和该方法的有效性。

In order to control the chaos in chemistry system well,taking the dynamic evolutional equation of dimensional one as study objective,the complex dynamics characteristics of Willamowski-Rssler model were analyzed,including phase diagram,Lyapunov exponent,Poincaré diagram.All of the above characteristics can prove that there is chaos Abstractor in the three-dimension dynamic system,and provide a better understanding for complex behavior.A new controller with only one term was proposed through linear transformation based on LaSalle theory.Theoretical analysis and numerical simulation show that the controller can effectively eliminate the chaos of Willamowski-Rssler system,and stabilize the system at a balance point.Therefore,the results show that chaos in chemistry is controllable,and the controlling method is effective.