一类Van der Pol-Duffing系统的变结构滑模控制

Variable structure sliding mode control of a class of Van der Pol-Duffing system

研究了一类含有平方项和5次幂项的Van der Pol-Duffing系统的跟踪控制问题.首先,基于Lyapunov指数理论和分岔理论分析了该系统的复杂动力学行为,包括周期运动、倍周期分岔、混沌运动等;然后,在系统参数已知和未知的两种情况下,基于Lyapunov稳定性定理分别构造了两类简单的变结构滑模控制器对该系统的混沌行为进行跟踪控制,并均跟踪控制到了预期的运动状态.最后,利用数值仿真验证了上述两类滑模控制器对该系统跟踪控制的有效性.

Tracking control problem of a class of Van der Pol-Duffing system with square term and fifth power term is studied.Firstly,based on Lyapunov exponent theory and bifurcation theory,the complex dynamic behaviors of the system are analyzed,including periodic motion,period doubling bifurcation,chaotic motion,etc.Then,under two situations which are known parameters and unknown parameters of the system,two types of simple variable structure sliding mode controllers are constructed to track control the chaotic behavior of the system based on Lyapunov stability theorem,and make the system track control to the expected motion state.Finally,the effectiveness of two types of sliding mode controllers for tracking control of the Van der Pol-Duffing system is verified by numerical simulation.