分数阶单摆系统的自适应比例积分滑模同步  

Self-Adaptive Proportion Integral Sliding Mode Synchronization of Fractional-Order Simple Pendulum Systems

作　　者：程春蕊[1] 毛北行[1] CHENG Chun-rui;MAO Bei-xing(College of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450015,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450015

出　　处：《数学的实践与认识》2021年第17期216-221,共6页Mathematics in Practice and Theory

基　　金：国家自然科学青年基金(NSFC11801528)。

摘　　要：针对分数阶无阻尼和有阻尼的单摆系统,分别提出了一种新的自适应比例积分滑模控制方法.在分数阶微积分的基础上,引入了新的分数阶比例积分滑模面,并利用分数阶Lyapunov稳定性定理,证明了在滑模面上误差系统能够收敛到平衡点.为了保证滑模运动的发生设计了适当的自适应律,并证明了所提出的自适应比例积分滑模控制方法在到达阶段具有收敛性,在滑模阶段具有稳定性.最后,通过数值算例验证了所提方案是有效的.A new adaptive proportional integral sliding mode control method is proposed for fractional order undamped and damped pendulum systems.Based on fractional calculus,a new fractional integral sliding mode surface is introduced,and its convergence to the zero equilibrium is proved using the fractional Lyapunov stability theorem.On this basis,an appropriate adaptive law is designed to ensure the sliding mode motion of the system,and the convergence and stability of the proposed adaptive proportional integral sliding mode control method are proved in both reaching and sliding mode phases.Finally,Numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.

关 键 词：分数阶系统 滑模 单摆系统 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]