Boundary Control of an Axially Moving String Via Lyapunov Method
Boundary Control of an Axially Moving String Via Lyapunov Method
复制标题
DOI：
10.1115/1.2802425
复制
发表时间：
1999-03
影响因子：
1.7
通讯作者：
R. Fung;Chun-Chang Tseng
中科院分区：
文献类型：
--
作者：
R. Fung;Chun-Chang Tseng
本文研究了轴向运动弦线系统的振动主动控制问题，通过在其右侧边界处引入质量-阻尼-弹簧（MDS）控制器。用非线性偏微分方程描述分布参数系统，并直接将其作为被控对象。采用滑模控制方法结合李亚普诺夫方法设计了一种新的边界控制律。结果表明，边界反馈状态仅包括弦在RHS边界处的位移、速度和斜率。利用半群理论证明了控制系统的渐近稳定性。最后，用有限差分法对理论结果进行了验证.
This paper presents the active vibration control of an axially moving string system through a mass-damper-spring (MDS) controller at its right-hand side (RHS) bound-ary. A nonlinear partial differential equation (PDE) describes a distributed parameter system (DPS) and directly selected as the object to be controlled. A new boundary control law is designed by sliding mode associated with Lyapunov method. It is shown that the boundary feedback states only include the displacement, velocity, and slope of the string at RHS boundary. Asymptotical stability of the control system is proved by the semigroup theory. Finally, finite difference scheme is used to validate the theoretical results.