轴向运动弦线横向振动控制的Lyapunov方法

研究轴向运动弦线和作动器组成的耦合系统的横向振动控制．此系统被作动器分成未控和受控两部分,通过作用在作动器上的控制力对受控部分进行主动控制．分析未控弦线的横向振动的有界性．采用Lyapunov方法获得控制规律,并证实受控弦线横向振动的指数稳定性．在初始扰动和激励力作用下,通过数值仿真证实控制规律的有效性．

Transverse vibration control of an axially moving string system by Lyapunov method

Vibration control of an axially moving string system consisting of a controlled span coupled to a tensioner is investigated in this paper. The axially moving string system is divided into two spans, i.e., a controlled span and an uncontrolled span, by a tensioner located in the middle section of the string. The transverse vibration of the controlled span of the string is controlled by the control force acting on the tensioner, and the constrained point is considered as the right boundary of the controlled span. The Lyapunov method is then employed to design the controlled law for ensuring the vibration reduction of the controlled span, and the exponential stability of the closed loop system under the boundary control is also proved. Finally, results for the response of the controlled string under initial disturbance and excitations are presented, and the effectiveness of the controller is demonstrated by simulations.