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.