Transverse vibration control of axially moving string system by linear backward

Vibration control of an axially moving string system consisting of a controlled span coupled to a tensioner is investigated. 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 a force applied to the tensioner, and the constrained point is considered as the right boundary of the control span. The energy method is employed to design the controlled law for ensuring the vibration reduction of the controlled span, and the asymptotic exponential stability of the closed loop system under the boundary control is proved with semigroup theory. 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.