Adaptive vibration reduction of an axially moving string via a tensioner

Adaptive vibration control is investigated for axially moving strings with a tensioner. The tensioner is treated as an actuator. The Lyapunov analysis is employed to design a control law that asymptotically stabilizes the string. The proposed controller can estimate the parameters online. The Lyapunov stability guarantees the convergence of the transverse vibration of the controlled span of the string as well as the estimation error of the unknown parameters to zero. The proposed controller is numerically tested for the string under initial and external disturbances. Simulation results demonstrate the effectiveness of the controller.