Transverse Vibration Control of Axially Moving Web Systems by Regulation of Axial Tension

In this paper, an active control scheme to suppress the transverse vibrations of an axially moving web system by regulating its transport velocity to track a desired profile is investigated. The spatially varying tension and the time-varying transport velocity of the moving web are inter-related. The system dynamics includes the equations of motion of the moving web and the dynamics of the drive rollers at boundaries of the web span. The two roller motors provide control torque inputs to the web system. The strategy for vibration control is the regulation of the axial tension in reference to a designed profile, so that the vibration energy of the moving web system decays. The designed profile for the axial tension is designed via the total mechanical energy of the axially moving web system. The Lyapunov method is employed to derive the model-based torque control laws ensuring that the transverse vibration and the velocity tracking error converge to zero exponentially. The effectiveness of the proposed control scheme is demonstrated via numerical simulations.