Transverse vibration control of axially moving web systems by regulation of axial tension

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