Control of Axially Moving Systems: A Review

This paper presents a comprehensive review of significant works on active vibration control of axially moving systems. Owing to their broad applications, vibration suppression techniques for these systems have generated active research over decades. Mathematical equations for five different models (i.e., string, beam, coupled, plate, and approximated model) are outlined. Active vibration control of axially moving systems can be performed based on a finite-dimensional model described by ordinary differential equations (ODEs) or an infinite-dimensional model described by partial differential equations (PDEs). For ODE models, the sliding mode control is most representative. For PDE models, however, there exist various methods, including wave cancellation, Lyapunov method, adaptive control, and hybrid control. Control applications (lifting systems, steel industry, flexible electronics, and roll-to-roll systems) are also illustrated. Finally, several issues for future research in vibration control of axially moving systems are discussed.