Boundary Control of an Axially Moving System with High Acceleration/Deceleration

Abstract

Generally, the dynamics of an axially moving belt are modeled by a group of PDEs and a set of boundary conditions, which are described by ODEs. This hybrid dynamic model is difficult to control due to the infinite dimensionality of the system. The most conventional approach for the control design of axially moving belt system is the modal control approach based on truncated finite-dimensional model. But the vital disadvantage of the modal control approach is control spillover phenomenon because of the effects of residual mode and unmodeled mode, which are excluded in the truncated finite-dimensional model. The boundary control approach is much more practical than the modal control approach in sense that it excludes the spillover phenomenon. Thus, in recent years, the boundary control has been widely used to suppress vibration of the flexible structure systems, such as flexible riser, string, beam, and especially in the area of axially moving structure. In this chapter, the boundary control design via Lyapunov’s direct method is discussed, in which the uniform boundedness of closed-loop system is guaranteed under disturbance. Finally, the numerical simulation with the finite difference method is presented to verify the validity of the proposed controller.