Nonlinear vibration control of an axially moving belt system by disturbance adaption

Abstract

In this paper, the modeling and vibration control problem of an axially moving belt with high acceleration/deceleration under unknown disturbances are addressed. The dynamic model of the belt system is represented by a nonhomogeneous hyperbolic partial differential equation and two ordinary differential equations. Boundary control with disturbance adaption is developed to stabilize the transverse vibration of an axially moving belt system. The S-curve acceleration/deceleration method is introduced to plan the axially moving speed of the belt. The stability and uniform boundedness of the system are proved via Lyapunov's direct method. Numerical simulations are given to validate the effectiveness of the control law.