Boundary control of an axially moving system with high acceleration/deceleration and disturbance observer

In this article, a boundary control with disturbance observer is presented for vibration reduction of an axially moving belt system. After taking into account the dynamics of high acceleration/deceleration and spatiotemporally-varying distributed disturbance, the hybrid dynamic model of the belt system is described by a nonhomogeneous hyperbolic partial differential equation and two ordinary differential equations. Based on Lyapunov's synthesis method, a boundary control is designed to reduce the vibration of the belt. A disturbance observer is proposed to attenuate the effects of unknown boundary disturbance and the S-curve acceleration/deceleration method is introduced to regulate the speed of the belt system. With the proposed boundary control, the uniform boundedness and stability of the closed-loop system are demonstrated via Lyapunov's synthesis method, and the control spillover problems are also avoided. Simulation results are provided to illustrate the effectiveness of the proposed control scheme.