Boundary control of an axially moving accelerated/decelerated belt system

In this paper, a boundary controller with disturbance observer is proposed for the vibration suppression of an axially moving belt system. The model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations with consideration of the high-acceleration/deceleration and unknown spatiotemporally varying distributed disturbance. Applying the finite-dimensional backstepping control and Lyapunov's direct method, a boundary controller is developed to stabilize the belt system at the small neighborhood of its equilibrium position and a disturbance observer is introduced to attenuate the effect of unknown external disturbance. The S-curve acceleration/deceleration method is adopted to plan the speed of the belt. With the proposed control scheme, the spillover instability problems are avoided, the uniform boundedness and the stability of the closed-loop belt system can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme.