Boundary control of an axially moving belt

In this paper, vibration reduction of an axially moving belt system is studied by using boundary control method and Lyapunov´s direct method. To achieve more accurate and practical dynamic behavior of the moving belt system, the effects of time-varying speed is considered in belt´s dynamic model, which is modeled by a partial differential equations coupled with ordinary differential equations involving functions of space and time. Boundary controller is designed at the right boundary of the axially moving belt system based on Lyapunov´s direct method to reduce the belt´s vibrations. The uniform boundedness and closed-looped stability are proved based on proposed boundary control. Simulation results verify the effectiveness of the proposed boundary control.