Stabilization of an axially moving accelerated/decelerated system via an adaptive boundary control

In this study, an adaptive boundary control is developed for vibration suppression of an axially moving accelerated/decelerated belt system. The dynamic model of the belt system is represented by partial-ordinary differential equations with consideration of the high acceleration/deceleration and unknown distributed disturbance. By utilizing adaptive technique and Lyapunov-based back stepping method, an adaptive boundary control is proposed for vibration suppression of the belt system, a disturbance observer is introduced to attenuate the effects of unknown boundary disturbance, the adaptive law is developed to handle parametric uncertainties and the S-curve acceleration/deceleration method is adopted to plan the belt׳s speed. With the proposed control scheme, the well-posedness and stability of the closed-loop system are mathematically demonstrated. Simulations are displayed to illustrate the effectiveness of the proposed control.