Boundary and distributed control for a vibrating string system

In this article, our aim lies in the design of control schemes for suppressing the vibration of a flexible string system in the presence of external disturbances. To this end, the boundary and distributed controllers are developed to globally stabilize the string system at small neighbor region around the origin. Besides, the boundary disturbance observer is proposed to deal with the boundary disturbance, and the infinite dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. Under the control proposed, the bounded stability of the controlled system is testified employing rigorous analysis without resorting to discretization of the system infinite-dimensional model. Finally, the simulations confirm the efficiency of our conclusion.