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Abstract This paper is concerned with disturbance rejection control for a vibrating flexible string system in the presence of unknown disturbances. First, 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. Subsequently, the boundary control and distributed control are developed to suppress the vibration and globally stabilize the string system at its equilibrium position. Under the control proposed, the uniformly bounded stability of the controlled system is testified employing rigorous analysis without resorting to discretization of the partial differential equation dynamics depending on the time and space. Finally, the simulation and comparison results verify the performance of the derived control.
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