In this paper, the vibration control and input saturation constraint problem of an axially moving non-uniform system subject to unknown disturbances is investigated. The key control objectives are to control the vibration of the system and eliminate the effects of the input saturation constraint. To that end, a boundary control with an auxiliary system is designed by utilizing Lyapunov’s direct method. Additionally, a boundary disturbance observer is proposed to deal with the boundary disturbance, and an infinite-dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. With the designed boundary control, uniformly bounded stability of the controlled system is achieved through rigorous Lyapunov analysis without any model reduction. Finally, simulation results are given to show the effectiveness of the designed control scheme.
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