This paper addresses the boundary stabilization problem of a Timoshenko beam system with a tip mass under the external disturbance at the control end. Applying the idea of active disturbance rejection control, time-varying high-gain observers are designed to estimate the disturbances, and continuous anti-disturbances feedback controllers are developed. By choosing a suitable time-varying function, the disturbance error estimations can converge exponentially to zero. The well posedness of the closed-loop system is proved using the semigroup theory. With the proposed controllers, the exponential stability of the closed-loop system is demonstrated by constructing appropriate Lyapunov functional. A numerical simulation is given to illustrate the effectiveness of the proposed control strategy.

中文翻译：

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在未知非均匀有界扰动下具有尖端质量的Timoshenko梁系统的稳定性

本文讨论了在控制端受到外部干扰的情况下，带有尖端质量的蒂莫申科梁系统的边界稳定问题。应用主动干扰抑制控制的思想，设计了时变高增益观测器来估计干扰，并开发了连续的抗干扰反馈控制器。通过选择合适的时变函数，干扰误差估计可以指数收敛至零。利用半群理论证明了闭环系统的适定性。利用所提出的控制器，通过构造适当的Lyapunov函数来证明闭环系统的指数稳定性。数值仿真表明了所提出的控制策略的有效性。