In this work, we study the output tracking problem of an Euler–Bernoulli beam subject to non-collocated boundary controls and harmonic disturbances with unknown frequencies. We restructure the measurable tracking error by the auxiliary system and the internal model dynamic. An adaptive method is used to estimate the unknown parameters. Finally, we present an adaptive error-based dynamic compensator to realize tracking and compensate disturbance. The well-posedness and stability of closed-loop system are proved by employing the semigroup theory and energy multiplier method. In order to confirm the effectiveness of the proposed control schemes, the numerical simulations are presented.

在这项工作中，我们研究了欧拉-伯努利光束的输出跟踪问题，该光束受到非并置边界控制和谐波干扰和未知频率的影响。我们通过辅助系统和内部模型动态重构可测量的跟踪误差。自适应方法用于估计未知参数。最后，我们提出了一种基于自适应误差的动态补偿器来实现跟踪和补偿扰动。利用半群理论和能量乘数法证明了闭环系统的适定性和稳定性。为了确认所提出的控制方案的有效性，提出了数值模拟。