This paper focuses on the boundary control of a Timoshenko beam with a tip mass in space. Compared with an Euler–Bernoulli beam model, the coupling of the Timoshenko beam’s transverse vibration and its cross-sectional rotation makes it difficult to develop the controller. The Timoshenko beam is essentially a distributed parameter system, the motion of which can be described using partial differential equations. A prescribed performance function is introduced to the boundary control strategy to guarantee the transient and steady tracking errors. By applying the proposed controller, the outputs are ultimately restricted within a small residual set, which is arbitrarily predefined, and the minimum convergence rate can be ensured. The stability of the boundary control is analyzed using the LaSalle’s invariance principle and the theoretical solutions of the Timoshenko beam model. Finally, the performance of the presented boundary controller is verified by numerical case studies.

中文翻译：

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具有规定性能的 Timoshenko 梁的边界控制

本文重点研究具有空间尖端质量的 Timoshenko 梁的边界控制。与 Euler-Bernoulli 梁模型相比，Timoshenko 梁的横向振动与其横截面旋转的耦合使得开发控制器变得困难。Timoshenko 梁本质上是一个分布参数系统，其运动可以用偏微分方程来描述。在边界控制策略中引入了规定的性能函数，以保证瞬态和稳态跟踪误差。通过应用所提出的控制器，输出最终被限制在一个任意预定义的小残差集内，并且可以确保最小收敛速度。利用LaSalle不变性原理和Timoshenko梁模型的理论解分析了边界控制的稳定性。最后，通过数值案例研究验证了所提出的边界控制器的性能。