This article demonstrates the realization of angle tracking and deformation suppression by developing two boundary controllers for a flexible variable-length rotary crane arm with extraneous disturbances and asymmetric input-output constraints. The dynamic model description of this kind of crane arm system is several partial differential equations integrated into few ordinary differential equations. The S-curve acceleration and deceleration scheme is utilized to adjust the elongation rate of the arm. A kind of novel observer is put forward to tackle unknown extraneous disturbances. Auxiliary systems and barrier Lyapunov functions are introduced to meet the asymmetric input-output constraints. With the help of Lyapunov's theory, the global exponential stability and uniform boundedness are analyzed. The numerical simulations are finally provided to illuminate its availability of the designed control schemes.

中文翻译：

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柔性可变长度旋转起重机臂的非对称输入输出约束控制。

本文通过开发两个带有外部干扰和不对称输入输出约束的可变长度旋转起重机臂的边界控制器，演示了角度跟踪和变形抑制的实现。这种起重机臂系统的动力学模型描述是将几个偏微分方程集成到几个常微分方程中。S曲线加减速方案用于调整臂的伸长率。提出了一种新颖的观察者来解决未知的外来干扰。引入辅助系统和屏障李雅普诺夫函数来满足非对称输入输出约束。借助李雅普诺夫理论，分析了全局指数稳定性和一致有界性。