SUMMARYThis paper studies the stabilization problem for a class of underactuated systems in the presence of unknown disturbances. Due to less number of control inputs with respect to the degrees of freedom of the system, closed-loop asymptotic stability is a challenging issue in this field. In this paper, anti-swing controllers are designed for nominal and disturbed systems. In the case of the nominal system, the proposed two-loop controller is a combination of collocated partial feedback linearization and hierarchical sliding mode control (HSMC) theories. Then, due to the importance of robustness in control of physical systems, the proposed controller is developed for underactuated mechanical systems in the presence of additive disturbances. One of the main advantages of the proposed design method is that it does not need any switching algorithm. Finally, to illustrate the performance of the proposed controllers, they are applied to two underactuated mechanical systems: a pendubot and a Furuta pendulum. In addition, the practicality of the proposed approach is also verified experimentally using a quadrotor stand.

中文翻译：

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一种稳定 2 自由度欠驱动机械系统的稳健方法

摘要本文研究了一类欠驱动系统在存在未知扰动时的稳定问题。由于相对于系统自由度的控制输入数量较少，闭环渐近稳定性是该领域的一个具有挑战性的问题。在本文中，反摆动控制器是为标称和受扰系统设计的。在标称系统的情况下，所提出的双环控制器是并置部分反馈线性化和分层滑模控制 (HSMC) 理论的组合。然后，由于鲁棒性在物理系统控制中的重要性，所提出的控制器是针对存在加性扰动的欠驱动机械系统开发的。所提出的设计方法的主要优点之一是它不需要任何切换算法。最后，为了说明所提出的控制器的性能，它们被应用于两个欠驱动的机械系统：一个 pendubot 和一个 Furuta 摆。此外，还使用四旋翼支架对所提方法的实用性进行了实验验证。