A WAcrobot is an underactuated nonlinear system that has three degrees of freedom (DOF) and two inputs. This paper discusses the global stabilization control problem for this 3-DOF underactuated system. A new control strategy is developed to solve this problem. The strategy first changes the 3-DOF WAcrobot system to be a 2-DOF reduced-order model in finite time. This transforms the stabilizing control of the WAcrobot system into that of the reduced-order model. After that, nonsingular control laws that globally stabilize the reduced-order model at the origin are designed. It guarantees the stabilizing control objective of the WAcrobot to be achieved. Finally, a simulation experimental example demonstrates the validity of the presented theoretical results. Simulation results show the advantage of our strategy over others.

中文翻译：

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欠驱动WAcrobot系统的非线性全局稳定控制

WAcrobot是一种欠驱动的非线性系统，具有三个自由度（DOF）和两个输入。本文讨论了此3-DOF欠驱动系统的全局稳定控制问题。开发了一种新的控制策略来解决该问题。该策略首先在有限时间内将3自由度WAcrobot系统更改为2自由度降阶模型。这将WAcrobot系统的稳定控制转换为降阶模型的稳定控制。此后，设计了在原点全局稳定降阶模型的非奇异控制定律。它保证了WAcrobot的稳定控制目标得以实现。最后，一个仿真实验实例证明了所提出理论结果的有效性。仿真结果显示了我们的策略相对于其他策略的优势。