Although the literature on control of overhead crane systems is extensive and relatively mature, there is still a need to develop strategies that can simultaneously handle factors such as the double pendulum effect, variable cable length, input saturation, input dead zones, and external disturbances. This article is concerned with adaptive tracking control for underactuated overhead cranes in the presence of the above-mentioned challenging effects. The proposed controller is composed of the following two components. First, a tracking signal vector that effectively reduces system swing magnitudes is constructed to improve the transient performance and guarantee smooth operation of the system. Second, an adaptive law is designed to estimate and compensate for the overall effects of the friction, the external disturbances, and certain nonlinearities. The system stability has been proved rigorously via the Lyapunov method and Barbalat’s lemma. Extensions to the cases with input saturation and dead zones have also been discussed. Extensive numerical simulations have been conducted to verify the performance and robustness of the proposed controller, in comparison to some existing methods.

中文翻译：

---

可变电缆长度欠驱动双摆桥式起重机的自适应跟踪控制


尽管有关桥式起重机系统控制的文献广泛且相对成熟，但仍然需要开发能够同时处理双摆效应、可变电缆长度、输入饱和、输入死区和外部干扰等因素的策略。本文关注的是存在上述挑战性影响的欠驱动桥式起重机的自适应跟踪控制。所提出的控制器由以下两个组件组成。首先，构建有效降低系统摆幅幅度的跟踪信号向量，以改善瞬态性能，保证系统平稳运行。其次，设计自适应律来估计和补偿摩擦、外部干扰和某些非线性的总体影响。通过Lyapunov方法和Barbalat引理严格证明了系统的稳定性。还讨论了输入饱和和死区情况的扩展。与一些现有方法相比，已经进行了广泛的数值模拟来验证所提出的控制器的性能和鲁棒性。