This paper presents an extension of the IDA-PBC method, addressing the problem of joint position regulation for a class of underactuated mechanical systems with friction, which is modelled by the LuGre dynamic model. An IDA-PBC including friction compensation with the LuGre model is designed to achieve locally asymptotically joint position regulation of a class of underactuated mechanical systems. To the best knowledge of the authors, this is the first original LuGre model-based controller for position regulation of underactuated mechanical systems. More importantly, the proposed theoretical framework allows us to redesign any IDA-PBC originally designed without friction compensation, as long as the parameters of the LuGre model of each actuator are available. Additionally, friction compensation in mechanical systems is known to improve controller performance at low velocities, being an advantage over other controllers that do not consider it. As a case study, an underactuated mechanical system available in numerous automatic control laboratories, called pendubot, is worked out to illustrate its performance through real-time experiments. Finally, a comparison is carried out between the proposed controller and an IDA-PBC with Dahl model friction compensation to test its superiority.

本文介绍了 IDA-PBC 方法的扩展，解决了由 LuGre 动力学模型建模的一类带摩擦的欠驱动机械系统的关节位置调节问题。IDA-PBC 包括 LuGre 模型的摩擦补偿，旨在实现一类欠驱动机械系统的局部渐近关节位置调节。据作者所知，这是第一个基于 LuGre 模型的原始控制器，用于欠驱动机械系统的位置调节。更重要的是，只要每个执行器的 LuGre 模型参数可用，所提出的理论框架允许我们重新设计任何最初设计的没有摩擦补偿的 IDA-PBC。此外，众所周知，机械系统中的摩擦补偿可​​以提高控制器在低速下的性能，这比其他不考虑它的控制器具有优势。作为一个案例研究，在许多自动控制实验室中都有一个欠驱动的机械系统，称为pendubot，通过实时实验来说明其性能。最后，将所提出的控制器与具有达尔模型摩擦补偿的 IDA-PBC 进行了比较，以测试其优越性。