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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.

Joint position regulation of a class of underactuated mechanical systems affected by LuGre dynamic friction via the IDA-PBC method