Hybrid Sliding-Mode-Based Control of Underactuated Systems With Dry Friction

In this paper, hybrid control synthesis is proposed for a class of 2-degrees-of-freedom (DOF) underactuated mechanical systems with Coulomb friction in the joints. The control objective is to regulate both actuated and unactuated joints to desired positions. The proposed synthesis combines second-order sliding-mode (SOSM) control methods and a pure technical solution of imposing a relatively stronger dry friction on the unactuated joint as compared to that of the actuated joint. This design feature allows us to decouple the hybrid synthesis procedure into two steps. At the first step, a SOSM control algorithm is utilized to drive the unactuated link to the desired position in finite time. Once this task is achieved, the control input is switched to another SOSM algorithm which drives the actuated link to its desired position. As the amplitude of the controller used at the second step is smaller than the Coulomb friction level in the unactuated link, but it is greater than that in the actuated link, the unactuated link remains at rest, whereas the actuated link is regulated to the endpoint of interest. Performance issues of the developed synthesis, including robustness features of the closed-loop system, are illustrated in an experimental study made for a laboratory horizontal 2-DOF pendulum.