Predefined-time hierarchical sliding mode stabilisation control of underactuated Furuta pendulum system

The Furuta pendulum is a typical underactuated mechanical system that has two degrees of freedom (DOF) and only one control input. This paper studies the stabilising control problem for this mechanical system. A predefined-time stabilising control method is presented based on hierarchical sliding mode idea. First, the system's dynamical model is established by using the Euler-Lagrange modelling method. And it is divided into two subsystems. Second, a first-order sliding mode function is respectively designed for each subsystem. And a second-order sliding mode function is constructed by linearly combining two first-order sliding mode functions. After that, a stabilising control law is designed based on the second-order sliding mode function. It stabilises all sliding mode functions at the origin within a predefined time. This guarantees the predefined-time stabilisation of the Furuta pendulum system to be achieved. Finally, the effectiveness of the developed control strategy is verified using experimental examples.