Stabilization control of underactuated Furuta pendulum system based on fixed-time hierarchical sliding mode method

Furuta pendulum system is a typical underactuated system with two degrees of freedom (DOF) and a control input. This paper studies the stabilization control problem for this mechanical system. And a new fixed-time control method is developed to solve the motion control problem. The method firstly divides the Furuta pendulum system into two subsystems and constructs a fixed-time first-level sliding surface for each subsystem. And then, a second-level sliding surface is designed and its fixed-time convergence guarantees the fixed-time stabilization of two first-level sliding surfaces at the origin. After that, we design a sliding mode controller to stabilize the second-level sliding surface within a fixed time. As a result, the fixed-time convergence characteristics of first-level sliding surfaces enable the stabilization control objective of the Furuta pendulum system to be achieved within a fixed time. Finally, numerical simulation examples are used to verify the effectiveness of our presented control method.