Robust fixed-time sliding mode control of underactuated Furuta pendulum system

A Furuta pendulum is a typical underactuated mechanical system with two degrees of freedom (DOF) and only one input. We address the robust stabilization control problem for this 2-DOF underactuated system with a matched external disturbance. A fixed-time sliding mode control method is presented. First, the dynamic motion model of the system is established using the Euler-Lagrange modeling method. And then, we get the approximate linearization model of the system around the origin equilibrium point and construct a homeomorphic coordinate transformation for this model. After that, a sliding mode surface and a fixed-time robust controller are designed for the transformed system. The developed controller ensures the system's state variables to reach the sliding mode surface in a fixed time. This guarantees the fixed-time robust stabilization control objective to be achieved. Finally, two numerical examples demonstrate the validity of our presented control strategy.