Swing‐up and fixed‐time stabilization control of underactuated cart‐double pendulum system.

A cart‐double pendulum system is an underactuated mechanical system that has three degrees of freedom (DOF) and has two actuators. This paper discusses the stabilizing control problem for this non‐linear mechanical system. First, an input relationship is constructed to transform the 3‐DOF cart‐double pendulum system into a 2‐DOF reduced‐order system in a fixed time. Second, a swing‐up controller is designed for the reduced‐order system to make the system infinitely approach upright equilibrium point. After that, the swing‐up controller switches to a fixed‐time balance stabilization controller, which stabilizes the cart‐double pendulum at the upright equilibrium point in a fixed time. Finally, numerical examples verify the effectiveness of this presented control strategy. [ABSTRACT FROM AUTHOR]