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

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