An output regulation approach for swing-up and tracking control of double pendulum on a cart

It is well known that the control problem of the double pendulum on a cart (DPC) system is challenging since it is a complicated underactuated mechanical system with high nonlinearity. This paper first studies a swing-up and tracking control problem of the DPC system with time-varying reference signal. A novel switched swing-up and tracking controller is proposed, which can be carried out in two steps. In step one, the energy-based swing-up controller is used to drive the double pendulum to the neighborhood of the up-up equilibrium point. In step two, based on approximate nonlinear output regulation theory, the polynomial approximation based tracking controller is used to achieve high precision position tracking control. Finally, the simulation results illustrate the effectiveness of our design.