Energy and passivity based control of the double inverted pendulum on a cart

The paper considers the design of a nonlinear controller for the double inverted pendulum (DIP), a system consisting of two inverted pendulums mounted on a cart. The swingup controller bringing the pendulums from any initial position to the unstable up-up position is designed based on passivity properties and energy shaping. While the swingup controller drives the DIP into a region of attraction around the unstable up-up position, the balance controller designed on the basis of the linearized model stabilizes the DIP at the unstable equilibrium. The simulation results show the effectiveness of the proposed nonlinear design method for the DIP system.