Discrete Mechanics and Optimal Control and its Application to a Double Pendulum on a Cart

In this paper we present a new approach to determine trajectories for changing the state of the double pendulum on a cart from one equilibrium to another and show the experimental realization on a test bench. The control of these transitions is accomplished by a two-degrees-of-freedom control scheme. For the design of the feedforward and feedback control of the system two models of the double pendulum on a cart are introduced. The feedforward control is achieved by the optimal control method Discrete Mechanics and Optimal Control (DMOC). The trajectories can be optimized with respect to energy consumption and transition time. Additionally, for the applicatory design, the implementation of a feedback control by means of gain-scheduling is explained. As experimental result the realization of a trajectory on the test bench is presented.