The Digital Pendulum system is a modern version of a classical control problem -- that of erecting and balancing a free-swinging pendulum in its inverted position or moving a hanging pendulum in a controlled manner. The cart on the track is digitally controlled to swing up (or, self-erecting) and to balance the pendulum into an upright, sustained position or to move the cart with pendulum in an unperturbed down position. The cart track is of limited length, imposing constraints on the control algorithm. In pendulum mode, the system is used to control the twin-arm pendulum from an initial position, hanging at rest with the cart in the center of its travel along the track, to a final position with the pendulum upright and the cart restored to its central position.
In crane mode, the control problem is to move the position of the cart without undue movement of the pendulum. This problem is typical of that experienced when controlling a gantry crane.