In this paper a two level hierarchical system is considered. This system consists of two discs that have limited rotational movement. It is assumed that one disc has large inertia and low angular acceleration and the other disc has low inertia and high angular acceleration. The disc with large angular acceleration is mounted on the periphery of the disc with low acceleration. The angular velocity and orientation of both discs is controllable. It is shown how the theory of asymptotic output tracking for linear systems, combined with some easily programmable mathematical optimization problems leads to very good results when designing a controller for asymptotically tracking a moving object, in particular meeting the angular acceleration limits imposed on the two discs. The paradigm for this system is the human eye-head-neck system and the tracking of a moving object at a distance from the eye.