Ball in Hoop Revisited as Laboratory Benchmark for Advanced Control

In this talk, we revisit Ball and hoop system, a well-established laboratory model used in education of linear control systems, and show that it is also suitable for demonstration of more advanced control techniques. In contrast to the standard use, we describe the dynamics of the system at full length by a hybrid model; in addition to the mode where the ball rolls on the (outer) hoop we also consider the mode where the ball drops out of the hoop and enters a free-fall mode. Furthermore, we add another (inner) hoop in the center upon which the ball can land from the free-fall mode. This hybrid description of the Ball and hoop system enables us to generate dynamically rich trajectories (for instance, the ball can go through the top of the hoop or even fly in free fall) and pose challenging control task. We present two such tasks and show how they can be solved by trajectory generation and stabilization. We also describe how such a laboratory model can be built and we experimentally verify the validity of our approach to solution of the proposed tasks.