Identi cation and Nonlinear Controller Design for the Bouncing Ball Experiment

The dynamics of a ball driven by a massive sinusoidally vibrating plate are highly nonlinear and undergo a number of bifurcations of xed points with various periodicities. This paper is concerned with a rst step on experimentally analyzing these dynamics using the "Bouncing Ball Apparatus". Signal processing methods and parameter identi cation routines have been implemented and a straight forward predictor as well as a robust nonlinear controller were designed using phase as a control variable. Fast global convergence was gained for periodic orbits of di erent order and periodicity within a wide range of frequencies. Additional enhancement was achieved by cascading the controller structure and adding adaptive algorithms.