The Bouncing Ball Apparatus as an Experimental Tool

The bouncing ball apparatus exhibits a rich variety of nonlinear dynamical behavior and is one of the simplest mechanical systems to produce chaotic behavior. A computer control system is designed for output calibration, state determination, system identification and control of the bouncing ball apparatus designed by Launch Point Technologies. Two experimental methods are used to determine the coefficient of restitution of the ball, an extremely sensitive parameter of the apparatus. The first method uses data directly from a stable 1-cycle orbit. The second method is based on the ball map combined with data from a stable 1-cycle orbit. For control purposes, two methods are used to construct linear maps. The first map is determined by collecting data directly from the apparatus. The second map is determined from linearization of the ball map. The maps are used to estimate the domains of attraction to the stable 1-cycle orbit. These domains of attraction are used with a chaotic control algorithm to control the ball to a stable 1-cycle, from any initial state. Results are compared and it is found that the linear map obtained directly from the data gives the more accurate representation of the domain of attraction.