Control of 2-periodic motion for bouncing ball

Controlling the height of a bouncing ball on a vibrating plate is a prototype problem for the control of nonlinear periodic motions. Further, analysis of the bouncing ball system is convenient in that a discrete-time system can be derived from the continuous dynamics without the explicit construction of a Poincare map. If the plate vibrates sinusoidally with a particular frequency, only certain bounce-heights can be achieved in periodic motion. In this paper we describe a control scheme wherein the instantaneous frequency of the vibrating plate is modulated, so that arbitrary controlled bounce-heights are achieved in stable periodic motion involving two bounces per period. The base carrier frequency of the plate is held constant.