Control of 2-periodic motion for bouncing ball

Author

Ghosh, J. ; Paden, B.

Author_Institution

Dept. of Mech. & Environ. Eng., California Univ., Santa Barbara, CA, USA

Volume

6

fYear

1999

fDate

1999

Firstpage

4048

Abstract

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

Keywords

Poincare mapping; discrete time systems; motion control; nonlinear control systems; periodic control; stability; vibration control; 2-periodic motion control; bounce-height; bouncing ball; continuous dynamics; discrete-time system; height control; instantaneous frequency; nonlinear periodic motion; vibrating plate; Adaptive control; Difference equations; Frequency modulation; Gravity; Motion control; Nonlinear equations; Stability; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 1999. Proceedings of the 1999

Conference_Location

San Diego, CA

ISSN

0743-1619

Print_ISBN

0-7803-4990-3

Type

conf

DOI

10.1109/ACC.1999.786299

Filename

786299