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research-article

Tracking of a bouncing ball in a planar billiard through continuous-time approximations

[+] Author and Article Information
Laura Menini

Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma Tor Vergata, Roma, 00133, Italy
menini@disp.uniroma2.it

Corrado Possieri

Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino, Torino, 10129, Italy
possieri@ing.uniroma2.it

Antonio Tornambè

Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma Tor Vergata, Roma, 00133, Italy
tornambe@disp.uniroma2.it

1Corresponding author.

ASME doi:10.1115/1.4039876 History: Received July 14, 2017; Revised March 26, 2018

Abstract

The main goal of this paper is to design a state feedback control that makes a point mass track a non-Zeno reference trajectory in a planar billiard. This objective is achieved by firstly determining a continuous-time dynamical model, whose trajectories approximate the solutions of the hybrid system. Hence, a state feedback that makes the hybrid system track a reference trajectory of the continuous-time one is proposed. Finally, these two techniques are combined in order to find a state feedback that achieves tracking of the trajectories of the unforced system. Examples are reported all throughout the paper to illustrate the theoretical results.

Copyright (c) 2018 by ASME
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