@inproceedings{244ee4c5b9064578adfd95d753d3710b,
title = "Ball on Ball: Modeling and control of a novel experiment set-up",
abstract = "This paper introduces a new control application. The goal is to balance a bowling ball on top of another bowling ball which rotates in three axes. The first ball is placed on three so-called omni-wheels in a way that it can rotate in all directions. The second ball moves freely atop the first ball. This approach uses a model based controller design. The mathematical model for the system is first derived using the Lagrange equations. One aspect of this model is that the rolling of one ball on another is a nonholonomic constraint. A significant simplification of the mathematical model can be achieved with a suitable state transformation. A linear approximation of the model at the equilibrium point is presented along with the controller design. Implementation on the laboratory model demonstrate the successful application of the model based control concept.",
keywords = "ball on ball, rigid body dynamics, nonlinear system, model based design, mechatronic system, state feedback, educational system, ball on ball, rigid body dynamics, nonlinear system, model based design, mechatronic system, state feedback, educational system, State feedback, Educational system, Mechatronic system, Nonlinear system, Rigid body dynamics, Ball on ball, Model based design",
author = "Reinhard Gahleitner",
note = "Funding Information: 1 The author gratefully acknowledges the support of Bernecker &1 TRheaeinaeutrtho(Bor&Rgr)a,teefsulplelyciaallcyknTowholemdgagsesDtiheckeersuppapnpdorFtraonfzBEernneheucbker Fiffure 2. Front vieffi of the Baflfl on Baflfl system. in Rpraoivniedrin(gB&mRos)t, eosfptehceialhlyardTwhaormeacsomDpicokneernatsn,dwFhriachnzmEandheubtheer Fiffure 2. Front vieffi of the Baflfl on Baflfl system. & Rainer (B&R), especially Thomas Dicker and Franz Enhuber Fiffure 2. Front vieffi of the Baflfl on Baflfl system. rnealpirzoavtiiodninogfmthoistproofjetchtephoasrsdibwlea.reThcaonmkpsoanlesnotsg,owouhtichtomCahdriesttiahne convertersforthemotorscanbeseen.Abovethatarethe irnealprizoatviiondingofmthoisstproofjetchetphaosrsdibwlea.reThcanomkpsoalnesnotsgo, wouhitchtomCahderisttiahen convertersforthemotorscanbeseen.Abovethatarethe rHeoallliiznaettizonfoorftthheismpercohjaencticpaloscsoinbsletr.uTchtiaonnk.s also go out to Christian acoctnovresrtfefiritshfosrertvhoe moottoorrss,caannffbueflasrefefena.rAsbaonvdeotmhanti-affriehetehfles realization of this project possible. Thanks also go out to Christian converters for the motors can be seen. Above that are the Hollinetz for the mechanical construction. actors ffiith servo motors, anffuflar ffears and omni-ffiheefls Hollinetz for the mechanical construction. actors ffiith servo motors, anffuflar ffears and omni-ffiheefls Publisher Copyright: {\textcopyright} 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.; 8th Vienna Conference on Mathematical Modelling ; Conference date: 18-02-2015 Through 20-02-2015",
year = "2015",
month = feb,
day = "1",
doi = "10.1016/j.ifacol.2015.05.148",
language = "English",
volume = "28",
series = "IFAC-PapersOnLine",
pages = "796--801",
booktitle = "Proceedings MATHMOD Conference 2015",
edition = "1",
url = "http://www.mathmod.at",
}