Ball on Ball: Modeling and control of a novel experiment set-up

Reinhard Gahleitner

doi:10.1016/j.ifacol.2015.05.148

Ball on Ball: Modeling and control of a novel experiment set-up

Reinhard Gahleitner

Research Center Wels

Research output: Chapter in Book/Report/Conference proceedings › Conference contribution › peer-review

5 Citations (Scopus)

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.

Original language	English
Title of host publication	Proceedings MATHMOD Conference 2015
Pages	796-801
Number of pages	6
Volume	28
Edition	1
DOIs	https://doi.org/10.1016/j.ifacol.2015.05.148
Publication status	Published - 1 Feb 2015
Event	8th Vienna Conference on Mathematical Modelling - Wien, Austria Duration: 18 Feb 2015 → 20 Feb 2015 http://www.mathmod.at

Publication series

Name	IFAC-PapersOnLine

Conference

Conference	8th Vienna Conference on Mathematical Modelling
Country/Territory	Austria
City	Wien
Period	18.02.2015 → 20.02.2015
Internet address	http://www.mathmod.at

Keywords

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

Access to Document

10.1016/j.ifacol.2015.05.148

Cite this

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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",

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doi = "10.1016/j.ifacol.2015.05.148",

language = "English",

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T1 - Ball on Ball: Modeling and control of a novel experiment set-up

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N1 - 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: © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - 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.

AB - 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.

KW - ball on ball

KW - rigid body dynamics

KW - nonlinear system

KW - model based design

KW - mechatronic system

KW - state feedback

KW - educational system

KW - ball on ball

KW - rigid body dynamics

KW - nonlinear system

KW - model based design

KW - mechatronic system

KW - state feedback

KW - educational system

KW - State feedback

KW - Educational system

KW - Mechatronic system

KW - Nonlinear system

KW - Rigid body dynamics

KW - Ball on ball

KW - Model based design

UR - https://www.scopus.com/pages/publications/84954167243

U2 - 10.1016/j.ifacol.2015.05.148

DO - 10.1016/j.ifacol.2015.05.148

M3 - Conference contribution

VL - 28

T3 - IFAC-PapersOnLine

SP - 796

EP - 801

BT - Proceedings MATHMOD Conference 2015

T2 - 8th Vienna Conference on Mathematical Modelling

Y2 - 18 February 2015 through 20 February 2015

ER -

Ball on Ball: Modeling and control of a novel experiment set-up

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Keywords

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