Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Kinematic and Workspace-Based Synthesis of a 2-DOF Mechanism for Haptic Applications Read chapter Read first chapter

2015 | OriginalPaper | Chapter

A Robust Control Scheme Against Some Parametric Uncertainties for the NXT Ballbot

Authors : R. A. García-García, M. Arias-Montiel

Published in: Multibody Mechatronic Systems

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this work a Linear Matrix Inequalities (LMIs) approach to provide robustness to an optimal control scheme for the NXT ballbot is proposed. The mathematical model of the system is obtained taking into account the actuators dynamics and in this overall model uncertain parameters appear. These uncertainties can affect (in a negative form) the control algorithm performance, so we define a polytopic model considering some parameters vary within some bounded sets. This polytopic model is used to synthesize a robust control scheme against parameters variation using LMIs. Numerical results show a significant improvement in the closed loop system in comparison with a classic Linear Quadratic Regulator (LQR) control. Finally, some experimental results are presented to show the viability of implementing the control strategy proposed.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter Design of Electronic Control Board to Obtain the Photovoltaic Module Power Voltage Curve as Temperature Function
next chapter Fuzzy Logic Control on FPGA Using LabVIEW
Literature
1.
2.
Asgari P, Zarafshan P, Moosavian SAA (2013) Dynamics modelling and stable motion control of a ballbot equipped with a manipulator. In: Proceedings of the 2013 international conference on robotics and mechatronics, pp. 259−264
3.
Fankhauser P, Gwerder C (2010) Modeling and control of a ballbot. Bachelor Thesis, Autonomous Systems Lab, Swiss Federal Institute of Technology Zurich
4.
Fong J, Uppill S (2009) Design and build a ballbot, Bachelor Thesis, Faculty of Engineering, Computer and Mathematical Sciences, University of Adelaide
5.
Mampetta A (2006) Automatic transition of ballbot from statically stable state to dynamically stable state. Master’s Thesis, Robotics Institute, Carnegie Mellon University
6.
Nagarajan U, Kantor G, Hollis R (2013) The ballbot: an omnidirectional balancing mobile robot. Int J Robot Res 1−14. Published online 13 November 2013
7.
Skrabel C (2013) Mechanical design of a ballbot platform, Bachelor Thesis, Autonomous Systems Lab, Swiss Federal Institute of Technology Zurich)
8.
Prieto S, Navarro T, Plaza M, Polo O (2012) A monoball robot based on lego mindstorm. IEEE Control Syst 32(2):71−83CrossRef
9.
Yamamoto Y (2009) NXT ballbot model-based design—control of self-balancing robot on a ball, built with Lego Mindstorm NXT, 1st edn. Cynernet Systems CO., LTD
10.
Bradley P, De la Puente J, Zamorano J, Brosnan D (2012) A platform for real-time control education with lego mindstorms. In: Proceedings of the 9th IFAC symposium advances in control education, pp. 112–117
11.
Kim Y (2011) Control systems lab using a lego mindstorms nxt motor system. IEEE Trans Educ 54(3):452−461CrossRef
12.
Pinto M, Moreira AP, Matos A (2012) Localization of mobile robots using an extended Kalman filter in a lego nxt. IEEE Trans Educ 55(1):135−144CrossRef
13.
Pinto-Salamanca ML, Bermúdez-Bohórquez GR (2007) Parameters determination of a mobil robot of lego minstorms. Ingeniería Investigación y Desarrollo 5(2):7−13
14.
15.
Vukic Z, Kuljaca L, Donlagic D, Tesnjak S (2003) Nonlinear control systems. Marcel Dekker Inc, BaselCrossRef
16.
Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system anc control theory. Society for Industrial and Applied Mathematics SIAM, PhiladelphiaCrossRef
17.
Ostertag E (2011) Mono and multivariable control and estimation—linear, quadratic and LMI methods. Springer, BerlinCrossRefMATH
18.
Olalla C, Leyva R, El-Aroudi A, y Queinnec I (2009) Robust LQR control for PWM converters: an LMI approach. IEEE Trans Indus Electron 56(7):2548−2558CrossRef
19.
Erkus B, Lee YJ (2004) Linear matrix inequalities and MATLAB LMI toolbox. University of Southern California Group Meeting Report, Los Angeles
Metadata
Title
A Robust Control Scheme Against Some Parametric Uncertainties for the NXT Ballbot
Authors
R. A. García-García
M. Arias-Montiel
Copyright Year
2015
Book
Multibody Mechatronic Systems

Print ISBN: 978-3-319-09857-9

Electronic ISBN: 978-3-319-09858-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-09858-6_24