Skip to main content

Nonlinear Control for Vibration Rejection in a System Containing a Flexible Beam and Belts

  • Conference paper
  • First Online:
Advances in Service and Industrial Robotics (RAAD 2018)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 67))

Included in the following conference series:

  • 2236 Accesses

Abstract

Belt driven systems are part of many industrial devices, like cutting machines and 3D-printers. In this paper the dynamic modeling and a nonlinear control approach of a belt driven system containing a flexible beam are presented. Due to the special kinematics, the stiffness of the belt is nonlinear. This together with the elastic beam, leads to nonlinear partial differential equations of motion. By omitting negligible dynamical effects, a nonlinear controller can be designed that uses measurements of accelerations and shear forces of the flexible beam. In detail, an integrator backstepping design for an infinite dimensional system is performed. The proposed control approach is compared with a conventional PD control law and a validation by means of simulation results is shown.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New Jersey (2002)

    MATH  Google Scholar 

  2. Thull, D., Wild, D., Kugi, A.: Infinit dimensionale Regelung eines Brückenkrans mit schweren Ketten. atAutomatisierungstechnik 8, 400–410 (2005)

    Google Scholar 

  3. Andre a Novel, B., Coron, J.M.: Exponential stabilization of an overhead crane with flexible cable via backstepping approach. Automatica 36, 587–593 (2000)

    Article  MathSciNet  Google Scholar 

  4. Staudecker, M., Schlacher, K., Hansl, R.: Passivity based control and time optimal trajectory planning of a single mast stacker crane. The International Federation of Automatic Control, Seoul, Korea (2008)

    Article  Google Scholar 

  5. Jörgl, M., Gattringer, H.: Dynamical modeling and flatness based control of a belt drive system. In: Proceedings in Applied Mathematics and Mechanics (2014)

    Google Scholar 

  6. Bremer, H.: Elastic Multibody Dynamics: A Direct Ritz Approach. Springer, Heidelberg (2008)

    Book  Google Scholar 

  7. Siciliano, B., Sciavicco, L., Villani, L., Oriolo, G.: Robotics: Modelling, Planning and Control. Springer, London (2010)

    Google Scholar 

Download references

Acknowledgments

This work has been supported by the Austrian COMET-K2 program of the Linz Center of Mechatronics (LCM).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matthias Jörgl .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jörgl, M., Gattringer, H., Müller, A. (2019). Nonlinear Control for Vibration Rejection in a System Containing a Flexible Beam and Belts. In: Aspragathos, N., Koustoumpardis, P., Moulianitis, V. (eds) Advances in Service and Industrial Robotics. RAAD 2018. Mechanisms and Machine Science, vol 67. Springer, Cham. https://doi.org/10.1007/978-3-030-00232-9_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00232-9_42

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00231-2

  • Online ISBN: 978-3-030-00232-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics