Skip to main content

Fractional Describing Function of Systems with Nonlinear Friction

  • Chapter
Intelligent Engineering Systems and Computational Cybernetics

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Slotine JE, Li W (1991) Applied Nonlinear Control. Prentice-Hall, NJ

    Google Scholar 

  2. Podlubny I (1999) Fractional Differential Equations. Academic, San Diego, CA

    MATH  Google Scholar 

  3. Duarte F, Machado JA (2006) Fractional Dynamics in the Describing Function Analysis of Nonlinear Friction. In: 2nd IFAC Workshop on Fractional Differentiation and Its Applications, Porto, Portugal

    Google Scholar 

  4. Azenha A, Machado JA (1996) Limit Cycles Prediction of Robot Systems with Nonlinear Phenomena in the Joints. In: 27th International Symposium on Industrial Robots, Milan, Italy, 1996, pp 1003–1008

    Google Scholar 

  5. Armstrong B, Dupont B, de Wit C (1994) A Survey of Models, Analysis Tools and Compensation Methods for the Machines with Friction. Automatica 30:1083–1183

    Article  MATH  Google Scholar 

  6. Armstrong B, Amin B (1996) PID Control in the Presence of Static Friction: A Comparison of Algebraic and Describing Function Analysis. Automatica 32:679–692

    Article  MATH  MathSciNet  Google Scholar 

  7. Haessig DA, Friedland B (1991) On the Modelling and Simulation of Friction. ASME Journal of Dynamic Systems, Measurement and Control 113:354–362

    Article  Google Scholar 

  8. Karnopp D (1985) Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems. ASME Journal of Dynamic Systems, Measurement and Control 107:100–103

    Article  Google Scholar 

  9. Cox CS (1987) Algorithms for Limit Cycle Prediction: A Tutorial Paper. International Journal of Electrical Engineering Education 24:165–182

    Google Scholar 

  10. Azenha A, Machado JA (1998) On the Describing Function Method and Prediction of Limit Cycles in Nonlinear Dynamical Systems. System Analysis-Modelling-Simulation 33:307–320

    MATH  Google Scholar 

  11. Barbosa R, Machado JA (2002) Describing Function Analysis of Systems with Impacts and Backlash. Nonlinear Dynamics 29:235–250

    Article  MATH  Google Scholar 

  12. Barbosa R, Machado JA, Ferreira I (2003) Describing Function Analysis of Mechanical Systems with Nonlinear Friction and Backlash Phenomena. In: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, Sevilla, Spain, 2003, pp 299–304

    Google Scholar 

  13. Duarte F, Machado JA (2005) Describing Function Method in Nonlinear Friction. In: IEEE, 1st International Conference on Electrical Engineering, Coimbra, Portugal, 2005

    Google Scholar 

  14. Atherton DP (1975) Nonlinear Control Engineering. IEEE, 1st International Conference on Electrical Engineering, Van Nostrand Reinhold Company, London

    Google Scholar 

  15. Dupont PE (1992) The Effect of Coulomb Friction on the Existence and Uniqueness of the Forward Dynamics Problem. In: Proceedings of the IEEE International Conference on Robotics and Automation, Nice, France, pp 1442–1447

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fernando B. M. Duarte .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Duarte, F.B.M., Machado, J.A.T. (2009). Fractional Describing Function of Systems with Nonlinear Friction. In: Machado, J.A.T., Pátkai, B., Rudas, I.J. (eds) Intelligent Engineering Systems and Computational Cybernetics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8678-6_22

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-8678-6_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8677-9

  • Online ISBN: 978-1-4020-8678-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics