Skip to main content
SpringerLink
Log in

Optimal Fractional-Order Damping Strategies

  • Chapter
Fractional Processes and Fractional-Order Signal Processing

Part of the book series: Signals and Communication Technology ((SCT))

  • 1856 Accesses

Abstract

Chapter 10 studies the optimal non-delayed fractional-order damping, time-delayed fractional-order damping, and optimal distributed order fractional damping based on ISE, ITSE, IAE and ITAE performance criteria. The comparisons of the step responses of the integer-order and the three types of fractional-order damping systems indicate that the optimal fractional-order damping systems achieve much better step responses than optimal integer-order systems in some instances, but sometimes the integer-order damping systems performs as well as fractional-order ones. Furthermore, time delay can sometimes be used to gain benefit in control systems, and, especially, the fractional-order damping plus properly chosen delay can bring outstanding performance. Time-delayed fractional-order damping systems can produce a faster rise time and less overshoot than others.

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

Access this chapter

Log in via an institution
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 EPUB and 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

References

  1. Brančík, L.: Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. In: Proceedings of the 7th Conference MATLAB’99, Prague, Czech Republic, Nov. 1999, pp. 27–39 (1999)

    Google Scholar 

  2. Cao, Y.: Correcting the minimum ITAE standard forms of zero-displacement-error systems. J. Zhejiang Univ. Sci. 23(4), 550–559 (1989)

    Google Scholar 

  3. Dalir, M., Bashour, M.: Applications of fractional calculus. Appl. Math. Sci. 4(21–24), 1021–1032 (2010)

    MathSciNet  MATH  Google Scholar 

  4. D’Azzo, J.J., Houpis, C.H., Sheldon, S.N.: Linear Control System Analysis and Design, 5th edn. CRC Press, Boca Raton (2003)

    Book  MATH  Google Scholar 

  5. De Espíndola, J.J., Bavastri, C.A., De Oliveira Lopes, E.M.: Design of optimum systems of viscoelastic vibration absorbers for a given material based on the fractional calculus model. J. Vib. Control 14(9–10), 1607–1630 (2008)

    Article  MathSciNet  Google Scholar 

  6. Dorf, R.C.: Modern Control Systems. Addison-Wesley/Longman, Reading/Harlow (1989)

    MATH  Google Scholar 

  7. Hartley, T.T., Lorenzo, C.F.: A frequency-domain approach to optimal fractional-order damping. Nonlinear Dyn. 38(1–2), 69–84 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Koeller, R.C.: Applications of fractional calculus to the theory of viscoelasticity. J. Appl. Mech. 51(2), 299–307 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  9. Komkov, V.: Optimal Control Theory for the Damping of Vibrations of Simple Elastic Systems. Springer, Berlin (1972)

    MATH  Google Scholar 

  10. Lion, A.: On the thermodynamics of fractional damping elements. Contin. Mech. Thermodyn. 9(2), 83–96 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lorenzo, C.F., Hartley, T.T.: Variable order and distributed order fractional operators. Nonlinear Dyn. 29(1–4), 57–98 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ogata, K.: Modern Control Engineering. Prentice-Hall, Englewood Cliffs (1970)

    Google Scholar 

  13. Padovan, J., Guo, Y.: General response of viscoelastic systems modelled by fractional operators. J. Franklin Inst. 325(2), 247–275 (1988)

    Article  MATH  Google Scholar 

  14. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  15. Rossikhin, Y.A., Shitikova, M.V.: Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems. Acta Mech. 120(1–4), 109–125 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rüdinger, F.: Tuned mass damper with fractional derivative damping. Eng. Struct. 28(13), 1774–1779 (2006)

    Article  Google Scholar 

  17. Shafieezadeh, A., Ryan, K., Chen, Y.Q.: Fractional order filter enhanced LQR for seismic protection of civil structures. J. Comput. Nonlinear Dyn. 3(2), 020201.1–1021404.7 (2008)

    Google Scholar 

  18. Sheng, H., Li, Y., Chen, Y.Q.: Application of numerical inverse Laplace transform algorithms in fractional calculus. J. Franklin Inst. 348(2), 315–330 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Shokooh, A.: A comparison of numerical methods applied to a fractional model of damping materials. J. Vib. Control 5(3), 331–354 (1999)

    Article  Google Scholar 

  20. Tavazoei, M.S.: Notes on integral performance indices in fractional-order control systems. J. Process Control 20(3), 285–291 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Dalian Jiaotong University, Dalian, People’s Republic of China

    Hu Sheng

  2. Department of Electrical and Computer Engineering, CSOIS, Utah State University, Old Main Hill 4160, Logan, UT, 84322-4120, USA

    YangQuan Chen

  3. School of Electronic and Information Engineering, Dalian University of Technology, Dalian, People’s Republic of China

    TianShuang Qiu

Authors
  1. Hu Sheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YangQuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. TianShuang Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hu Sheng .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag London Limited

About this chapter

Cite this chapter

Sheng, H., Chen, Y., Qiu, T. (2012). Optimal Fractional-Order Damping Strategies. In: Fractional Processes and Fractional-Order Signal Processing. Signals and Communication Technology. Springer, London. https://doi.org/10.1007/978-1-4471-2233-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-2233-3_10

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2232-6

  • Online ISBN: 978-1-4471-2233-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation