Skip to main content
SpringerLink
Log in

Singularity Issues in Closed Loop Identification

  • Chapter
Model Identification and Adaptive Control

Abstract

This chapter addresses issues relating to the properties of estimation using closed loop data. This has been a topic of interest for at least four decades. Here we address specific problems which occur in these methods due to singularities. It is shown that unless special precautions are included in the algorithms, these singularities will lead to problems with the recovered, open loop transfer function estimates. These problems are investigated in this chapter and remedies suggested under finite sample conditions.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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. H. Akaike. On the use of a linear model for the identification of feedback systems. Ann. Inst Stat Math., 20:425–439, 1968.

    Article  MathSciNet  MATH  Google Scholar 

  2. K.J. Astrom and T. Hagglund. PID Controllers: Theory Design and Tuning. 2nd Edition. Instrument Society of America, America, 1995.

    Google Scholar 

  3. B.D.O. Anderson B. Codrons and M. Gevers. Closed-loop identification with an unstable or nonminimum phase controller. Proceedings IFAC System Identifica-tion, June 2000.

    Google Scholar 

  4. V.N. Fetisov B.G. Vorchik and S.E. Schteinberg. Identification of closed loop stochastic systems. Automation Rem. Control, 34(7), July 1973.

    Google Scholar 

  5. T. Bohlin. On the problem of ambiguities in maximum likelihood identification. Automatica, 7:199–210, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  6. G.E.P. Box and J.F. Macgregor. The analysis of closed loop dynamic stochastic systems. Tech Report 309, Dept. Stat University of Wisconsin, 1972.

    Google Scholar 

  7. P.M.T. Broersen. A comparison of transfer function estimators. IEEE Trans. Instrumentation and Measurement, 44:657–661, 1995.

    Article  Google Scholar 

  8. U. Forssell. Closed-loop Identification: Methods, Theory and Applications. Phd. thesis, Linkoping University, 1999.

    Google Scholar 

  9. G.C. Goodwin, S.F. Graebe, and M. Salgado. Principles of Control System Design. Prentice Hall, Englewood Cliffs, to appear 2000.

    Google Scholar 

  10. G.C. Goodwin and R.L. Payne. Dynamic System Identification: Experiment Design and Data Analysis. Academic Press, New York, 1977.

    MATH  Google Scholar 

  11. G.C. Goodwin and J.S. Welsh. Analysis of a novel method of autotuning a multivariable plant based on quantisation. Proceedings American Control Conference, pages 3347–3351, June 1999.

    Google Scholar 

  12. C.W.J. Granger. Economic process involving feedback. Inform. Control, 6:28–48, 1963.

    MathSciNet  MATH  Google Scholar 

  13. W. Heath. Statistical properties of non-parametric transfer function estimates for open and closed loop systems. CIDAC Technical Report 9902, University of Newcastle, 1999.

    Google Scholar 

  14. L. Ljung I. Gustavsson and T. Soderstrom. Identification of process in closed loop: Identifiability and accuracy aspects. Automatica, 13:59–76, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  15. I.Gustavsson L. Ljung and T. Soderstrom. Identification of linear multivari- ablesystem operating under linear feedback control IEEE Thins. Aut. Control, AC-19(6), Dec. 1974.

    Google Scholar 

  16. E.C. Levy . Complex curve fitting. IRE Trans. Aut Control, AC-4:37–44, 1959.

    Google Scholar 

  17. L. Ljung. System Identification: Theory for the User. Prentice Hall, Upper Saddle River, New Jersey, 2nd edition, 1999.

    Google Scholar 

  18. T. McKelvey. Frequency domain identification. Proceedings IFAC System Iden-tification, June 2000.

    Google Scholar 

  19. I. Kollar P. Guillaume and R. Pintelon. Statistical analysis of nonparametric transfer function estimates. IEEE Trans, Instrumentation and Measurement, 45(2):594–600, 1996.

    Article  Google Scholar 

  20. M.S. Phadke and S.M. Wu. Identification of multi input multi output transfer function and noise model of a blast furnace from closed-loop data. IEEE Trans. Aut Control, AC-19(6):944, 1974.

    Article  Google Scholar 

  21. M.B. Priestley. Spectral Analysis and Time Series. Academic Press, New York, 1981.

    MATH  Google Scholar 

  22. T. Soderstrom and P. Stoica. System Identification. Prentice Hall, Hertfordshire (UK), 1989.

    Google Scholar 

  23. I. Gustavsson T. Soderstrom and L. Ljung. Identifiability conditions for linear systems op ear ting in closed loop. Int. J. Control 21 (2): 243–255, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  24. G.C. Goodwin T.S. Ng and B.D.O. Anderson. Identifiability of mimo linear dynamic systems operating in closed loop. Automatical 13:477–485, 1977.

    Article  MATH  Google Scholar 

  25. V.G. Vorchik. Plant identification in a closed loop system. Aut. Telemekhanika, 4:32–48, April 1975.

    Google Scholar 

  26. P. Wellstead. Reference signals for closed loop identification. Int. X Control, 26(6):945–962, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  27. P. Wellstead . Non-parametric methods of system identification. Automatical 17(l):55–69, 1981.

    Article  MATH  Google Scholar 

  28. P.E. Wellstead and J.M. Edmunds. Least-squares identification of closed loop systems. Int. J. Control, 21(4):688–699, 1975

    Article  Google Scholar 

  29. J.S. Welsh and G.C. Goodwin. Finite sample properties of indirect non- parametric closed loop identification. CIDAC Technical Report 0030, University of Newcastle, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Newcastle, Callaghan, NSW, Australia, 2308

    Graham C. Goodwin & James S. Welsh

Authors
  1. Graham C. Goodwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James S. Welsh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Newcastle, Callaghan, 2308, NSW, Australia

    Graham Goodwin BSc, BE PhD, FIEEE, Hon FIE Aust., FTS, FAA

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London Limited

About this chapter

Cite this chapter

Goodwin, G.C., Welsh, J.S. (2001). Singularity Issues in Closed Loop Identification. In: Goodwin, G. (eds) Model Identification and Adaptive Control. Springer, London. https://doi.org/10.1007/978-1-4471-0711-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0711-8_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1185-6

  • Online ISBN: 978-1-4471-0711-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation