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Correlation Methods

  • Karel J. Keesman
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)

Abstract

In many applications noise is clearly present. Under those circumstances, the reliability of the direct estimates of the impulse response function g(t) or frequency function G(e ) can be significantly reduced. Therefore, in Chap. 4 correlation methods, which are less sensitive to noise and thus very useful under practical circumstances, are presented. In particular, the so-called Wiener–Hopf relationship is derived from input–output data and analyzed with respect to its filter properties. The chapter finishes with spectral analysis methods that provide a transfer-function estimate using power spectra.

Keywords

Autocorrelation Function Spectral Analysis Method Hopf Equation White Noise Signal Frequency Domain Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [AMLL02]
    A. Al Mamun, T.H. Lee, T.S. Low, Frequency domain identification of transfer function model of a disk drive actuator. Mechatronics 12(4), 563–574 (2002) CrossRefGoogle Scholar
  2. [Bai03a]
    E.-W. Bai, Frequency domain identification of Hammerstein models. IEEE Trans. Autom. Control 48(4), 530–542 (2003) CrossRefGoogle Scholar
  3. [Bai03b]
    E.-W. Bai, Frequency domain identification of Wiener models. Automatica 39(9), 1521–1530 (2003) MathSciNetMATHCrossRefGoogle Scholar
  4. [BE83]
    D.R. Brillinger, P.R. Krishnaiah (eds.), Handbook of Statistics 3: Time Series in the Frequency Domain (North-Holland, Amsterdam, 1983) Google Scholar
  5. [Bri81]
    D.R. Brillinger, Time Series: Data Analysis and Theory (Holden-Day, Oakland, 1981) MATHGoogle Scholar
  6. [CC94]
    J.-M. Chen, B.-S. Chen, A higher-order correlation method for model-order and parameter estimation. Automatica 30(8), 1339–1344 (1994) MathSciNetMATHCrossRefGoogle Scholar
  7. [CHY02]
    Y.-Y. Chen, P.-Y. Huang, J.-Y. Yen, Frequency-domain identification algorithms for servo systems with friction. IEEE Trans. Control Syst. Technol. 10(5), 654–665 (2002) CrossRefGoogle Scholar
  8. [EO68]
    L.D. Enochson, R.K. Otnes, Programming and analysis for digital time series data. Technical report, US Dept. of Defense, Shock and Vibration Info. Center, 1968 Google Scholar
  9. [ES81]
    H. El-Sherief, Multivariable system structure and parameter identification using the correlation method. Automatica 17(3), 541–544 (1981) MathSciNetMATHCrossRefGoogle Scholar
  10. [GL09b]
    J. Gillberg, L. Ljung, Frequency-domain identification of continuous-time ARMA models from sampled data. Automatica 45(6), 1371–1378 (2009) MATHCrossRefGoogle Scholar
  11. [God80]
    K.R. Godfrey, Correlation methods. Automatica 16(5), 527–534 (1980) MATHCrossRefGoogle Scholar
  12. [HvdMS02]
    R.H.A. Hensen, M.J.G. van de Molengraft, M. Steinbuch, Frequency domain identification of dynamic friction model parameters. IEEE Trans. Control Syst. Technol. 10(2), 191–196 (2002) CrossRefGoogle Scholar
  13. [JW68]
    G.M. Jenkins, D.G. Watts, Spectral Analysis and Its Applications (Holden-Day, Oakland, 1968) MATHGoogle Scholar
  14. [Kay88]
    S.M. Kay, Modern Spectral Estimation: Theory and Application. Prentice-Hall Signal Processing Series (Prentice-Hall, New York, 1988) MATHGoogle Scholar
  15. [KKZ77]
    V.I. Kostyuk, V.E. Kraskevitch, K.K. Zelensky, Frequency domain identification of complex systems. Syst. Sci. 3(1), 5–12 (1977) MathSciNetMATHGoogle Scholar
  16. [Kol93]
    I. Kollar, On frequency-domain identification of linear systems. IEEE Trans. Instrum. Meas. 42(1), 2–6 (1993) MathSciNetCrossRefGoogle Scholar
  17. [Lju99b]
    L. Ljung, System Identification—Theory for the User, 2nd edn. (Prentice Hall, New York, 1999) Google Scholar
  18. [LL96]
    W. Li, J.H. Lee, Frequency-domain closed-loop identification of multivariable systems for feedback control. AIChE J. 42(10), 2813–2827 (1996) CrossRefGoogle Scholar
  19. [Mar87]
    S.L. Marple, Digital Spectral Analysis with Applications (Prentice-Hall, New York, 1987) Google Scholar
  20. [PS97]
    R. Pintelon, J. Schoukens, Frequency-domain identification of linear timeinvariant systems under nonstandard conditions. IEEE Trans. Instrum. Meas. 46(1), 65–71 (1997) CrossRefGoogle Scholar
  21. [PS01]
    R. Pintelon, J. Schoukens, System Identification: A Frequency Domain Approach (Wiley–IEEE Press, New York, 2001) CrossRefGoogle Scholar
  22. [RSP97]
    Y. Rolain, J. Schoukens, R. Pintelon, Order estimation for linear time-invariant systems using frequency domain identification methods. IEEE Trans. Autom. Control 42(10), 1408–1417 (1997) MathSciNetMATHCrossRefGoogle Scholar
  23. [SGR+00]
    A. Stenman, F. Gustafsson, D.E. Rivera, L. Ljung, T. McKelvey, On adaptive smoothing of empirical transfer function estimates. Control Eng. Pract. 9, 1309–1315 (2000) CrossRefGoogle Scholar
  24. [SM97]
    P. Stoica, R.L. Moses, Introduction to Spectral Analysis (Prentice-Hall, New York, 1997) MATHGoogle Scholar
  25. [SOS00]
    L. Sun, H. Ohmori, A. Sano, Frequency domain approach to closed-loop identification based on output inter-sampling scheme, in Proceedings of the American Control Conference, vol. 3 (2000), pp. 1802–1806 Google Scholar
  26. [SVPG99]
    J. Schoukens, G. Vandersteen, R. Pintelon, P. Guillaume, Frequency-domain identification of linear systems using arbitrary excitations and a nonparametric noise model. IEEE Trans. Autom. Control 44(2), 343–347 (1999) MathSciNetMATHCrossRefGoogle Scholar
  27. [TY90]
    A.P. Tzes, S. Yurkovich, Frequency domain identification scheme for flexible structure control. J. Dyn. Syst. Meas. Control, Trans. ASME 112(3), 427–434 (1990) MATHCrossRefGoogle Scholar
  28. [Wel77]
    P.E. Wellstead, Reference signals for closed-loop identification. Int. J. Control 26(6), 945–962 (1977) MathSciNetMATHCrossRefGoogle Scholar
  29. [WG04]
    E. Wernholt, S. Gunnarsson, On the use of a multivariable frequency response estimation method for closed loop identification, in Proceedings of the IEEE Conference on Decision and Control, vol. 1 (2004), pp. 827–832 Google Scholar
  30. [WZG01]
    Q.-G. Wang, Y. Zhang, X. Guo, Robust closed-loop identification with application to auto-tuning. J. Process Control 11(5), 519–530 (2001) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Systems and Control GroupWageningen UniversityWageningenNetherlands

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