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Signal Design for the Identification of Nonlinear and Time-Varying Systems

  • Ai Hui TanEmail author
  • Keith Richard Godfrey
Chapter
Part of the Advances in Industrial Control book series (AIC)

Abstract

The identification setting is turned to systems with nonlinearities and time-varying properties. The treatment of systems with nonlinearities is first considered where the signal design is shown to be highly dependent on the objectives of the identification test. The identification of the best linear approximation is discussed next. This concept is very useful when a nonlinear process is to be linearised around its operating point. While the best linear approximation depends on the perturbation signal applied, those with Gaussian amplitude distribution are advantageous, particularly, in the identification of block-oriented systems. For the measurement of Volterra kernels, it is shown that multisine signals with specially designed harmonics enable the kernels to be measured without interharmonic distortion. Finally, a method based on frequency domain analysis which allows the quantification of the effects of nonlinearities, noise and time variation is expounded. The technique requires only a single experiment and in the case of multi-input systems, makes use of a set of signals which are uncorrelated with one another. The effectiveness of the technique is illustrated on a mist reactor system.

References

  1. Ase H, Katayama T (2015) A subspace-based identification of Wiener-Hammerstein benchmark model. Control Eng Pract 44:126–137CrossRefGoogle Scholar
  2. Cham CL, Tan AH, Tan WH (2016) Design and construction of a mist reactor system. In: Proceedings of the IEEE region 10 conference (TENCON), Singapore, 22–25 November, pp 3382–3385Google Scholar
  3. Cham CL, Tan AH, Tan WH (2017) Identification of a multivariable nonlinear and time-varying mist reactor system. Control Eng Pract 63:13–23CrossRefGoogle Scholar
  4. Evans C, Rees D, Jones L, Weiss M (1996) Periodic signals for measuring nonlinear Volterra kernels. IEEE Trans Instrum Meas 45:362–371CrossRefGoogle Scholar
  5. Han HT, Ma HG, Tan LN, Cao JF, Zhang JL (2014) Non-parametric identification method of Volterra kernels for nonlinear systems excited by multitone signal. Asian J Control 16:519–529MathSciNetCrossRefGoogle Scholar
  6. Lataire J, Louarroudi E, Pintelon R (2012) Detecting a time-varying behavior in frequency response function measurements. IEEE Trans Instrum Meas 61:2132–2143CrossRefGoogle Scholar
  7. Pintelon R, Schoukens J (2012) System identification: a frequency domain approach. Wiley, HobokenCrossRefGoogle Scholar
  8. Pintelon R, Louarroudi E, Lataire J (2013) Detecting and quantifying the nonlinear and time-variant effects in FRF measurements using periodic excitations. IEEE Trans Instrum Meas 62:3361–3373CrossRefGoogle Scholar
  9. Schoukens M, Pintelon R, Rolain Y (2014) Identification of Wiener-Hammerstein systems by a nonparametric separation of the best linear approximation. Automatica 50:628–634MathSciNetCrossRefGoogle Scholar
  10. Schoukens J, Pintelon R, Rolain Y, Dobrowiecki T (2001) Frequency response function measurements in the presence of nonlinear distortions. Automatica 37:939–946MathSciNetCrossRefGoogle Scholar
  11. Schoukens J, Vaes M, Pintelon R (2016) Linear system identification in a nonlinear setting: nonparametric analysis of nonlinear distortions and their impact on the best linear approximation. IEEE Control Syst Mag 36:38–69MathSciNetCrossRefGoogle Scholar
  12. Tan AH (2007) Design of truncated maximum length ternary signals where their squared versions have uniform even harmonics. IEEE Trans Autom Control 52:957–961MathSciNetCrossRefGoogle Scholar
  13. Tan AH (2018) Multi-input identification using uncorrelated signals and its application to dual-stage hard disk drives. IEEE Trans Magn 54: Article 9300604CrossRefGoogle Scholar
  14. Tan AH, Godfrey KR (2002) Identification of Wiener-Hammerstein models using linear interpolation in the frequency domain (LIFRED). IEEE Trans Instrum Meas 51:509–521CrossRefGoogle Scholar
  15. Tan AH, Cham CL, Godfrey KR (2015) Comparison of three modeling approaches for a thermodynamic cooling system with time-varying delay. IEEE Trans Instrum Meas 64:3116–3123CrossRefGoogle Scholar
  16. Vanbeylen L (2015) A fractional approach to identify Wiener-Hammerstein systems. Automatica 50:903–909MathSciNetCrossRefGoogle Scholar
  17. Weiss M, Evans C, Rees D, Jones L (1996) Structure identification of block-oriented nonlinear systems using periodic test signal. In: Proceedings of the IEEE instrumentation and measurement technology conference, Brussels, Belgium, 4–6 June, pp 8–13Google Scholar
  18. Weiss M, Evans C, Rees D (1998) Identification of nonlinear cascade systems using paired multisine signals. IEEE Trans Instrum Meas 47:332–336CrossRefGoogle Scholar
  19. Wong HK, Schoukens J, Godfrey KR (2013) Design of multilevel signals for identifying the best linear approximation of nonlinear systems. IEEE Trans Instrum Meas 62:519–524CrossRefGoogle Scholar
  20. Zhang B, Billings SA (2017) Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain. Mech Syst Signal Process 84:39–57CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringMultimedia UniversityCyberjayaMalaysia
  2. 2.School of EngineeringUniversity of WarwickCoventryUK

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