Design of Computer-Optimised Signals for Linear System Identification

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


The design of computer-optimised signals is considered. Unlike pseudorandom signals which have fixed spectra, the objective now is to design a signal with a spectrum as close as possible to a specified spectrum. The optimisation algorithms come in different forms, depending on the class of signal, and particularly the number of signal levels. The first class of signals considered is the multisine sum of harmonics signals which can take any value between their minimum and maximum. In contrast, the second class dealt with comprises discrete interval signals, which are either binary or ternary. The third class considered is the multilevel multiharmonic signals which have a small number of signal levels, where this number is specified by the user. It is then shown that it is also possible to combine the advantages of pseudorandom and computer-optimised designs leading to a class of hybrid signals, which are generated as a combination of pseudorandom signals and computer-optimised ones. Finally, the concept of optimal input signals is briefly described where the power spectra are optimised based on initial models to satisfy an application-related objective.


  1. Annergren M, Larsson CA, Hjalmarsson H, Bombois X, Wahlberg B (2017) Application-oriented input design in system identification: optimal input design for control. IEEE Control Syst Mag 37:31–56CrossRefGoogle Scholar
  2. Boyd S (1986) Multitone signals with low crest factor. IEEE Trans Circ Syst 33:1018–1022CrossRefGoogle 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. Faifer M, Ottoboni R, Toscani S, Cherbaucich C, Mazza P (2015) Metrological characterization of a signal generator for the testing of medium-voltage measurement transducers. IEEE Trans Instrum Meas 64:1837–1846CrossRefGoogle Scholar
  5. Gersho A, Gopinath B, Odlyzko AM (1979) Coefficient inaccuracy in transversal filtering. Bell Syst Technol J 58:2301–2316MathSciNetCrossRefGoogle Scholar
  6. Godfrey KR, Tan AH, Barker HA, Chong B (2005) A survey of readily accessible perturbation signals for system identification in the frequency domain. Control Eng Pract 13:1391–1402CrossRefGoogle Scholar
  7. Guillaume P, Schoukens J, Pintelon R, Kollár I (1991) Crest-factor minimization using nonlinear Chebyshev approximation methods. IEEE Trans Instrum Meas 40:982–989CrossRefGoogle Scholar
  8. Kazazis S, Esterer N, Depalle P, McAdams S (2017) A performance evaluation of the Timbre Toolbox and the MIRtoolbox on calibrated test sounds. In: Proceedings of the international symposium on musical acoustics, Montreal, Canada, 18–22 June, pp 144–147Google Scholar
  9. Kollár I (1994) Frequency domain system identification toolbox for use with MATLAB. The MathWorks Inc., Natick, MAGoogle Scholar
  10. Kulesza Z (2014) Dynamic behaviour of cracked rotor subjected to multisine excitation. J Sound Vib 333:1369–1378CrossRefGoogle Scholar
  11. McCormack AS, Godfrey KR, Flower JO (1995) The design of multilevel multiharmonic signals for system identification. IEE Proc Control Theory Appl 142:247–252CrossRefGoogle Scholar
  12. Newman DJ (1965) An L1 extremal problem for polynomials. Proc Am Math Soc 16:1287–1290zbMATHGoogle Scholar
  13. Oliva Uribe D, Schoukens J, Stroop R (2018) Improved tactile resonance sensor for robotic assisted surgery. Mech Syst Sig Process 99:600–610CrossRefGoogle Scholar
  14. Pintelon R, Schoukens J (2012) System identification: a frequency domain approach. Wiley, Hoboken, NJCrossRefGoogle Scholar
  15. Pintelon R, Louarroudi E, Lataire J (2014) Quantifying the time-variation in FRF measurements using random phase multisines with nonuniformly spaced harmonics. IEEE Trans Instrum Meas 63:1384–1394CrossRefGoogle Scholar
  16. Roinila T, Vilkko M, Sun J (2014) Online grid impedance measurement using discrete-interval binary sequence injection. IEEE J Emerg Sel Top Power Electron 2:985–993CrossRefGoogle Scholar
  17. Rudin W (1959) Some theorems on Fourier coefficients. Proc Am Math Soc 10:855–859MathSciNetCrossRefGoogle Scholar
  18. Sanchez B, Louarroudi E, Jorge E, Cinca J, Bragos R, Pintelon R (2013) A new measuring and identification approach for time-varying bioimpedance using multisine electrical impedance spectroscopy. Physiol Meas 34:339–357CrossRefGoogle Scholar
  19. Schoukens J, Pintelon R, Rolain Y, Dobrowiecki T (2001) Frequency response function measurements in the presence of nonlinear distortions. Automatica 37:939–946MathSciNetCrossRefGoogle Scholar
  20. Schroeder MR (1970) Synthesis of low-peak-factor signals and binary sequences with low autocorrelation. IEEE Trans Inf Theory 16:85–89CrossRefGoogle Scholar
  21. Shapiro HS (1951) Extremal problems for polynomials. M.S. thesis, Massachusetts Institute of Technology, MAGoogle Scholar
  22. Stoev J, Schoukens J (2016) Nonlinear system identification—application for industrial hydro-static drive-line. Control Eng Pract 54:154–165CrossRefGoogle Scholar
  23. Tan AH, Godfrey KR (2004) An improved routine for designing multi-level multi-harmonic signals. In: Proceedings of the UKACC international conference on control (paper ID–027), Bath, UK, 6–9 SeptGoogle Scholar
  24. Tan AH, Godfrey KR, Barker HA (2005) Design of computer-optimized pseudo-random maximum length signals for linear identification in the presence of nonlinear distortions. IEEE Trans Instrum Meas 54:2513–2519CrossRefGoogle Scholar
  25. van den Bos A, Krol RG (1979) Synthesis of discrete-interval binary signals with specified Fourier amplitude spectra. Int J Control 30:871–884MathSciNetCrossRefGoogle Scholar
  26. van der Maas R, van der Maas A, Dries J, de Jager B (2016) Efficient nonparametric identification for high-precision motion systems: a practical comparison based on a medical X-ray system. Control Eng Pract 56:75–85CrossRefGoogle Scholar
  27. Van der Ouderaa E, Schoukens J, Renneboog J (1988) Peak factor minimization using a time-frequency swapping algorithm. IEEE Trans Instrum Meas 37:145–147CrossRefGoogle Scholar
  28. Wahlberg B, Hjalmarsson H, Annergren M (2010) On optimal input design in system identification for control. In: Proceedings of the IEEE conference on decision and control, Atlanta, GA, 15–17 Dec, pp 5548–5553Google Scholar
  29. Widanage WD, Barai A, Chouchelamane GH, Uddin K, McGordon A, Marco J, Jennings P (2016) Design and use of multisine signals for Li–ion battery equivalent circuit modelling. Part 1: signal design. J Power Sources 324:70–78CrossRefGoogle Scholar
  30. Yang Y, Wang L, Wang P, Yang X, Zhang F, Wen H, Teng Z (2015) Design of tri-level excitation signals for broadband bioimpedance spectroscopy. Physiol Meas 36:1995–2007CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

Personalised recommendations