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Design of Computer-Optimised Signals for Linear System Identification

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Industrial Process Identification

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

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.

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References

  • 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 37:31–56

    Article  Google Scholar 

  • Boyd S (1986) Multitone signals with low crest factor. IEEE Trans Circ Syst 33:1018–1022

    Article  Google Scholar 

  • Cham CL, Tan AH, Tan WH (2017) Identification of a multivariable nonlinear and time-varying mist reactor system. Control Eng Pract 63:13–23

    Article  Google Scholar 

  • 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 64:1837–1846

    Article  Google Scholar 

  • Gersho A, Gopinath B, Odlyzko AM (1979) Coefficient inaccuracy in transversal filtering. Bell Syst Technol J 58:2301–2316

    Article  MathSciNet  Google Scholar 

  • 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 13:1391–1402

    Article  Google Scholar 

  • Guillaume P, Schoukens J, Pintelon R, Kollár I (1991) Crest-factor minimization using nonlinear Chebyshev approximation methods. IEEE Trans Instrum Meas 40:982–989

    Article  Google Scholar 

  • 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 144–147

    Google Scholar 

  • Kollár I (1994) Frequency domain system identification toolbox for use with MATLAB. The MathWorks Inc., Natick, MA

    Google Scholar 

  • Kulesza Z (2014) Dynamic behaviour of cracked rotor subjected to multisine excitation. J Sound Vib 333:1369–1378

    Article  Google Scholar 

  • McCormack AS, Godfrey KR, Flower JO (1995) The design of multilevel multiharmonic signals for system identification. IEE Proc Control Theory Appl 142:247–252

    Article  Google Scholar 

  • Newman DJ (1965) An L1 extremal problem for polynomials. Proc Am Math Soc 16:1287–1290

    MATH  Google Scholar 

  • Oliva Uribe D, Schoukens J, Stroop R (2018) Improved tactile resonance sensor for robotic assisted surgery. Mech Syst Sig Process 99:600–610

    Article  Google Scholar 

  • Pintelon R, Schoukens J (2012) System identification: a frequency domain approach. Wiley, Hoboken, NJ

    Book  Google Scholar 

  • 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 63:1384–1394

    Article  Google Scholar 

  • Roinila T, Vilkko M, Sun J (2014) Online grid impedance measurement using discrete-interval binary sequence injection. IEEE J Emerg Sel Top Power Electron 2:985–993

    Article  Google Scholar 

  • Rudin W (1959) Some theorems on Fourier coefficients. Proc Am Math Soc 10:855–859

    Article  MathSciNet  Google Scholar 

  • 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 34:339–357

    Article  Google Scholar 

  • Schoukens J, Pintelon R, Rolain Y, Dobrowiecki T (2001) Frequency response function measurements in the presence of nonlinear distortions. Automatica 37:939–946

    Article  MathSciNet  Google Scholar 

  • Schroeder MR (1970) Synthesis of low-peak-factor signals and binary sequences with low autocorrelation. IEEE Trans Inf Theory 16:85–89

    Article  Google Scholar 

  • Shapiro HS (1951) Extremal problems for polynomials. M.S. thesis, Massachusetts Institute of Technology, MA

    Google Scholar 

  • Stoev J, Schoukens J (2016) Nonlinear system identification—application for industrial hydro-static drive-line. Control Eng Pract 54:154–165

    Article  Google Scholar 

  • 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 Sept

    Google Scholar 

  • 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 54:2513–2519

    Article  Google Scholar 

  • van den Bos A, Krol RG (1979) Synthesis of discrete-interval binary signals with specified Fourier amplitude spectra. Int J Control 30:871–884

    Article  MathSciNet  Google Scholar 

  • 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 56:75–85

    Article  Google Scholar 

  • Van der Ouderaa E, Schoukens J, Renneboog J (1988) Peak factor minimization using a time-frequency swapping algorithm. IEEE Trans Instrum Meas 37:145–147

    Article  Google Scholar 

  • 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 5548–5553

    Google Scholar 

  • 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 324:70–78

    Article  Google Scholar 

  • 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 36:1995–2007

    Article  Google Scholar 

Download references

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Correspondence to Ai Hui Tan .

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Tan, A.H., Godfrey, K.R. (2019). Design of Computer-Optimised Signals for Linear System Identification. In: Industrial Process Identification. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-030-03661-4_3

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