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2017 | OriginalPaper | Chapter

13. Adaptive Attenuation of Multiple Sparse Unknown and Time-Varying Narrow-Band Disturbances

Authors : Ioan Doré Landau, Tudor-Bogdan Airimitoaie, Abraham Castellanos-Silva, Aurelian Constantinescu

Published in: Adaptive and Robust Active Vibration Control

Publisher: Springer International Publishing

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Abstract

This chapter considers the possible solutions for adaptive attenuation of multiple sparse unknown and time-varying narrow-band disturbances. One takes also into account the possible presence of low damped complex zeros in the vicinity of the attenuation region. The problem of the design of the underlined linear controller for the known disturbance case is itself a challenging problem and is discussed first. The adaptive schemes proposed are obtained by extending the linear solutions to the case of unknown characteristics of the disturbances. Comparative experimental evaluation of the various solutions on a test bench are given.

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previous chapter Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances

next chapter Design of Linear Feedforward Compensation of Broad-band Disturbances from Data

The complex variable \(z^{-1}\) is used to characterize the system’s behaviour in the frequency domain and the delay operator \(q^{-1}\) will be used for the time domain analysis.

As indicated earlier, it is assumed that a reliable model identification is achieved and therefore the estimated model is assumed to be equal to the true model.

For frequencies bellow \(0.17\,{f_S}\) (\({f_S}\) is the sampling frequency) the design can be done with a very good precision directly in discrete time [5].

Its structure in a mirror symmetric form guarantees that the roots are always on the unit circle.

The argument \((q^{-1})\) will be dropped in some of the following equations.

For the development of the equation for the adaptation error one assumes that the estimated parameters have constant values which allows to use the commutativity property of the various operators.

The details of the developments leading to this equation are given in the Appendix C.

Neglecting the non-commutativity of the time-varying operators.

The disturbance passes through a so called “primary path” which is not represented in Fig. 13.5.

The chirp will be considered only for complexity evaluation, for other results concerning chirp disturbance see [33, 34].

Landau ID, Alma M, Constantinescu A, Martinez JJ, Noë M (2011) Adaptive regulation - rejection of unknown multiple narrow band disturbances (a review on algorithms and applications). Control Eng Pract 19(10):1168–1181. doi:10.1016/j.conengprac.2011.06.005 CrossRef

Landau I, Constantinescu A, Rey D (2005) Adaptive narrow band disturbance rejection applied to an active suspension - an internal model principle approach. Automatica 41(4):563–574MathSciNetCrossRefMATH

Landau I, Alma M, Martinez J, Buche G (2011) Adaptive suppression of multiple time-varying unknown vibrations using an inertial actuator. IEEE Trans Control Syst Technol 19(6):1327–1338. doi:10.1109/TCST.2010.2091641 CrossRef

Procházka H, Landau ID (2003) Pole placement with sensitivity function shaping using 2nd order digital notch filters. Automatica 39(6):1103–1107. doi:10.1016/S0005-1098(03)00067-0 MathSciNetCrossRefMATH

Landau I, Zito G (2005) Digital control systems - design, identification and implementation. Springer, London

Nehorai A (1985) A minimal parameter adaptive notch filter with constrained poles and zeros. IEEE Trans Acoust Speech Signal Process ASSP-33:983–996

Astrom KJ, Wittenmark B (1984) Computer controlled systems. Theory and design. Prentice-Hall, Englewood Cliffs

Chen X, Tomizuka M (2012) A minimum parameter adaptive approach for rejecting multiple narrow-band disturbances with application to hard disk drives. IEEE Trans Control Syst Technol 20(2):408–415. doi:10.1109/TCST.2011.2178025 CrossRef

Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, LondonCrossRefMATH

10.

Castellanos-Silva A, Landau ID, Dugard L, Chen X (2016) Modified direct adaptive regulation scheme applied to a benchmark problem. Eur J Control 28:69–78. doi:10.1016/j.ejcon.2015.12.006 MathSciNetCrossRefMATH

11.

Tsypkin Y (1997) Stochastic discrete systems with internal models. J Autom Inf Sci 29(4&5):156–161CrossRef

12.

de Callafon RA, Kinney CE (2010) Robust estimation and adaptive controller tuning for variance minimization in servo systems. J Adva Mech Design Syst Manuf 4(1):130–142

13.

Tay TT, Mareels IMY, Moore JB (1997) High performance control. Birkhauser, Boston

14.

Airimitoaie TB, Landau I, Dugard L, Popescu D (2011) Identification of mechanical structures in the presence of narrow band disturbances - application to an active suspension. In: 2011 19th mediterranean conference on control automation (MED), pp 904–909. doi:10.1109/MED.2011.5983076

15.

Tichavský P, Nehorai A (1997) Comparative study of four adaptive frequency trackers. IEEE Trans Autom Control 45(6):1473–1484MATH

16.

Rao D, Kung SY (1984) Adaptive notch filtering for the retrieval of sinusoids in noise. IEEE Trans Acoust Speech Signal Process 32(4):791–802. doi:10.1109/TASSP.1984.1164398 CrossRef

17.

Regalia PA (1991) An improved lattice-based adaptive IIR notch filter. IEEE Trans Signal Process 9(9):2124–2128. doi:10.1109/78.134453 CrossRef

18.

Chen BS, Yang TY, Lin BH (1992) Adaptive notch filter by direct frequency estimation. Signal Process 27(2):161–176. doi:10.1016/0165-1684(92)90005-H CrossRefMATH

19.

Li G (1997) A stable and efficient adaptive notch filter for direct frequency estimation. IEEE Trans Signal Process 45(8):2001–2009. doi:10.1109/78.611196 CrossRef

20.

Hsu L, Ortega R, Damm G (1999) A globally convergent frequency estimator. IEEE Trans Autom Control 4(4):698–713MathSciNetCrossRefMATH

21.

Obregon-Pulido G, Castillo-Toledo B, Loukianov A (2002) A globally convergent estimator for n-frequencies. IEEE Trans Autom Control 47(5):857–863MathSciNetCrossRef

22.

Stoica P, Nehorai A (1988) Performance analysis of an adaptive notch filter with constrained poles and zeros. IEEE Trans Acoust Speech Signal Process 36(6):911–919

23.

M’Sirdi N, Tjokronegoro H, Landau I (1988) An RML algorithm for retrieval of sinusoids with cascaded notch filters. In: 1988 International conference on acoustics, speech, and signal processing, 1988. ICASSP-88, vol 4, pp 2484–2487. doi:10.1109/ICASSP.1988.197147

24.

Airimitoaie TB, Landau ID (2014) Indirect adaptive attenuation of multiple narrow-band disturbances applied to active vibration control. IEEE Trans Control Syst Technol 22(2):761–769. doi:10.1109/TCST.2013.2257782 CrossRef

25.

Castellanos-Silva A, Landau ID, Airimitoaie TB (2013) Direct adaptive rejection of unknown time-varying narrow band disturbances applied to a benchmark problem. Eur J Control 19(4):326– 336. doi:10.1016/j.ejcon.2013.05.012 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

26.

Landau ID, Silva AC, Airimitoaie TB, Buche G, Noé M (2013) An active vibration control system as a benchmark on adaptive regulation. In: Control conference (ECC), 2013 European, pp 2873–2878 (2013)

27.

Aranovskiy S, Freidovich LB (2013) Adaptive compensation of disturbances formed as sums of sinusoidal signals with application to an active vibration control benchmark. Eur J Control 19(4):253–265. doi:10.1016/j.ejcon.2013.05.008 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

28.

Airimitoaie TB, Silva AC, Landau ID (2013) Indirect adaptive regulation strategy for the attenuation of time varying narrow-band disturbances applied to a benchmark problem. Eur J Control 19(4):313–325. doi:10.1016/j.ejcon.2013.05.011 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

29.

de Callafon RA, Fang H (2013) Adaptive regulation via weighted robust estimation and automatic controller tuning. Eur J Control 19(4):266–278. doi:10.1016/j.ejcon.2013.05.009 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

30.

Karimi A, Emedi Z (2013) H\(_\infty \) gain-scheduled controller design for rejection of time-varying narrow-band disturbances applied to a benchmark problem. Eur J Control 19(4):279–288. doi:10.1016/j.ejcon.2013.05.010 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

31.

Chen X, Tomizuka M (2013) Selective model inversion and adaptive disturbance observer for time-varying vibration rejection on an active-suspension benchmark. Eur J Control 19(4):300–312 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

32.

Wu Z, Amara FB (2013) Youla parameterized adaptive regulation against sinusoidal exogenous inputs applied to a benchmark problem. Eur J Control 19(4):289–299 (Benchmark on Adaptive Regulation: Rejection of unknown/time-varying multiple narrow band disturbances)

33.

Castellanos-Silva A (2014) Compensation adaptative par feedback pour le contrôle actif de vibrations en présence d’incertitudes sur les paramétres du procédé. Ph.D. thesis, Université de Grenoble

34.

Landau ID, Silva AC, Airimitoaie TB, Buche G, Noé M (2013) Benchmark on adaptive regulation - rejection of unknown/time-varying multiple narrow band disturbances. Eur J Control 19(4):237–252. doi:10.1016/j.ejcon.2013.05.007

Title: Adaptive Attenuation of Multiple Sparse Unknown and Time-Varying Narrow-Band Disturbances
Authors: Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Publisher: Springer International Publishing
Book: Adaptive and Robust Active Vibration Control
Print ISBN: 978-3-319-41449-2

Electronic ISBN: 978-3-319-41450-8

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-41450-8_13

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