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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
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.
- 2.
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.
- 3.
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].
- 4.
Its structure in a mirror symmetric form guarantees that the roots are always on the unit circle.
- 5.
The argument \((q^{-1})\) will be dropped in some of the following equations.
- 6.
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.
- 7.
The details of the developments leading to this equation are given in the Appendix C.
- 8.
Neglecting the non-commutativity of the time-varying operators.
- 9.
The disturbance passes through a so called “primary path” which is not represented in Fig. 13.5.
- 10.
References
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
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):563–574
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
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
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
Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, London
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
Tsypkin Y (1997) Stochastic discrete systems with internal models. J Autom Inf Sci 29(4&5):156–161
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
Tay TT, Mareels IMY, Moore JB (1997) High performance control. Birkhauser, Boston
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
Tichavský P, Nehorai A (1997) Comparative study of four adaptive frequency trackers. IEEE Trans Autom Control 45(6):1473–1484
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
Regalia PA (1991) An improved lattice-based adaptive IIR notch filter. IEEE Trans Signal Process 9(9):2124–2128. doi:10.1109/78.134453
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
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
Hsu L, Ortega R, Damm G (1999) A globally convergent frequency estimator. IEEE Trans Autom Control 4(4):698–713
Obregon-Pulido G, Castillo-Toledo B, Loukianov A (2002) A globally convergent estimator for n-frequencies. IEEE Trans Autom Control 47(5):857–863
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
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
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
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)
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)
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)
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)
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)
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)
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)
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)
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
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Landau, I.D., Airimitoaie, TB., Castellanos-Silva, A., Constantinescu, A. (2017). Adaptive Attenuation of Multiple Sparse Unknown and Time-Varying Narrow-Band Disturbances. In: Adaptive and Robust Active Vibration Control. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-41450-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-41450-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-41449-2
Online ISBN: 978-3-319-41450-8
eBook Packages: EngineeringEngineering (R0)