Skip to main content

2017 | OriginalPaper | Buchkapitel

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

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

Erschienen in: Adaptive and Robust Active Vibration Control

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
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
The chirp will be considered only for complexity evaluation, for other results concerning chirp disturbance see [33, 34].
 
Literatur
1.
2.
Zurück zum Zitat 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, 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
3.
Zurück zum Zitat 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 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
5.
Zurück zum Zitat Landau I, Zito G (2005) Digital control systems - design, identification and implementation. Springer, London Landau I, Zito G (2005) Digital control systems - design, identification and implementation. Springer, London
6.
Zurück zum Zitat Nehorai A (1985) A minimal parameter adaptive notch filter with constrained poles and zeros. IEEE Trans Acoust Speech Signal Process ASSP-33:983–996 Nehorai A (1985) A minimal parameter adaptive notch filter with constrained poles and zeros. IEEE Trans Acoust Speech Signal Process ASSP-33:983–996
7.
Zurück zum Zitat Astrom KJ, Wittenmark B (1984) Computer controlled systems. Theory and design. Prentice-Hall, Englewood Cliffs Astrom KJ, Wittenmark B (1984) Computer controlled systems. Theory and design. Prentice-Hall, Englewood Cliffs
8.
Zurück zum Zitat 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 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
9.
Zurück zum Zitat Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, LondonCrossRefMATH Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, LondonCrossRefMATH
11.
Zurück zum Zitat Tsypkin Y (1997) Stochastic discrete systems with internal models. J Autom Inf Sci 29(4&5):156–161CrossRef Tsypkin Y (1997) Stochastic discrete systems with internal models. J Autom Inf Sci 29(4&5):156–161CrossRef
12.
Zurück zum Zitat 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 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.
Zurück zum Zitat Tay TT, Mareels IMY, Moore JB (1997) High performance control. Birkhauser, Boston Tay TT, Mareels IMY, Moore JB (1997) High performance control. Birkhauser, Boston
14.
Zurück zum Zitat 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 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.
Zurück zum Zitat Tichavský P, Nehorai A (1997) Comparative study of four adaptive frequency trackers. IEEE Trans Autom Control 45(6):1473–1484MATH Tichavský P, Nehorai A (1997) Comparative study of four adaptive frequency trackers. IEEE Trans Autom Control 45(6):1473–1484MATH
20.
21.
Zurück zum Zitat Obregon-Pulido G, Castillo-Toledo B, Loukianov A (2002) A globally convergent estimator for n-frequencies. IEEE Trans Autom Control 47(5):857–863MathSciNetCrossRef 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.
Zurück zum Zitat 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 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.
Zurück zum Zitat 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 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.
25.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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 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.
Zurück zum Zitat 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 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
Metadaten
Titel
Adaptive Attenuation of Multiple Sparse Unknown and Time-Varying Narrow-Band Disturbances
verfasst von
Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-41450-8_13