Skip to main content
Top

2017 | OriginalPaper | Chapter

12. Direct Adaptive Feedback Attenuation of 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

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter presents the basic algorithm for direct adaptive feedback attenuation of unknown and time-varying narrow-band disturbances. This algorithm implements the Internal Model Principle for disturbance attenuation using a Youla–Kučera parametrization for the controller. The use of a FIR Youla–Kučera filter allows to develop a direct adaptive scheme where the poles of the closed-loop defined by the central controller remain unchanged. Specific robustness issues for the design of the central controller are discussed. Experimental results obtained on the bench tests presented in Chap. 2 will illustrate the performance of the algorithm.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Footnotes
1
Called tonal disturbances.
 
2
Throughout the chapter, it is assumed that the number of narrow-band disturbances is known (it can be estimated from data if necessary) but not their frequency characteristics.
 
3
The Youla–Kučera parametrization has been presented in Chap. 7.
 
4
The disturbance passes through a so called primary path which is not represented in this figure, and p(t) is its output.
 
5
The argument \((z^{-1})\) will be omitted in some of the following equations to make them more compact.
 
6
It is assumed that a reliable model identification is achieved and therefore the estimated model is assumed to be equal to the true model.
 
7
Throughout the book, \(n_X\) denotes the degree of the polynomial X.
 
8
Of course, it is assumed that \(D_{p}\) and B do not have common factors.
 
9
In adaptive control and estimation the predicted output at \(t+1\) can be computed either on the basis of the previous parameter estimates (a priori, time t) or on the basis of the current parameter estimates (a posteriori, time \(t+1\)).
 
10
Of course the value of 2 s can be changed, but the principle of measurement remains the same.
 
11
Any design method allowing to satisfy these constraints can be used.
 
12
For results obtained with an indirect adaptive control scheme see [7].
 
13
The case of multiple unknown narrow-band disturbances will be discussed in Chap. 13.
 
Literature
1.
go back to reference Widrow B, Stearns S (1985) Adaptive signal processing. Prentice-Hall, Englewood CliffsMATH Widrow B, Stearns S (1985) Adaptive signal processing. Prentice-Hall, Englewood CliffsMATH
2.
go back to reference Beranek L, Ver I (1992) Noise and vibration control engineering: principles and applications. Wiley, New York Beranek L, Ver I (1992) Noise and vibration control engineering: principles and applications. Wiley, New York
3.
go back to reference Fuller C, Elliott S, Nelson P (1997) Active control of vibration. Academic Press, New YorkCrossRef Fuller C, Elliott S, Nelson P (1997) Active control of vibration. Academic Press, New YorkCrossRef
4.
go back to reference Elliott S (2001) Signal processing for active control. Academic Press, San Diego Elliott S (2001) Signal processing for active control. Academic Press, San Diego
7.
go back to reference 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
9.
10.
go back to reference Castellanos Silva A, Landau ID, Ioannou P (2014) Direct adaptive regulation in the vicinity of low damped complex zeros - application to active vibration control. In: 22nd Mediterranean conference on control and automation (MED), pp 255–260 (2014) Castellanos Silva A, Landau ID, Ioannou P (2014) Direct adaptive regulation in the vicinity of low damped complex zeros - application to active vibration control. In: 22nd Mediterranean conference on control and automation (MED), pp 255–260 (2014)
12.
13.
14.
go back to reference 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
16.
go back to reference 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
18.
go back to reference 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
19.
go back to reference Landau ID, Airimitoaie TB, Castellanos Silva A (2015) Adaptive attenuation of unknown and time-varying narrow band and broadband disturbances. Int J Adapt Control Signal Process 29(11):1367–1390MathSciNetCrossRefMATH Landau ID, Airimitoaie TB, Castellanos Silva A (2015) Adaptive attenuation of unknown and time-varying narrow band and broadband disturbances. Int J Adapt Control Signal Process 29(11):1367–1390MathSciNetCrossRefMATH
20.
go back to reference Alma M, Martinez J, Landau I, Buche G (2012) Design and tuning of reduced order H\(_\infty \) feedforward compensators for active vibration control. IEEE Trans Control Syst Technol 20(2):554–561. doi:10.1109/TCST.2011.2119485 CrossRef Alma M, Martinez J, Landau I, Buche G (2012) Design and tuning of reduced order H\(_\infty \) feedforward compensators for active vibration control. IEEE Trans Control Syst Technol 20(2):554–561. doi:10.​1109/​TCST.​2011.​2119485 CrossRef
21.
go back to reference Valentinotti S (2001) Adaptive rejection of unstable disturbances: application to a fed-batch fermentation. Thèse de doctorat, École Polytechnique Fédérale de Lausanne Valentinotti S (2001) Adaptive rejection of unstable disturbances: application to a fed-batch fermentation. Thèse de doctorat, École Polytechnique Fédérale de Lausanne
22.
go back to reference Valentinotti S, Srinivasan B, Holmberg U, Bonvin D, Cannizzaro C, Rhiel M, von Stockar U (2003) Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite. Control Eng Pract 11(6):665–674. doi:10.1016/S0967-0661(02)00172-7 CrossRef Valentinotti S, Srinivasan B, Holmberg U, Bonvin D, Cannizzaro C, Rhiel M, von Stockar U (2003) Optimal operation of fed-batch fermentations via adaptive control of overflow metabolite. Control Eng Pract 11(6):665–674. doi:10.​1016/​S0967-0661(02)00172-7 CrossRef
23.
go back to reference Ben Amara F, Kabamba P, Ulsoy A (1999) Adaptive sinusoidal disturbance rejection in linear discrete-time systems - Part I: theory. J Dyn Syst Meas Control 121:648–654CrossRef Ben Amara F, Kabamba P, Ulsoy A (1999) Adaptive sinusoidal disturbance rejection in linear discrete-time systems - Part I: theory. J Dyn Syst Meas Control 121:648–654CrossRef
24.
go back to reference F Ben Amara, Kabamba P, Ulsoy A (1999) Adaptive sinusoidal disturbance rejection in linear discrete-time systems - Part II: experiments. J Dyn Syst Meas Control 121:655–659CrossRef F Ben Amara, Kabamba P, Ulsoy A (1999) Adaptive sinusoidal disturbance rejection in linear discrete-time systems - Part II: experiments. J Dyn Syst Meas Control 121:655–659CrossRef
25.
go back to reference Bodson M, Douglas S (1997) Adaptive algorithms for the rejection of sinusosidal disturbances with unknown frequency. Automatica 33:2213–2221MathSciNetCrossRefMATH Bodson M, Douglas S (1997) Adaptive algorithms for the rejection of sinusosidal disturbances with unknown frequency. Automatica 33:2213–2221MathSciNetCrossRefMATH
26.
go back to reference Marino R, Santosuosso G, Tomei P (2003) Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency. Automatica 39:1755–1761MathSciNetCrossRefMATH Marino R, Santosuosso G, Tomei P (2003) Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency. Automatica 39:1755–1761MathSciNetCrossRefMATH
28.
go back to reference Gouraud T, Gugliemi M, Auger F (1997) Design of robust and frequency adaptive controllers for harmonic disturbance rejection in a single-phase power network. In: Proceedings of the European control conference, Bruxelles Gouraud T, Gugliemi M, Auger F (1997) Design of robust and frequency adaptive controllers for harmonic disturbance rejection in a single-phase power network. In: Proceedings of the European control conference, Bruxelles
29.
go back to reference Hillerstrom G, Sternby J (1994) Rejection of periodic disturbances with unknown period - a frequency domain approach. In: Proceedings of American control conference, Baltimore, pp 1626–1631 Hillerstrom G, Sternby J (1994) Rejection of periodic disturbances with unknown period - a frequency domain approach. In: Proceedings of American control conference, Baltimore, pp 1626–1631
30.
go back to reference Johnson C (1976) Theory of disturbance-accomodating controllers. In: Leondes CT (ed) Control and dynamical systems, vol 12, pp 387–489 Johnson C (1976) Theory of disturbance-accomodating controllers. In: Leondes CT (ed) Control and dynamical systems, vol 12, pp 387–489
33.
go back to reference Bodson M (2005) Rejection of periodic distrubances of unknown and time-varying frequency. Int J Adapt Control Signal Process 19:67–88 Bodson M (2005) Rejection of periodic distrubances of unknown and time-varying frequency. Int J Adapt Control Signal Process 19:67–88
34.
go back to reference Tsypkin Y (1991) Adaptive-invariant discrete control systems. In: Thoma M, Wyner A (eds) Foundations of adaptive control. Lecture notes in control and information science, vol 160. Springer, Heidelberg, pp 239–268 Tsypkin Y (1991) Adaptive-invariant discrete control systems. In: Thoma M, Wyner A (eds) Foundations of adaptive control. Lecture notes in control and information science, vol 160. Springer, Heidelberg, pp 239–268
35.
go back to reference Mullhaupt Ph, Valentinotti S, Srinivasan B, Bonvin D (2012) Asymptotic rejection of nonvanishing disturbances despite plant-model mismatch. Int J Adapt Control Signal Process 26(12):1090–1110 Mullhaupt Ph, Valentinotti S, Srinivasan B, Bonvin D (2012) Asymptotic rejection of nonvanishing disturbances despite plant-model mismatch. Int J Adapt Control Signal Process 26(12):1090–1110
36.
go back to reference Jafari S, Ioannou P, Fitzpatrick B, Wang Y (2013) Robust stability and performance of adaptive jitter supression in laser beam pointing. In: 52nd IEEE conference on decision and control. Florence, Italy Jafari S, Ioannou P, Fitzpatrick B, Wang Y (2013) Robust stability and performance of adaptive jitter supression in laser beam pointing. In: 52nd IEEE conference on decision and control. Florence, Italy
37.
go back to reference Jafari S, Ioannou P, Fitzpatrick B, Wang Y (2013) Robustness and performance of adaptive suppresion of unknown periodic disturbances. IEEE Trans Autom Control (Under review) Jafari S, Ioannou P, Fitzpatrick B, Wang Y (2013) Robustness and performance of adaptive suppresion of unknown periodic disturbances. IEEE Trans Autom Control (Under review)
38.
go back to reference Castellanos-Silva A, Landau ID, Ioannou P (2015) Robust direct adaptive regulation of unknown disturbances in the vicinity of low-damped complex zeros-application to AVC. IEEE Trans Control Syst Technol 24(2):733–740. doi:10.1109/TCST.2015.2445859 Castellanos-Silva A, Landau ID, Ioannou P (2015) Robust direct adaptive regulation of unknown disturbances in the vicinity of low-damped complex zeros-application to AVC. IEEE Trans Control Syst Technol 24(2):733–740. doi:10.​1109/​TCST.​2015.​2445859
39.
go back to reference 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
40.
go back to reference Martinez JJ, Alma M (2012) Improving playability of blu-ray disc drives by using adaptive suppression of repetitive disturbances. Automatica 48(4):638–644MathSciNetCrossRefMATH Martinez JJ, Alma M (2012) Improving playability of blu-ray disc drives by using adaptive suppression of repetitive disturbances. Automatica 48(4):638–644MathSciNetCrossRefMATH
48.
go back to reference Sun Z, Tsao T (2000) Adaptive control with asymptotic tracking performance and its application to an electro-hydraulic servo system. J Dyn Syst Meas Control 122:188–195CrossRef Sun Z, Tsao T (2000) Adaptive control with asymptotic tracking performance and its application to an electro-hydraulic servo system. J Dyn Syst Meas Control 122:188–195CrossRef
49.
go back to reference Zhang Y, Mehta P, Bitmead R, Johnson C (1998) Direct adaptive control for tonal disturbance rejection. In: Proceedings of the American control conference, Philadelphia, pp 1480–1482 Zhang Y, Mehta P, Bitmead R, Johnson C (1998) Direct adaptive control for tonal disturbance rejection. In: Proceedings of the American control conference, Philadelphia, pp 1480–1482
50.
go back to reference Feng G, Palaniswami M (1992) A stable adaptive implementation of the internal model principle. IEEE Trans Autom Control 37:1220–1225MathSciNetCrossRefMATH Feng G, Palaniswami M (1992) A stable adaptive implementation of the internal model principle. IEEE Trans Autom Control 37:1220–1225MathSciNetCrossRefMATH
Metadata
Title
Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances
Authors
Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-41450-8_12