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2017 | OriginalPaper | Chapter

4. Parameter Adaptation Algorithms

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

Parameter adaptation algorithms are the key step for estimating the parameters of the discrete time dynamic model of the system to be controlled and for building an adaptive active vibration control system. A coverage of the subject is provided from the perspective of the user. Stability and convergence issues are addressed.

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Footnotes
1
A symmetric square matrix F is termed positive definite if \(x^T F x > 0\), \(\forall ~x > 0\), \(x\in \mathbb {R}^n\). In addition: (i) all the terms of the main diagonal are positive, (ii) the determinants of all the principal minors are positive.
 
2
As it will be shown in Sect. 4.4, this closeness is characterized in terms of the property that \(D(z^{-1})/A(z^{-1})\) should be a strictly positive real transfer function.
 
3
It is assumed that the matrix \(\sum ^t_{i=1} \phi (i-1)\phi ^T(i-1)\) is invertible. This corresponds to an excitation condition.
 
4
It can be shown that the size of the adaptation gain is related to the parameter error [1].
 
5
In Chap. 5, it will be shown how the predictor should be modified in order to obtain unbiased estimated parameters.
 
6
A passive system is characterized by the fact that the sum of the input/output products over any time horizon is larger than a finite negative constant.
 
Literature
1.
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
2.
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
3.
go back to reference Widrow B, Hoff M (1960) Adaptive swithching circuits. Oric IRE WESCON Conv Rec 4(Session 16):96–104 Widrow B, Hoff M (1960) Adaptive swithching circuits. Oric IRE WESCON Conv Rec 4(Session 16):96–104
6.
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 (1972) Synthesis of hyperstable discrete model reference adaptive systems. In: Proceedings of 5th Asilomar conference on circuits and systems (8–10 November 1971), pp 591–595 Landau I (1972) Synthesis of hyperstable discrete model reference adaptive systems. In: Proceedings of 5th Asilomar conference on circuits and systems (8–10 November 1971), pp 591–595
8.
go back to reference Landau I (1973) Algorithme pour l’identification à l’aide d’un modèle ajustable parallèle. Comptes Rendus de l’Académie des Sciences 277(Séria A):197–200 Landau I (1973) Algorithme pour l’identification à l’aide d’un modèle ajustable parallèle. Comptes Rendus de l’Académie des Sciences 277(Séria A):197–200
9.
go back to reference Landau I (1974) A survey of model reference adaptive techniques - theory and applications. Automatica 10:353–379CrossRefMATH Landau I (1974) A survey of model reference adaptive techniques - theory and applications. Automatica 10:353–379CrossRefMATH
10.
go back to reference Landau I (1974) An asymptotic unbiased recursive identifier for linear systems. In: Proceedings of IEEE conference on decision and control, pp 288–294 Landau I (1974) An asymptotic unbiased recursive identifier for linear systems. In: Proceedings of IEEE conference on decision and control, pp 288–294
13.
go back to reference Burgess J (1981) Active adaptive sound control in a duct: a computer simulation. J Acoust Soc Am 70:715–726CrossRef Burgess J (1981) Active adaptive sound control in a duct: a computer simulation. J Acoust Soc Am 70:715–726CrossRef
14.
go back to reference Widrow B, Shur D, Shaffer S (1981) On adaptive inverse control. In: Proceedings of the 15th Asilomar conference on circuits, systems and computers. Pacific Grove, CA, USA Widrow B, Shur D, Shaffer S (1981) On adaptive inverse control. In: Proceedings of the 15th Asilomar conference on circuits, systems and computers. Pacific Grove, CA, USA
15.
go back to reference Eriksson L (1991) Development of the filtered-U LMS algorithm for active noise control. J Acoust Soc Am 89(1):257–261CrossRef Eriksson L (1991) Development of the filtered-U LMS algorithm for active noise control. J Acoust Soc Am 89(1):257–261CrossRef
16.
go back to reference Wang A, Ren W (2003) Convergence analysis of the filtered-U algorithm for active noise control. Signal Process 83:1239–1254CrossRef Wang A, Ren W (2003) Convergence analysis of the filtered-U algorithm for active noise control. Signal Process 83:1239–1254CrossRef
18.
go back to reference Goodwin G, Sin K (1984) Adaptive filtering prediction and control. Prentice Hall, New JerseyMATH Goodwin G, Sin K (1984) Adaptive filtering prediction and control. Prentice Hall, New JerseyMATH
19.
go back to reference Ljung L, Söderström T (1983) Theory and practice of recursive identification. The MIT Press, CambridgeMATH Ljung L, Söderström T (1983) Theory and practice of recursive identification. The MIT Press, CambridgeMATH
20.
go back to reference Landau I (1979) Adaptive control: the model reference approach. Marcel Dekker, New YorkMATH Landau I (1979) Adaptive control: the model reference approach. Marcel Dekker, New YorkMATH
22.
go back to reference Anderson B, Bitmead R, Johnson C, Kokotovic P, Kosut R, Mareels I, Praly L, Riedle B (1986) Stability of adaptive systems. The MIT Press, CambridgeMATH Anderson B, Bitmead R, Johnson C, Kokotovic P, Kosut R, Mareels I, Praly L, Riedle B (1986) Stability of adaptive systems. The MIT Press, CambridgeMATH
23.
24.
go back to reference Crawford D, Stewart R (1997) Adaptive IIR filtered-V algorithms for active noise control. J Acoust Soc Am 101(4) Crawford D, Stewart R (1997) Adaptive IIR filtered-V algorithms for active noise control. J Acoust Soc Am 101(4)
25.
go back to reference Fraanje R, Verhaegen M, Doelman N (1999) Convergence analysis of the iltered-U LMS algorithm for active noise control in case perfect cancellation is not possible. Signal Process 73:255–266 Fraanje R, Verhaegen M, Doelman N (1999) Convergence analysis of the iltered-U LMS algorithm for active noise control in case perfect cancellation is not possible. Signal Process 73:255–266
Metadata
Title
Parameter Adaptation Algorithms
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_4