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Introduction to Adaptive and Robust Active Vibration Control Read chapter Read first chapter

2017 | OriginalPaper | Chapter

16. Youla–Kučera Parametrized Adaptive Feedforward Compensators

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

In this chapter one considers a Youla–Kučera parametrization of the feedforward compensator in the context of the “positive” feedback coupling which appears in active vibration control systems. The central Youla–Kučera controller will stabilize the internal “positive” feedback loop and an infinite (or finite) impulse response adaptive Youla–Kučera filter will be used to optimize the performance. The algorithms are evaluated in real time on the active flexible mechanical structure actuated by an inertial actuator which has been presented in Chap. 2.

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previous chapter Adaptive Feedforward Compensation of Disturbances
Footnotes
1
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) or on the basis of the current parameter estimates (a posteriori).
 
2
The parenthesis \((q^{-1})\) or \((z^{-1})\) will be omitted in some of the following equations to make them more compact.
 
3
Nevertheless, exact algorithms can be developed taking into account the non-commutativity of the time-varying operators—see [3].
 
4
One cannot use in practice Algorithm I as the true model of the secondary path is not known. Instead one can use Algorithm II with an estimation of the secondary path model.
 
5
Convergence analysis in a stochastic environment can be applied only for vanishing adaptation gains.
 
6
An array implementation as in [8] can be also considered.
 
7
The orders of the initial H\(_\infty \) controller were: \(n_{R_{H_\infty }} = 70\) and \(n_{S_{H_\infty }} = 70\).
 
Literature
1.
2.
Landau ID, Airimitoaie TB, Alma M (2013) IIR Youla–Kučera parameterized adaptive feedforward compensators for active vibration control with mechanical coupling. IEEE Trans Control Syst Technol 21(3):765–779CrossRef
3.
Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control, 2nd edn. Springer, LondonCrossRefMATH
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Ljung L, Söderström T (1983) Theory and practice of recursive identification. The MIT Press, CambridgeMATH
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Ljung L (1977) On positive real transfer functions and the convergence of some recursive schemes. IEEE Trans Autom Control AC-22:539–551
6.
Landau I, Airimitoaie T, Alma M (2011) A Youla–Kučera parametrized adaptive feedforward compensator for active vibration control. In: Proceedings of the 18th IFAC world congress, Milano, Italy, pp 3427–3432
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8.
Montazeri P, Poshtan J (2010) A computationally efficient adaptive IIR solution to active noise and vibration control systems. IEEE Trans Autom Control AC-55:2671–2676
9.
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
10.
Goodwin G, Sin K (1984) Adaptive filtering prediction and control. Prentice Hall, New JersyMATH
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Tay TT, Mareels IMY, Moore JB (1997) High performance control. Birkhäuser, Boston
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Heuberger P, Van den Hof P, Bosgra O (1995) A generalized orthonormal basis for linear dynamical systems. IEEE Trans Autom Control 40(3):451–465. doi:10.​1109/​9.​376057
Metadata
Title
Youla–Kučera Parametrized Adaptive Feedforward Compensators
Authors
Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Copyright Year
2017
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_16