On the use of Youla–Kucera parametrisation in adaptive active noise and vibration control – a review

ABSTRACT

Youla–Kucera parametrisation plays a very important role in adaptive active vibration control and adaptive active noise control. This concerns both vibration and noise attenuation by feedback as well as by feedforward compensation when a measurement of an image of the disturbance (noise or vibration) is available. The paper will review the basic algorithms and various extensions trying to emphasise the advantages of using Youla–Kucera parametrisation. Specific aspects related to the use of this approach in adaptive active vibration and noise control will be mentioned. A brief review of applications and experimental testing will be provided.

Abbreviations: ANC: Active noise control system; AVC: Active vibration control system; FIRYK: Youla–Kucera parametrised FIR adaptive feedforward compensator using an FIR Youla–Kucera filter; IIR: IIR adaptive feedforward compensator; IIRYK:Youla–Kucera parametrised IIR adaptive feedforward compensator using an IIR Youla–Kucera filter; IMP: Internal model principle; PAA: Parameter adaptationalgorithm; QFIR: Youla–Kucera FIR filter; QIIR: Youla–Kucera IIR filter; SPR: Strictly positive real (transfer function); YK: Youla–Kucera

KEYWORDS:

• Adaptive control
• feedback control
• feedforward control
• Youla–Kucera parametrisation
• active noise control
• active vibration control

Acknowledgements

The author would like to thank Tudor-Bogdan Airimitoaie for the help in the preparation of the final version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 Of course, combination of the two types of disturbances is possible

2 The basic adaptive control paradigm deals with unknown and time-varying plants while making assumptions on the disturbances and reference

3 The complex variable $z^{-1}$ will be used for characterising the system's behaviour in the frequency domain and the delay operator $q^{-1}$ will be used for describing the system's behaviour in the time domain.

4 It is assumed that a reliable model identification is achieved and therefore the estimated model is assumed to be equal to the true model.

5 As a consequence of the presence of the filter F both in N and in D, strictly speaking N and D will no more be coprime. This factorisation is used in (de Callafon & Fang, 2013)

6 Of course, it is assumed that $D_p$ and B do not have common factors.

7 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).

8 Its structure in a mirror symmetric form guarantees that the roots are always on the unit circle.

9 Like for the feedback compensation it is assumed that a reliable model identification is achieved and therefore the estimated models are considered to be equal to the real models

10 The parenthesis $\left(q^{-1}\right)$ will be omitted in some of the following equations to make them more compact.

11 However, exact algorithms can be developed taking into account the noncommutativity of the time-varying operators – see Landau, Lozano, et al. (2011)