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Adaptive and Robust Active Vibration Control pp 311–349Cite as

Adaptive Feedforward Compensation of Disturbances

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Part of the book series: Advances in Industrial Control ((AIC))

Abstract

Adaptive feedforward compensation algorithms for the attenuation of broad-band disturbances are developed in this chapter. The proposed algorithms take into account the “positive” feedback coupling which appears in active vibration control systems using feedforward compensation. One considers also the case when a fixed feedback controller is present. 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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Notes

  1. 1.

    Different solutions for reducing the effect of this internal positive feedback are reviewed in [8, 9].

  2. 2.

    Design of adaptive AVC does not require either the model of the disturbance or the model of the primary path.

  3. 3.

    The complex variable \(z^{-1}\) will be used for characterizing 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. 4.

    The following notation for polynomials is used: \(A(q^{-1})=a_0+\sum _{i=1}^{n_A}a_iq^{-i}=a_0\,+\,q^{-1}A^*(q^{-1})\).

  5. 5.

    \(\hat{y}(t+1)\) is available before adaptation of parameters starts at \(t+1\).

  6. 6.

    In many cases, the argument \(q^{-1}\) or \(z^{-1}\) will be dropped out.

  7. 7.

    In the field of adaptive feedforward compensation names are associated to various adaptation algorithms. Algorithm II uses the same filtering of the regressor as FULMS algorithm but with a matrix adaptation gain which lead to a structure called “pseudolinear regression” [14]. So Algorithm II can be termed FUPLR. Algorithm III is obtained from a stability point of view and it can be termed FUSBA (stability based algorithm).

  8. 8.

    See Appendix D, Sect. D.2 for further details.

  9. 9.

    The results are valid for the asymptotic behaviour obtained when using a decreasing adaptation gain.

  10. 10.

    The fact that the disturbance is a broad-band signal will imply that one has persistence of excitation.

  11. 11.

    The inertial actuator is driven by an external source.

  12. 12.

    An array implementation as in [17] can be also considered.

  13. 13.

    The scalar adaptation gain algorithms presented in this book can be denoted as NFULMS (normalized FULMS) for Algorithm II and SFUSBA (scalar FUSBA) for Algorithm III.

  14. 14.

    This algorithm can be termed FUeSBA since both the input and the error are filtered.

  15. 15.

    For the adaptive schemes, the PSD is evaluated after the adaptation transient has settled.

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Authors and Affiliations

  1. Department of Automatic Control, GIPSA-LAB (Grenoble INP/CNRS/UJF/Stendhal), 11 rue des Mathématiques, Grenoble Campus, BP46, Saint Martin d’heres , F-38402, France

    Ioan Doré Landau

  2. IMS-lab (University of Bordeaux, Bordeaux INP, CNRS) UMR 5218, Talence , F-33405, France

    Tudor-Bogdan Airimitoaie

  3. Grenoble, France

    Abraham Castellanos-Silva

  4. Saint-Lazare, QC, Canada

    Aurelian Constantinescu

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  1. Ioan Doré Landau
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Correspondence to Ioan Doré Landau .

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Landau, I.D., Airimitoaie, TB., Castellanos-Silva, A., Constantinescu, A. (2017). Adaptive Feedforward Compensation of Disturbances. In: Adaptive and Robust Active Vibration Control. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-41450-8_15

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