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Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances

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Adaptive and Robust Active Vibration Control

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

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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.

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Notes

  1. 1.

    Called tonal disturbances.

  2. 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. 3.

    The Youla–Kučera parametrization has been presented in Chap. 7.

  4. 4.

    The disturbance passes through a so called primary path which is not represented in this figure, and p(t) is its output.

  5. 5.

    The argument \((z^{-1})\) will be omitted in some of the following equations to make them more compact.

  6. 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. 7.

    Throughout the book, \(n_X\) denotes the degree of the polynomial X.

  8. 8.

    Of course, it is assumed that \(D_{p}\) and B do not have common factors.

  9. 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. 10.

    Of course the value of 2 s can be changed, but the principle of measurement remains the same.

  11. 11.

    Any design method allowing to satisfy these constraints can be used.

  12. 12.

    For results obtained with an indirect adaptive control scheme see [7].

  13. 13.

    The case of multiple unknown narrow-band disturbances will be discussed in Chap. 13.

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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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  2. Tudor-Bogdan Airimitoaie
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  3. Abraham Castellanos-Silva
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  4. Aurelian Constantinescu
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Correspondence to Ioan Doré Landau .

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Landau, I.D., Airimitoaie, TB., Castellanos-Silva, A., Constantinescu, A. (2017). Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances. In: Adaptive and Robust Active Vibration Control. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-41450-8_12

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  • DOI: https://doi.org/10.1007/978-3-319-41450-8_12

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