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2017 | OriginalPaper | Buchkapitel

12. Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances

verfasst von : Ioan Doré Landau, Tudor-Bogdan Airimitoaie, Abraham Castellanos-Silva, Aurelian Constantinescu

Erschienen in: Adaptive and Robust Active Vibration Control

Verlag: Springer International Publishing

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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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Fußnoten
1
Called tonal disturbances.
 
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
The Youla–Kučera parametrization has been presented in Chap. 7.
 
4
The disturbance passes through a so called primary path which is not represented in this figure, and p(t) is its output.
 
5
The argument \((z^{-1})\) will be omitted in some of the following equations to make them more compact.
 
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
Throughout the book, \(n_X\) denotes the degree of the polynomial X.
 
8
Of course, it is assumed that \(D_{p}\) and B do not have common factors.
 
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
Of course the value of 2 s can be changed, but the principle of measurement remains the same.
 
11
Any design method allowing to satisfy these constraints can be used.
 
12
For results obtained with an indirect adaptive control scheme see [7].
 
13
The case of multiple unknown narrow-band disturbances will be discussed in Chap. 13.
 
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Metadaten
Titel
Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances
verfasst von
Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-41450-8_12