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2017 | OriginalPaper | Chapter

7. Digital Control Strategies for Active Vibration Control—The Bases

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

This chapter reviews basic digital control strategies and their application to active vibration control. The design of polynomial controllers (RS controllers) is discussed both from performance and robustness perspectives. The importance of sensitivity functions is enhanced. A number of basic concepts are defined and explained. A real-time example of an active vibration control (suppression of a tonal vibration) illustrates the design methodology presented in this chapter.

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Footnotes
1
See functions bezoutd.m (MATLAB®) or bezoutd.sci (Scilab) on the book website.
 
2
Of course it is assumed that \(D_{p}\) and \(BH_{R}\) do not have common factors.
 
3
See [5] for the case of open-loop unstable systems.
 
4
See [9] for a proof. In the case of unstable open-loop systems but stable in closed-loop, this integral is positive.
 
5
The structure of the \(H_S\) is \(H_s= (1+\alpha _1q^{-1}+\alpha _2q^{-2})(1+\alpha '_1q^{-1}+\alpha '_2q^{-2})\).
 
6
This is indeed true even in adaptive control since the uncertainties in the high-frequency region are not in general handled by the adaptive controller.
 
7
The input sensitivity function correspond to the system considered previously which includes in the controller an internal model with zero damping located at \(0.15f_s\).
 
8
The bilinear transformation assures a better approximation of a continuous-time model by a discrete-time model in the frequency domain than the replacement of differentiation by a difference, i.e., \(s=(1-z^{-1})T_{s}\) (see [6]).
 
9
The factor \(\gamma \) has no effect on the final result (coefficients of R and S). It is possible, however, to implement the filter without normalizing the numerator coefficients.
 
10
These filters can be computed using the functions filter22.sci (Scilab) and filter22.m (MATLAB®) to be downloaded from the book website.
 
11
To be downloaded from the book website.
 
12
This particular YK parametrization allows to preserve the fixed parts \(H_R\) and \(H_S\) in the resulting controller given in Eq. (7.4).
 
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Metadata
Title
Digital Control Strategies for Active Vibration Control—The Bases
Authors
Ioan Doré Landau
Tudor-Bogdan Airimitoaie
Abraham Castellanos-Silva
Aurelian Constantinescu
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-41450-8_7