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TECHNICAL PAPERS

Adaptive Control of Rotor Vibration Using Compact Wavelets

[+] Author and Article Information
M. O. T. Cole

Department of Mechanical Engineering, Chiang Mai University, Chiang Mai 50200, Thailand and Department of Mechanical Engineering, Faculty of Engineering and Design, University of Bath, Bath BA2 7AY, UKmatt@dome.eng.cmu.ac.th

P. S. Keogh, C. R. Burrows, M. N. Sahinkaya

Department of Mechanical Engineering, Faculty of Engineering and Design, University of Bath, Bath BA2 7AY, UK

J. Vib. Acoust 128(5), 653-665 (Feb 07, 2006) (13 pages) doi:10.1115/1.2203352 History: Received April 27, 2005; Revised February 07, 2006

This paper investigates the use of dyadic wavelets for the control of multifrequency rotor vibration. A scheme for real-time control of rotor vibration using an adaptive wavelet decomposition and reconstruction of time-varying signals is proposed. Quasi-periodic control forces are constructed adaptively in real-time to optimally cancel vibration produced by nonsmooth disturbance forces. Controller adaptive gains can be derived using a model-based synthesis or from system identification routines. The controller is implemented on a flexible rotor system incorporating two radial magnetic bearings, with standard proportional-integral-derivative control employed in a parallel feedback loop for rotor levitation. An experimental investigation of controller performance is used to deduce the best choice of wavelet basis for various operating conditions. These include steady synchronous forcing, step changes in synchronous forcing and multifrequency forcing produced by a rotor impact mechanism.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 3

Schematic of adaptive wavelet-based control scheme for rotor vibration attenuation

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Figure 4

Schematics of experimental flexible rotor with magnetic bearings (a) system layout (b) impact mechanism located in plane G

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Figure 1

Daubechies wavelet functions with p vanishing moments (a)p=1, D1, or Haar wavelet (b)p=2, D2 wavelet, and (c), p=4, D4 wavelet

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Figure 2

Two iterations of the fast wavelet transform realized with discrete time filters: The wavelet coefficients for scale level j−1 come from processing the scaling function coefficients at scale level j

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Figure 5

Rotor residual unbalance response: Mean orbit amplitude and phase in (a) sensor planes A and F and (b) sensor planes C and D

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Figure 6

Real-time wavelet analysis of rotor vibration measured in plane F, showing wavelet coefficient series and corresponding signal components at four scale levels. The controller is activated at zero revolutions. The rotational frequency is 20Hz.

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Figure 7

Rotor vibration response and control force for controller based on Daubechies D2 wavelet. Rotor displacement and control force are shown for planes F and D, respectively. The controller is activated at zero revolutions. The rotational frequency is 16Hz.

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Figure 8

Rotor impact test at 20Hz: Rotor vibration and control force are shown for planes F and D, respectively. Control force construction is based on the D1 Haar wavelet.

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Figure 9

Rotor impact test at 20Hz: D1 wavelet coefficients for measured vibration signal (x-axis)

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Figure 10

Rotor impact test at 20Hz: Rotor vibration and control force are shown for planes F and D, respectively. Control force construction is based on a D2 wavelet.

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Figure 11

Rotor impact test at 20Hz: D2 wavelet coefficients for measured vibration signal (x-axis)

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Figure 12

Rotor impact test at 20Hz: Rotor vibration and control force are shown for planes F and D, respectively. Control force construction is based on the D4 wavelet.

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Figure 13

Rotor mass loss test at 20Hz: Rotor vibration and control force are shown for planes F and D, respectively. Control force construction is based on a D1 Haar wavelet.

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Figure 14

Rotor mass loss test at 20Hz: D1 wavelet coefficients for measured vibration signal (x-axis)

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Figure 15

Rotor mass loss test at 20Hz: Rotor vibration and control force are shown for planes F and D, respectively. Control force construction is based on a D2 wavelet.

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