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Research Papers

On a Robust Modeling of Piezo-Systems

[+] Author and Article Information
Christophe Corbier

 Sciences of Information and System Laboratory, UMR CNRS 6168, Arts et Métiers Paris-Tech, Aix-en-Provence 13617, Francecorbier.christophe@gmail.com

Abdou Fadel Boukari

 Mechatronics Sciences of Information and System Laboratory, UMR CNRS 6168, Arts et Métiers Paris-Tech, Aix-en-Provence 13617, Franceabdoufbb@yahoo.fr

Jean-Claude Carmona

 Automatics Sciences of Information and System Laboratory, UMR CNRS 6168, Arts et Métiers Paris-Tech, Aix-en-Provence 13617, Francejean-claude.carmona@ensam.eu

Victor Alvarado Martinez

 Automatics Department of Electronics National Center of Research and Technological Development, Int. Internado Palmira s/n, Col. Palmira 62490, Cuernavaca, Mor. Mexicovictor@alvarado.fr

George Moraru

 Manufacturing Sciences of Information and System Laboratory, UMR CNRS 6168, Arts et Métiers Paris-Tech, Aix-en-Provence 13617, Francegeorge.moraru@ensam.fr

François Malburet

 Dynamics Sciences of Information and System Laboratory, UMR CNRS 6168, Arts et Métiers Paris-Tech, Aix-en-Provence 13617, Francefrançois.malburet@ensam.fr

J. Dyn. Sys., Meas., Control 134(3), 031002 (Mar 27, 2012) (8 pages) doi:10.1115/1.4005499 History: Received July 15, 2010; Revised November 05, 2011; Published March 27, 2012; Online March 27, 2012

This paper proposes a new modeling approach which is experimentally validated on piezo-electric systems in order to provide a robust Black-box model for complex systems control. Industrial applications such as vibration control in machining and active suspension in transportation should be concerned by the results presented here. Generally one uses physical based approaches. These are interesting as long as the user cares about the nature of the system. However, sometimes complex phenomena occur in the system while there is not sufficient expertise to explain them. Therefore, we adopt identification methods to achieve the modeling task. Since the microdisplacements of the piezo-system sometimes generate corrupted data named observation outliers leading to large estimation errors, we propose a parameterized robust estimation criterion based on a mixed L2 – L1 norm with an extended range of a scaling factor to tackle efficiently these outliers. This choice is motivated by the high sensitivity of least-squares methods to the large estimation errors. Therefore, the role of the L1 -norm is to make the L2 -estimator more robust. Experimental results are presented and discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Piezo-actuation principle

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Figure 2

Control loop proposition

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Figure 3

Alternative control loop

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Figure 4

Experimental piezo-system

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Figure 5

Description of the estimation phase in the prediction error framework

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Figure 6

Experimental setup

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Figure 7

Excitation input signal: PRBS

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Figure 8

Output signal of Piezo-electric

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Figure 9

Probability density function of L2 estimation for an OE(12,12) model

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Figure 10

Parameterized robust estimation criterion as a function of nF at nB  = 9 when η = 0.0625σ

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Figure 11

Robust model M1 : OE(9,12) compared to the spectral estimation of the piezo-system at η = 0.0625σ = 0.2255

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Figure 12

L1 -contribution function as a function of nF at nB  = 12 when η = 0.0875σ

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Figure 13

Robust model M2 : OE(12,12) compared to the spectral estimation of the piezo-system at η = 0.0875σ = 0.2619

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Figure 14

The model OE(12,12) in least squares estimation. The great sensitivity to the large deviations is clearly shown.

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