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Research Papers

Dynamic Gains Differentiator for Hydraulic System Control

[+] Author and Article Information
L. Sidhom

Assistant Professor
Laboratoire Ampère,
UMR CNRS 5005,
INSA-Lyon,
Université de Lyon,
Lyon F-69621, Villeurbanne, France
e-mail: lilia.sidhom@gmail.com

X. Brun

Professor
Laboratoire Ampère,
UMR CNRS 5005,
INSA-Lyon,
Université de Lyon,
Lyon F-69621, Villeurbanne, France
e-mail: xavier.brun@insa-lyon.fr

M. Smaoui

Laboratoire Ampère,
UMR CNRS 5005,
INSA-Lyon,
Université de Lyon,
Lyon F-69621, Villeurbanne, France
e-mail: mohamed.smaoui@insa-lyon.fr

E. Bideaux

Professor
Laboratoire Ampère,
UMR CNRS 5005,
INSA-Lyon,
Université de Lyon,
Lyon F-69621, Villeurbanne, France
e-mail: eric.bideaux@insa-lyon.fr

D. Thomasset

Professor
Laboratoire Ampère,
UMR CNRS 5005,
INSA-Lyon,
Université de Lyon,
Lyon F-69621, Villeurbanne, France
e-mail: daniel.thomasset@insa-lyon.fr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 17, 2013; final manuscript received November 23, 2014; published online January 9, 2015. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 137(4), 041017 (Apr 01, 2015) (13 pages) Paper No: DS-13-1027; doi: 10.1115/1.4029271 History: Received January 17, 2013; Revised November 23, 2014; Online January 09, 2015

This paper deals with online numerical differentiation of a noisy time signal where new higher order sliding mode differentiators are proposed. The key point of these algorithms is to include a dynamic on the differentiator parameters. These dynamics tune-up automatically the algorithm gains in real-time. Convergence properties of the new schemes are derived using a Lyapunov approach. Their effectiveness is illustrated via simulations and experimental tests, where comparative studies are performed between classical schemes and the new ones. Such algorithms are also used in the feedback control of an electrohydraulic system.

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References

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Figures

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Fig. 1

Errors with different frequency of g(t): (a) Error: first-derivative and (b) Error: first-derivative

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Fig. 2

N2OD outputs: variable frequency signal

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Fig. 3

Estimation of the second-derivative. (a) 2OD (λ0 = 8,λ1 = 7,λ1 = 3) and (b) N2OD (K0 = 7,K1 = 4).

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Fig. 7

Simulation model of friction

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Fig. 4

Estimation of the first-derivative: (a) ST (λ0 = 10,λ1 = 8), (b) N10D(K0 = 8), (c) 2OD (λ0 = 8,λ1 = 7,λ1 = 3), and (d) N2OD (K0 = 7,K1 = 4)

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Fig. 5

Electrohydraulic test bench

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Fig. 6

Simplified diagram of servosystem

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Fig. 8

Schematic diagram: controller/differentiator

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Fig. 9

Tracking position error (mm): (2OD, test 1)

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Fig. 10

Estimation velocity and acceleration; (2OD, test 1): (a) Estimated velocity and (b) Estimated acceleration

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Fig. 11

Control input (V): (2OD, test 1)

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Fig. 12

Tracking position error (mm): (N2OD, test 1)

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Fig. 13

Estimation velocity and acceleration; (N2OD, test 1): (a) Estimated velocity and (b) Estimated acceleration

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Fig. 14

Tracking position error (mm): (2OD, test 2)

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Fig. 15

Estimation velocity and acceleration; (2OD, test 2): (a) Estimated velocity and (b) Estimated acceleration

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Fig. 16

Estimation velocity and acceleration; (N2OD, test 2): (a) Estimated velocity and (b) Estimated acceleration

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