The aim of this paper is to develop identification that is capable of capturing the characteristics of nonlinear tangential elastic and friction forces arising in submicron motions. Using novel Hilbert transform based signal processing and making use of the intimate relations between internal elastic and friction forces, the latter can be simultaneously recovered from measured data. The experiments were performed on a stage equipped with linear motors, while being driven by slow, quasi-harmonic excitation at frequencies of 1–40 Hz. The identified elastic force incorporates the inevitable nonlinear nature of the stage. The proposed identification technique can be useful for the analysis of modeling contact dynamics between moving and sliding parts in situ. This technique can possibly develop improved closed-loop control algorithms.

References

References
1.
Yang
,
C.
,
Zhang
,
Z.
, and
Zhao
,
Q.
,
2010
, “
The Study on Precision Positioning System of Two-Dimensional Platform Based on High Speed and Large Range
,”
Precis. Eng.
,
34
(
3
), pp.
640
646
.
2.
Olsson
,
H.
,
Åström
,
K. J.
,
de Wit Canudas
,
C.
,
Gäfvert
,
M.
, and
Lischinsky
,
P.
,
1998
, “
Friction Models and Friction Compensation
,”
Eur. J. Control
,
4
(
3
), pp.
176
195
.
3.
Berger
,
E.
,
2002
, “
Friction Modeling for Dynamic System Simulation
,”
ASME Appl. Mech. Rev.
,
55
(
6
), pp.
535
577
.
4.
Swevers
,
J.
,
Al-Bender
,
F.
,
Ganseman
,
C.
, and
Prajogo
,
T.
,
2000
, “
An Integrated Friction Model Structure With Improved Presliding Behaviour for Accurate Friction Compensation
,”
IEEE, Trans. Autom. Control
,
45
(
4
), pp.
675
686
.
5.
Andersson
,
S.
,
Soderberg
,
A.
, and
Bjorklund
,
S.
,
2007
, “
Friction Models for Sliding Dry, Boundary and Mixed Lubricated Contacts
,”
Tribol. Int.
,
40
(
4
), pp.
580
587
.
6.
Ferretti
,
G.
,
Magnani
,
G.
,
Martucci
,
G.
,
Rocco
,
P.
, and
Stampacchia
,
V.
,
2003
, “
Friction Model Validation in Sliding and Presliding Regimes With High Resolution Encoders
,”
Experimental Robotics VIII
,
B.
Siciliano
and
P.
Dario
, eds.,
Springer
,
Berlin/Heidelberg
, pp.
328
337
.
7.
Parlitz
,
U.
,
Hornstein
,
A.
,
Engster
,
D.
,
Al-Bender
,
F.
,
Lampaert
,
V.
,
Tjahjowidodo
,
T.
,
Fassois
,
S. D.
, and
Rizos
,
D.
,
2004
, “
Identification of Pre-Sliding Friction Dynamics
,”
Chaos
,
14
(
2
), pp.
420
430
.
8.
Oomen
,
T.
,
van Herpen
,
R.
,
Quist
,
S.
,
van de Wal
,
M.
,
Bosgra
,
O.
, and
Steinbuch
,
M.
,
2014
, “
Connecting System Identification and Robust Control for Next-Generation Motion Control of a Wafer Stage
,”
IEEE Trans. Control Syst. Technol.
,
22
(
1
), pp.
102
118
.
9.
He
,
S.
, and
Singh
,
R.
,
2005
, “
Estimation of Amplitude and Frequency Dependent Parameters of Hydraulic Engine Mount Given Limited Dynamic Stiffness Measurements
,”
Noise Control Eng. J.
,
53
(
6
), pp.
271
285
.
10.
Feldman
,
M.
,
2013
, “
Mapping Nonlinear Forces With Congruent Vibration Functions
,”
MSSP
,
37
(
1–2
), pp.
315
337
.
11.
Feldman
,
M.
,
2011
,
Hilbert Transform Applications in Mechanical Vibration
,
Wiley
,
New York
.
12.
Inaudi
,
J. A.
, and
Kelly
,
J. M.
,
1995
, “
Linear Hysteretic Damping and the Hilbert Transform
,”
J. Eng. Mech.
,
121
(
5
), pp.
626
632
.
13.
Yan
,
G.
,
Stefano
,
A. D.
, and
Ou
,
G.
,
2012
, “
A General Nonlinear System Identification Method Based Upon Time-Varying Trend of Instantaneous Frequencies and Amplitudes
,”
Adv. Struct. Eng.
,
15
(
5
), pp.
781
792
.
14.
BLM Series Linear Motors
,” Aerotech, Inc., Pittsburgh, PA, Last accessed: Jan. 29,
2014
, http://www.aerotech.com/media/272552/blm.pdf
15.
“LM Guide (Full-Ball Type),” THK, Last accessed: Jan. 29,
2014
, https://tech.thk.com/en/products/thkdlinks.php?id=315
16.
“RGH22 Linear Encoder System,” RENISHAW, Last accessed: Jan. 29,
2014
, http://www.renishaw.com/en/rgh22-linear-encoder-system–6443
17.
Smyth
,
A. W.
,
Masri
,
S. F.
,
Kosmatopoulos
,
E. B.
,
Chassiakos
,
A. G.
, and
Caughey
,
T. K.
,
2002
, “
Development of Adaptive Modeling Techniques for Non-Linear Hysteretic Systems
,”
Int. J. Non-Linear Mech.
,
37
(
8
), pp.
1435
1451
.
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