In this paper, the backlash hysteresis nonlinearity is examined, and a mathematical model based on the particular behavior of the backlash is developed. A geometrical interpretation of this model using switching operators is provided to facilitate an understanding of it. Simulation of output prediction of the backlash mechanism using an arbitrary input signal is performed to verify the correctness of the developed model. A linearization scheme based on the model is also developed to compensate for the backlash nonlinearity. The scheme was applied for tracking an arbitrary signal similar to that used in the modeling. The results show that our model-based linearization scheme although running in an open loop fashion, provides a simpler way to perform tracking control for structures with backlash hysteresis nonlinearity.

Issue Section:
Mechanisms and Robotics
Topics:
Modeling, Signals, Simulation, Tracking control
1.
Sato
K.
,
Murayama
Y.
,
Imada
S.
, and
Shimokohbe
A.
, “
Control and Elimination of Lead Screw Backlash for Ultra-Precision Positioning
,”
JSME International Journal, Series C
, Vol.
38
, pp.
36
–
41
,
1995
.
2.
Chang
S.-L.
, and
Tsai
L.-W.
, “
On the Redundant-Drive Backlash-Free Robotic Mechanisms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, pp.
247
–
254
,
1993
.
3.
Tao
G.
, and
Kokotovi
P. V.
, “
Adaptive Control of Systems With Unknown Output Backlash
,”
IEEE Trans. on Automatic Control
, Vol.
40
, pp.
326
–
330
,
1995
.
4.
Cetinkung, S., and Donmez, A., “CMAC Learning Controller for Servo Control of High Precision Machine Tools,” Proceedings of the American Control Conference, San Francisco, CA, pp. 1976–1980, June 1993.
5.
de la Sen, M., Pefia, A., and Esnaola, J., “Detection of Limit Cycles in Discrete Systems With Backlash and Resolution by Using a Discretization-Oriented Describing Function,” Proceedings of the IEEE Conference on Decision & Control, Vol. 4, San Antonio, TX, pp. 2978–2983, Dec. 1993.
6.
Slotine, J.-J. E., and Li, W., Applied Nonlinear Control, Prentice Hall, New York, pp. 177–179, 1991.
7.
Heyns, L. J., and Kru¨ger, J. J., “Describing Function-Based Analysis of a Nonlinear Hydraulic Transmission Line,” Proceedings of the American Control Conference, IL, pp. 132–136, June 1992.
8.
Ge
P.
, and
Jouaneh
M.
, “
Modeling Hysteresis in Piezoceramic Actuators
,”
Precision Engineering
, Vol.
17
, pp.
211
–
221
,
1995
.
9.
Mayergoyz, I. D., Mathematical Models of Hysteresis, Springer Verlag, New York, NY, 1991.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.