Piezoelectric actuators with their sub-nanometer resolution and fast frequency response are becoming increasingly important in today’s micro-and nano-positioning technology. Along this line, this paper undertakes the development of a nonlinear modeling, system identification and control framework for piezoelectric actuators used in such positioning systems. More specifically, a general nonlinear modeling framework for a single piezoelectric actuator combined with a novel method for describing its hysteretic nonlinearity is proposed. For the actuator generated force, a polynomial form of the nonlinearity is assumed, and the time-varying history-dependent parameters of this polynomial are identified through the observed hysteretic characteristics of the actuator. Experimental results demonstrates the validity of the proposed the modeling and identification framework for an in-house high resolution piezoelectric-based stager with capacitive position sensor. Utilizing Lyapunov method and the sliding mode control strategy, the control force acting on the actuator is then designed such that the high frequency tracking control and the asymptotic stability of the system are attained. Simulation results indicate that controller suppresses the high frequency tracking error significantly, noticeably improving the tracking performance.

1.
Maygergoyz I., Mathematical models of hysteresis, Springer-Verlag, New York, 1991.
2.
Ping
G.
, and
Musa
J.
, “
Modeling hysteresis in piezoceramic actuators
,”
Precis. Eng.
,
17
, pp.
211
221
,
1995
.
3.
Ping
G.
, and
Musa
J.
, “
Generalized Preisach modelfor hysteresis nonlinearity of piezoceramic actuators
,”
Precis. Eng.
,
20
, pp.
99
111
,
1997
.
4.
Stepanenko Y., and Su C.Y., “Intelligent control of piezoelectric actuators,” Proc. 37th IEEE Conf. Decision and Control, 4, pp. 4234–4239, 1998.
5.
Goldfarb
M.
, and
Celanovic
N.
, “
A lumped parameter electromechanical model for describing the nonlinear behavior of piezoelectric actuators
,”
Trans. ASME J. Dyn. Syst. Meas. Control
,
119
, pp.
478
485
,
1997
.
6.
Hwang
C. L.
,
Chen
Y. M.
, and
Jan
C.
, “
Trajectory Tracking of large displacement piezoelectric actuators using a nonlinear observer-based variable structure control
,”
IEEE Trans. Control Syst. Technol.
,
13
, pp.
56
66
,
2005
.
7.
Bashash S., Jalili N., “Trajectory control of piezoelectric actuators using nonlinear variable Structure control,” Proc. International Symposium on Collaborative Research in Applied Science, 2005.
8.
Xu Y., and Meckl P.H., “Time-Optimal motion control of piezoelectric actuator: STM application,” Proc. of the 2004 American Control Conference, 5, pp. 4849–4854, 2004.
9.
Tzen
J. J.
,
Jeng
S. L.
, and
Chieng
W. H.
, “
Modeling of piezoelectric actuator for compensation and controller design
,”
Precis. Eng.
,
27
, pp.
70
76
,
2003
.
10.
Lining
S.
, “
Tracking control of piezoelectric actuator based on a new mathematical model
,”
J. Micromech. Microeng.
14
, pp.
1439
1444
,
2004
.
11.
Chaghai R., Lining S., Weibin R., and Liguo Ch., “Adaptive inverse control for piezoelectric actuator with dominant hysteresis,” Proc. IEEE International Conference on Control Applications. 2, pp. 973–976, 2004.
12.
Ang W. T., Garmon F. A., and Khosla P. K., Riviere C. N., “Modeling rate-dependent hysteresis in piezoelectric actuators,” Proc. IEEE International Conference on Intelligent Robots and Systems, 2, pp. 1975–1980, 2003.
13.
Aderiaens
H.
,
Koning
W.
, and
Baning
R.
, “
Modeling piezoelectric actuators
,”
IEEE/ASME Trans. Mechatronics
,
5
, pp.
331
341
,
2000
.
14.
Chen
B. M.
,
Lee
T. H.
,
Hang
C. C.
,
Guo
Y.
, and
Weerasooriya
S.
, “
An H almost disturbance decoupling robust controller design for a piezoelectric bimorph actuator with hyteresis
,”
IEEE Trans. Contr. Syst. Technol.
,
7
, pp.
160
174
,
1999
.
15.
Banks, H.T., Smith R.C., and Wang Y., Smart Material Structure, Modeling, Estimation and Control, John Wiley, 1996.
16.
Slotine
J. J.
, “
Sliding controller design for nonlinear system
,”
International Journal of Control
,
40
, pp.
421
434
,
1984
.
17.
Elmali H., Olgac N., “Theory and implementation of sliding mode control with perturbation estimation (SMCPE),” Proc. IEEE International Conference on Robotics and Automation, 3, pp. 2114–2119, 1992.
18.
Jalili N., Elmali H., Moura J., and Olgac N., “Tracking control of a rotating flexible beam using frequency-shaped sliding mode control,” Proc. of the 16th American Control Conference, 4, pp. 2552–2556, 1997.
19.
Jalili
N.
, and
Olgac
N.
, “
Time-optimal/ sliding mode control implementation for robust tracking of uncertain flexible structures
,”
Mechatronics
,
8
, pp.
121
142
,
1998
.
20.
Slotine J.J., Li W., Applied Nonlinear Control, Prentice-Hall, NJ, 1991.
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