Abstract
This paper proposes a new modeling scheme to describe the hysteresis and the preload characteristics of piezoelectric stack actuators in the inchworm. From the analysis of piezoelectric stack actuator behavior, the hysteresis can be described by the functions of a maximum input voltage and the preload. The dynamic characteristics are also identified by the frequency domain modeling technique based on the experimental data. The hysteresis is compensated by the inverse hysteresis model for precise control of inchworm displacement. Since the dynamic stiffness of an inchworm is generally low compared to its driving condition, the mechanical vibration may degrade accuracy of the inchworm. Therefore, the SMC (Sliding Mode Control) and the Kalman filter are developed for the motion control of the inchworm. The feasibility of the proposed modeling scheme and the control algorithm is tested and verified experimentally.
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Abbreviations
- Vin :
-
input voltage of piezoelectric actuator
- Xr, Xf :
-
displacements of piezoelectric actuator for extension and shrinkage
- u(k):
-
output of sliding mode controller
- S n :
-
signum function
- β :
-
model uncertainty
- L :
-
gain of Kalman filter
References
Choi, D. K., “Developing trend of automation elements for precise control,” International Journal of Control, Automation and Systems, Vol. 6,Issue 1, pp. 33–38, 2000.
Slocum, A., “Precision Machine Design,” Prentice-Hall, pp. 666–674, 1992.
Higuchi, T., Watanade, M. and Kudoh, K., “Precise Positioner Utilizing Rapid Deformations of a Piezoelectric Element,” J. of Japan Society of Precision Engineering, Vol. 54, No. 11, pp. 2107–2112, 1988.
Kim, J. H. and Kim, J., “A Hybrid Inchworm Linear Motor,” Mechatronics, Vol. 23,Issue 3, pp. 525–542, 2002.
Jung, H., “Hysteresis and Creep analysis of PZT Actuators and application,” Ph.D. Thesis, KAIST, 2000.
Kim, S. C. and Kim, S. H., “A Precision Linear Actuator Using Piezoelectrically Driven Friction Force,” Mechatronics, Vol. 11,Issue 8, pp. 969–985, 2001.
Kaizuka, H. and Siu, B., “A Simple Way to Reduce Hysteresis and Creep When Using Piezoelectric Actuators,” Japanese Journal of Applied Physics, Vol. 27, No. 5, pp. L773–L776, 1988.
Goldfarb, M. and Celanvovic, N., “A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators,” ASME J. of Mechanical Design, Vol. 119, No. 3, pp. 478–485, 1997.
Ge, P. and Jouaneh, M., “Modeling Hysteresis in Piezoceramic Actuators,” Precision Engineering, Vol. 17, No. 3, pp. 211–221, 1995.
Tzen, J., Jeng, S. and Chieng, W., “Modeling of Piezoelectric Actuator for Compensation and Controller Design,” Precision Engineering, Vol. 27, No. 1, pp. 70–86, 2003.
Green, M. and Limebeer, D., “Linear Robust Control,” Prentice Hall, pp. 215–262, 1995.
Yoon, J. H., Kim, Y. S. and Kim, I. S., “Motion Control of Inchworm,” J. of KSPE, Vol. 19, No. 9, pp. 179–185, 2002.
Edward, C. and Spurgeon, S. K., “Sliding Mode Control, Theory and applications,” Taylor and Francis Ltd, pp. 31–63, 1998.
Henmi, N. and Tanaka, M., “An Open-Loop Method for Point-to-Point Positioning of a Piezoelectric Actuator,” International Journal of Precision Engineering and Manufacturing, Vol. 8, No. 2, pp. 9–13, 2007.
Juang, J. N., “Applied System Identification,” Prentice Hall, pp. 229–254, 1994.
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Kim, I., Kim, YS. & Park, EC. Sliding mode control of the inchworm displacement with hysteresis compensation. Int. J. Precis. Eng. Manuf. 10, 43–49 (2009). https://doi.org/10.1007/s12541-009-0046-8
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DOI: https://doi.org/10.1007/s12541-009-0046-8