Technical Brief

Constructive Proof of Preisach Right Inverse With Applications to Inverse Compensation of Smart Actuators With Hysteresis

[+] Author and Article Information
Yangyang Dong

Department of Mechanical Engineering, D403H,
Harbin Institute of Technology,
Shenzhen Graduate School,
Shenzhen 518055, China
e-mail: dongyang1314@126.com

Hong Hu

Department of Mechanical Engineering, D403H,
Harbin Institute of Technology,
Shenzhen Graduate School,
Shenzhen 518055, China
e-mail: honghu@hit.edu.cn

Zijian Zhang

State Key Laboratory of Robotics and Systems,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: zhangzijian999@163.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 20, 2012; final manuscript received June 24, 2014; published online August 8, 2014. Assoc. Editor: Eric J. Barth.

J. Dyn. Sys., Meas., Control 136(6), 064502 (Aug 08, 2014) (7 pages) Paper No: DS-12-1350; doi: 10.1115/1.4027922 History: Received October 20, 2012; Revised June 24, 2014

Hysteresis poses a significant challenge for control of smart material actuators. If unaccommodated, the hysteresis can result in oscillation, poor tracking performance, and potential instability when the actuators are incorporated in control design. To overcome these problems, a fundamental idea in coping with hysteresis is inverse compensation based on the Preisach model. In this paper, we address systematically the problem of Preisach model inversion and its properties, employing the technique of three-step composition mapping and geometric interpretation of the Preisach model. A Preisach right inverse is achieved via the iterative algorithm proposed, which possesses same properties with the Preisach model. Finally, comparative experiments are performed on a piezoelectric stack actuator (PEA) to test the efficacy of the compensation scheme based on the Preisach right inverse.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Ping, G., and Jouaneh, M., 1996, “Tracking Control of a Piezoceramic Actuator,” IEEE Trans. Control Syst. Technol., 4(3), pp. 209–216. [CrossRef]
Hughes, D., and Wen, J. T., 1997, “Preisach Modeling of Piezoceramic and Shape Memory Alloy Hysteresis,” Smart Mater. Struct., 6, pp. 287–300. [CrossRef]
Venkataraman, R., 1999, “Modeling and Adaptive Control of Magnetostrictive Actuators,” Ph.D. thesis, College Park, MD, http://drum.lib.umd.edu/handle/1903/6043
Shunli, X., and Yangmin, L., 2013, “Optimal Design, Fabrication, and Control of an XY Micropositioning Stage Driven by Electromagnetic Actuators,” IEEE Trans. Ind. Electron., 60(10), pp. 4613–4626. [CrossRef]
Cardelli, E., Torre, E. D., and Tellini, B., 2000, “Direct and Inverse Preisach Modeling of Soft Materials,” IEEE Trans. Magn., 36(4), pp.1267–1271. [CrossRef]
Visintin, A., 1994, Differential Models of Hysteresis, Springer, Berlin, Germany, pp. 119–121.
Brokate, M., and Sprekels, J., 1996, Hysteresis and Phase Transitions, Springer, Berlin, Germany, pp. 105–107.
Mayergoyz, I. D., 1991, Mathematical Models of Hysteresis, Springer-Verlag, New York, pp. 212–217.
Sebastian, A., and Salapaka, S., 2003, “H Loop Shaping Design for Nano-positioning,” American Control Conference, Denver, CO, June 4–6, Vol. 5, pp. 3708–13.
Song, J. K., and Washington, G., 1999, “Thunder Actuator Modeling and Control With Classical and Fuzzy Control Algorithm,” Proc. SPIE, 3668, pp. 866–877. [CrossRef]
Andoh, F., Washington, G., and Utkin, V., 2001, “Shape Control of Distributed Parameter Reflectors Using Sliding Mode Control,” Proc. SPIE, 4334, pp. 164–175. [CrossRef]
Tao, G., and Kokotovic, P. V., 2003, Adaptive Control Design and Analysis, Wiley, New York, Chap. 10.
Hong, H., and Mrad, R. B., 2004, “A Discrete-Time Compensation Algorithm for Hysteresis in Piezoceramic Actuators,” Mech. Syst. Signal Process., 18(1), pp. 169–185. [CrossRef]
Davino, D., Giustiniani, A., and Visone, C., 2008, “Fast Inverse Preisach Models in Algorithms for Static and Quasistatic Magnetic-Field Computations,” IEEE Trans. Magn., 44(6), pp. 862–865. [CrossRef]
Dlala, E., Saitz, J., and Arkkio, A., 2006, “Inverted and Forward Preisach Models for Numerical Analysis of Electromagnetic Field Problems,” IEEE Trans. Magn., 42(8), pp.1963–1973. [CrossRef]
Tan, X., and Baras, J. S., 2004, “Modeling and Control of Hysteresis in Magneto-Stricture Actuators,” Automatics, 40(9), pp. 1469–1480. [CrossRef]
Iyer, R. V., Tan, X., and Krishnaprasad, P. S., 2005, “Approximate Inversion of the Preisach Hysteresis Operator With Application to Control of Smart Actuators,” IEEE Trans. Autom. Control, 50(6), pp. 798–810. [CrossRef]
Mittal, S., and Menq, C., H., 2000, “Hysteresis Compensation in Electromagnetic Actuators Through Preisach Model Inversion,” IEEE/ASME Trans. Mechatronics, 5(4), pp. 394–409. [CrossRef]
Aubin, J. P., and Frankowska, H., 1990, Set-Valued Analysis, Birkhäuser, Boston, MA, pp. 30–38.


Grahic Jump Location
Fig. 1

Basic hysteresis operator

Grahic Jump Location
Fig. 2

Preisach plane with limiting triangle P0

Grahic Jump Location
Fig. 3

Dividing functions (a) Hu(t) and Hd(t), (b) Vu(t) and Vd(t)

Grahic Jump Location
Fig. 4

Relationships between spaces

Grahic Jump Location
Fig. 5

Two different input signals with same RMS

Grahic Jump Location
Fig. 6

Division of the limiting triangle P0 in a finite number of squares and triangles

Grahic Jump Location
Fig. 7

Linearization of smart actuators with hysteresis

Grahic Jump Location
Fig. 8

Iterative search procedure to calculate the compensated input signal uc(nT0) in the case when uc(nT0) > uc((n − 1)T0)

Grahic Jump Location
Fig. 9

Experimental rig and block program of the data acquisition system

Grahic Jump Location
Fig. 10

An attenuate sinusoidal trajectory. (a) The comparative results between the desired, two compensated and noncompensated voltage-to-displacement curves. (b) Error plot.

Grahic Jump Location
Fig. 11

An arbitrary signal in the case when PEA subject to a small load of 440 g. (a) The comparative results between the desired, two compensated and noncompensated voltage-to-displacement curves. (b) Error plot.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In