0
Research Papers

Adaptive Control for a Class of Hysteretic Systems

[+] Author and Article Information
Seyyed Hossein Mousavi

e-mail: s.h.mousavi65@gmail.com

Alireza Khayatian

e-mail: khayatia@shirazu.ac.ir
Department of Power and Control Engineering,
Shiraz University,
Shiraz, Iran

1Corresponding Author

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 6, 2011; final manuscript received February 20, 2012; published online June 14, 2012. Assoc. Editor: Josè L. Escalona.

J. Comput. Nonlinear Dynam 8(1), 011003 (Jun 14, 2012) (8 pages) Paper No: CND-11-1085; doi: 10.1115/1.4006328 History: Received July 06, 2011; Revised February 20, 2012

In this paper, the generalized Prandtl-Ishlinskii model is used to design an adaptive controller for a class of nonlinear systems which contain hysteresis phenomenon within their dynamic equation as a function of state variables. The controller design is carried out through adaptive backstepping approach and the stability proof is given based on Lyapunov stability theory. In contrast to the systems in which hysteresis appear in their input, the inverse based methods cannot be applied to systems with hysteresis in their states. The proposed controller is able to cope with different kinds of hysteresis nonlinearity (saturated and unsaturated). Finally, to show the effectiveness of the proposed method, simulations are carried out for a second order “mass–nonlinear spring–damper” system.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ru, C., Chen, L., Shao, B., Rong, W., and Sun, L., 2009, “A Hysteresis Compensation Method of Piezoelectric Actuator: Model, Identification and Control,” Control Eng. Pract., 17, pp. 1107–1114. [CrossRef]
Huang, S., Tan, K. K., and Lee, T. H., 2009. “Adaptive Sliding-Mode Control of Piezoelectric Actuators,” IEEE Trans. Ind. Electron., 56(9), pp. 3514–3522. [CrossRef]
Ahn, K. K., and Kha, N. B., 2007, “Internal Model Control for Shape Memory Alloy Actuators Using Fuzzy Based Preisach Model,” Sensors Actuators A, 136, pp. 730–741. [CrossRef]
Gorbet, R. B., Wang, D., and Morris, K. A., 1998. “Preisach Model Identification of a Two-Wire SMA Actuator,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 287–300.
Ikhouanea, F., Manosab, V., and Rodellar, J., 2005, “Adaptive Control of a Hysteretic Structural System,” Automatica, 41, pp. 225–231. [CrossRef]
Bertotti, G., and Mayergoyz, I., 2006, The Science of Hysteresis, Vol. 1, Academic, London.
Ahn, K. K., and Kha, N. B., 2008, “Modeling and Control of Shape Memory Alloy Actuators Using Preisach Model, Genetic Algorithm and Fuzzy Logic,” Mechatronics, 18, pp. 141–152. [CrossRef]
Su, C. Y., Stepanenko, Y., Svoboda, J., and Leung, T. P., 2000. “Robust Adaptive Control of a Class of Nonlinear Systems With Unknown Backlash-Like Hysteresis,” IEEE Trans. Autom. Control, 45(12), pp. 2427–2432. [CrossRef]
Macki, J. W., Nistri, P., and Zecca, P., 1991, Mathematical Models for Hysteresis, Springer, New York.
Tao, G., and Kokotovic, P. V., 1995, “Adaptive Control of Plants With Unknown Hysteresis,” IEEE Trans. Autom. Control, 40, pp. 200–212. [CrossRef]
Tan, U. X., Latt, W. T., Widjaja, F., Shee, C. Y., Riviere, C. N., and Ang, W. T., 2009, “Tracking Control of Hysteretic Piezoelectric Actuator Using Adaptive Rate-Dependent Controller,” Sensors Actuators A, 150, pp. 116–123. [CrossRef]
Iyer, R. V., and Tan, X., 2009, “Control of Hysteretic Systems Through Inverse Compensation,” IEEE Control Systems, 29(1), pp. 83–99. [CrossRef]
Wang, Q., and Su, C. Y., 2006, “Robust Adaptive Control of a Class of Nonlinear Systems Including Actuator Hysteresis With Prandtl-Ishlinskii Presentations,” Automatica, 42, pp. 859–867. [CrossRef]
Janaidieh, M. A., Su, C. Y., and Rakheja, S., 2008, “A Generalized Asymmetric Play Hysteresis Operator for Modeling Hysteresis Nonlinearities of Smart Actuators,” Int. Conf. Control Autom. Robotics Vision, Dec, pp. 240–243.
Khalil, H., 2005, Nonlinear Systems, Prentice-Hall, Englewood Cliffs, NJ.
Kumon, M., Mizumoto, I., Indou, A., and Iwai, Z., 2008, “Reshape Memory Alloy Actuator With Simple Adaptive Control,” Int. J. Innovative Comput. Inform. Control, 4(12), pp. 3285–3295.

Figures

Grahic Jump Location
Fig. 1

Typical behavior of a saturated hysteresis

Grahic Jump Location
Fig. 2

Typical behavior of an unsaturated hysteresis

Grahic Jump Location
Fig. 4

Classical play operator

Grahic Jump Location
Fig. 5

Generalized play operator with r = 0, γl(x) = tanh(x − 1), and γr(x) = tanh(x + 1)

Grahic Jump Location
Fig. 6

Output response of the GPI model example

Grahic Jump Location
Fig. 7

Nonideal relay operator

Grahic Jump Location
Fig. 8

Physical schematic of the second order system

Grahic Jump Location
Fig. 9

Nonlinear restoring force, described by a Preisach model

Grahic Jump Location
Fig. 10

Identification of a Preisach based restoring force (solid line) using a GPI model (dotted line)

Grahic Jump Location
Fig. 11

Output tracking error while xd = sin(t) and the proposed controller is applied

Grahic Jump Location
Fig. 12

Control signal while xd = sin(t) and the proposed controller is applied

Grahic Jump Location
Fig. 13

Output tracking error while xd = sin(t) and the simple adaptive controller is applied

Grahic Jump Location
Fig. 14

Control signal while xd = sin(t) and the simple adaptive controller is applied

Grahic Jump Location
Fig. 15

Nonlinear restoring force described by an asymmetric Preisach model

Grahic Jump Location
Fig. 16

Output tracking error in the presence of asymmetric hysteresis and model uncertainty, while the proposed controller is applied

Grahic Jump Location
Fig. 17

Output tracking error in the presence of asymmetric hysteresis and model uncertainty, while the simple adaptive controller is applied

Tables

Errata

Discussions

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