Adaptive Sliding Model Control for Hysteresis System Based on Prandtl-Ishlinskii Model

WANG Xiangjiang^{1, 2}   WANG Xingsong¹  MAO Yan¹

(1. School of Mechanical Engineering, Southeast University, Nanjing 211189;
2. College of Mechanical Engineering, University of South China, Hengyang 421001)

Abstract: A giant magnetostrictive actuator(GMA) is designed, analyzed and experimentally studied. The electromechanical system model is built for the GMA, which is connected in series by two subsystems: rate-independent hysteretic model; transfer function which isn’t involved in the effect of hysteresis. In order to mitigate the effect of the hysteresis, the variable structure control based on Prandtl-Ishlinskii(PI) model is proposed, and the adaptive control law for the variable structure control is deduced from the Lyapunov stability theorem. The emulational and experimental results confirm the accuracy of the electromechanical system model and the availability of the controlling method

Key words: Hysteresis  Transfer function  Sliding model control  Adaptive  Stability

CLC No: TH1655

国家自然科学基金(1504750767)、江苏省自然科学基金(BK2005065)和教育部博士点基金(20050286022)资助项目. Received 20070528, received in revised form 20071026

References

[1] GE P, JOUANEH M. Generalized PREISACH model for hysteresis nonlinearity of piezoceramic actuators [J]. Precision Engineering, 1997, 20(2): 99-111.
[2] GE P, JOUANEH M. Tracking control of a piezoceramic actuator[J]. IEEE Trans. on Control Systems Techno- logy, 1996, 4(3): 209-215.
[3] BOLEY C D, HODGDON M L. Model and simulation of hysteresis in magnetic cores[J]. IEEE Trans. on Magnetics, 1989, 25(5): 3 922-3 924.
[4] MACKI J W, NISTRI P, ZECCA P. Mathematical models for hysteresis[J]. SIAM Review,1993, 35: 94-123.
[5] MITTAL S, MEAQ C H. Hysteresis compensation in electromagnetic actuator through PREISACH model inversion[J]. IEEE/ASME Trans. on Mechatronics, 2000, 5(4): 394-409.
[6] WANG Qingqing, SU Chunyi, CHEN Xinkai. Robust adaptive control of a class of nonlinear systems with Prandtl-Ishlinskii hysteresis[C]∥43rd IEEE Conference on Decision and Control December 14-17, 2004. Atlantis, 2004: 213-218.
[7] SU C Y, STEPANENKO Y, SVOBODA J, et al. Robust adaptive control of a class of nonlinear systems with backlash-like hysteresis[J]. IEEE Trans. on Automatic Control, 2000, 45(12): 2 427-2 432.
[8] TAO G, KOLOTOVIC P V. Adaptive control of plants with unknown hysteresis [J]. IEEE Trans. on Automatic Control, 1995, 40(2): 200-213.
[9] HWANG C L, JAN C, CHEN Y H. Piezomechanic using intelligent variable-structure control [J]. IEEE Trans. on Industrial Electronic, 2001, 48(1): 47-59.
[10] D’ANNUNZIO C M, ANN R, CHASSAING C E. Development of a control system for a nonlinear Terfenol-D actuator[C]∥Proceedings of SPIE-The International Society for Optical Engineering, Mathematics and Control in Smart Structures, Vasundara V. Varadan, Jagdish Chandra, 1996 (2 715): 588-599.
[11] XIA Chunlin , DING Fan, LU Yongxiang. Modeling of giant magnetostrictive actuator[J]. China Mechanical Engineering, 2000, 11(11): 1 288-1 292.