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Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

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Abstract

A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result, the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.

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References

  1. Yang S P, Shen Y J. Bifurcation and Singularity of Nonlinear Systems with Hysteresis. Beijing: Science Press, 2003. 4–5

    Google Scholar 

  2. Tao G, Kolotovic P V. Adaptive control of plants with unknown hysteresis. IEEE Trans Autom Control, 1995 40(2): 200–212

    Article  MATH  Google Scholar 

  3. Krasnoselskii M, Pokrovskii A. Systems with Hysteresis. Berlin: Spring-Verlag, 1989. 73–89

    Google Scholar 

  4. Mayergoyz I D. Mathematical Models of Hysteresis. New York: Spring-Verlag, 1991. 36–49

    MATH  Google Scholar 

  5. Mayergoyz I D. Mathematical models of hysteresis. IEEE Trans Mag, 1986 MAG-22(5): 603–608

    Article  Google Scholar 

  6. Adly A A, Abd-El-Hafiz S K. Using neural networks in the identification of Preisach-type hysteresis models. IEEE Trans Mag, 1998 34(3): 629–635

    Article  Google Scholar 

  7. Wei J D, Sun C T. Constructing hysteretic memory in neural networks. IEEE Trans Sys Man Cyber Part B: cyber, 2000 30(4): 601–609

    Article  Google Scholar 

  8. Li C T, Tan Y H. A neural networks model for hysteresis nonlinearity. Sen Actu A: Phys, 2004 112(1): 49–54

    Article  Google Scholar 

  9. Zhao X L, Tan Y H. Intelligent modeling for hysteresis nonlinearity in Piezoceramic actuator (in Chinese). J Syst Simulat, 2006 18(1): 23–25

    MathSciNet  Google Scholar 

  10. Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Sys Man Cyber, 1985 SMC-15: 116–132

    Google Scholar 

  11. Tsekouras G, Sarimveis H, Bafas G. A simple algorithm for training fuzzy systems using input-output data. Advan Eng Softw, 2003 34(5): 247–259

    Article  MATH  Google Scholar 

  12. Grisales V H, Gauthier A, Roux G. Fuzzy model identification of a biological process based on input-output data clustering. In: Proceedings of the IEEE International Conference on Fuzzy Systems. Reno, NV, United States, 2005. 927–932

    Google Scholar 

  13. Zeng K, Zhang N Y, Xu W L. Typical T-S fuzzy systems are universal approximators (in Chinese). Contr Theory Appl, 2001 18(2): 293–297

    MATH  Google Scholar 

  14. Tikk D. On nowhere denseness of certain fuzzy controllers containing prerestricted number of rules. Tatra Mount Math Pub, 1999 16(2): 369–377

    MATH  MathSciNet  Google Scholar 

  15. Tikk D, Baranyi P, Patton R J. Polytopic and T-S model are nowhere dense in the approximation model space. In: Proceedings of the International Conference on Systems, Man and Cybernetics. Tunisia: Institute of Electrical and Electronics Engineers Inc., 2002: 150–153

    Google Scholar 

  16. Jang J S R. ANFIS: Adaptive-network-based Fuzzy Inference Systems. IEEE Trans Sys Man Cyber, 1993 23(3): 665–685

    Article  MathSciNet  Google Scholar 

  17. Chiu S. Fuzzy model identification based on cluster estimation. J Intel Fuzzy Sys, 1994 2(3): 267–278

    Google Scholar 

  18. Zhang J G, Mao J Q, Xia T. Fuzzy-tree model and its applications to complex system modeling (in Chinese). Acta Autom Sin, 2000 26(3): 378–381

    Google Scholar 

  19. Yue Y F, Mao J Q. Fast adaptive modeling based on T-S model (in Chinese). Contr Decision, 2002 17(2): 155–158

    Google Scholar 

  20. Mao J Q, Zhang J G, Yue Y F, et al.Adaptive tree-structuredbased fuzzy inference systems. IEEE Trans Fuzzy Syst, 2005 13(1): 1–12

    Article  Google Scholar 

  21. Gelfand S B, Ravishankar C S. A tree-structured piecewise linear adaptive filter. IEEE Trans Inf Theory, 1993 39(6): 1907–1922

    Article  MATH  Google Scholar 

  22. Narendra K S, Parthasarathy K. Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw, 1990 1(1): 4–27

    Article  Google Scholar 

  23. Astrom K J, Eykhoff P. System identification, a survey. Automatica, 1971 7(2): 123–62

    Article  MathSciNet  Google Scholar 

  24. Psaltis D, Sideris A, Yamamura A. Multilayered neural network controller. IEEE Contr Syst Mag, 1988 8(2): 17–21

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191, China

    JianQin Mao

  2. China Airborne Missile Academy, Luoyang, 471009, China

    HaiShan Ding

Authors
  1. JianQin Mao
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  2. HaiShan Ding
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Corresponding author

Correspondence to JianQin Mao.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60534020), the National Basic Research Program of China (Grant No. G2002cb312205-04), the Research Fund for the Doctoral Program of Higher Education (Grant No. 20070006060), and the Key Subject Foundation of Beijing (Grant Nos. XK100060526, XK100060422)

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Mao, J., Ding, H. Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis. Sci. China Ser. F-Inf. Sci. 52, 656–673 (2009). https://doi.org/10.1007/s11432-009-0026-8

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  • DOI: https://doi.org/10.1007/s11432-009-0026-8

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