International Journal of Automotive Technology

  • 제8권4호
  • /
  • Pages.467-476
  • /
  • 2007
  • /
  • 1229-9138(pISSN)
  • /
  • 1976-3832(eISSN)
한국자동차공학회 (The Korean Society of Automotive Engineers)
권호 표지

ON CONTROLLING A CHAOTIC VEHICLE DYNAMIC SYSTEM BY USING DITHER

  • Chang, S.C. (Department of Mechanical and Automation Engineering, Dayeh University)
  • 발행 : 2007.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This work verifies the chaotic motion of a steer-by-wire vehicle dynamic system, and then elucidates an application of dither smoothing to control the chaos of a vehicle model. The largest Lyapunov exponent is estimated from the synchronization to identify periodic and chaotic motions. Then, a bifurcation diagram reveals complex nonlinear behaviors over a range of parameter values. Finally, a method for controlling a chaotic vehicle dynamic system is proposed. This method involves applying another external input, called a dither signal, to the system. The designed controller is demonstrated to work quite well for nonlinear systems in achieving robust stability and protecting the vehicle from slip or spin. Some simulation results are presented to establish the feasibility of the proposed method.

키워드

참고문헌

  1. Ackermann, J. and Sienel, W. (1993). Robust yaw damping of cars with front and rear wheel steering. IEEE Trans. Control Systems Technology, 1, 15-20 https://doi.org/10.1109/87.221348
  2. Bakker, E., Pacejka, H. B. and Lidner, L. (1989). A new tire model with an application in vehicle dynamics studies. Proc. Int. Congress and Exposition, SAE Paper No. 890087
  3. Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J. M. (1980a). Lyapunov exponents for smooth dynamical systems and hamiltonian systems; a method for computing all of them. Part I: Theory, Meccanica, 15, 9-20
  4. Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J. M. (1980b). Lyapunov exponents for smooth dynamical systems and hamiltonian systems; A method for computing all of them. Part II: Numerical Application, Meccanica, 15, 21-30
  5. Catino, B., Santini, S. and Bernardo, M. D. (2003). MCS adaptive control of vehicle dynamics: an application of bifurcation techniques to control system design. IEEE 42nd Conf. Decision Contr., 2252-2256
  6. Cai, C., Xu, Z., Xu, W. and Feng, B. (2002a). Notch filter feedback control in a class of chaotic systems. Automatica, 38, 695-701 https://doi.org/10.1016/S0005-1098(01)00239-4
  7. Cai, C., Xu, Z. and Xu, W. (2002b). Converting chaos into periodic motion by feedback control. Automatica, 38, 1927-1933 https://doi.org/10.1016/S0005-1098(02)00078-X
  8. Chang, S. C. and Lin, H. P. (2005). Nonlinear dynamics and chaos control for an electromagnetic system. J. Sound and Vibration, 279, 327-344 https://doi.org/10.1016/j.jsv.2003.11.033
  9. Chang, S. C. (2007) Adoption of state feedback to control dynamics of vehicle with steer-by-wire system. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering, 221, 1-12 https://doi.org/10.1243/09544070JAUTO354
  10. Cook, P. A. (1986). Nonlinear Dynamical Systems. Prentice-Hall. Englewood Cliffs
  11. Dai, L. and Han, Q. (2004). Stability and hopf bifurcation of a nonlinear model for a four-wheel-steering vehicle system. Communications in Nonlinear Science and Numerical Simulation, 9, 331-341 https://doi.org/10.1016/S1007-5704(02)00084-9
  12. Ditto, W. L., Rauseo, S. N. and Spano, M. L. (1990). Experimental control of chaos. Physical Review Letters, 65, 3211-3214 https://doi.org/10.1103/PhysRevLett.65.3211
  13. Feeny, B. F. and Moon, F. C. (2000). Quenching stickslip chaos with dither. J. Sound and Vibration, 273, 173-180
  14. Fun, C. C. and Tung, P. C. (1997). Experimental and analytical study of dither signals in a class of chaotic system. Physics Letters, A 229, 228-234 https://doi.org/10.1016/S0375-9601(97)00153-9
  15. Harada, M. and Harada, H. (1999). Analysis of lateral stability with integrated control of suspension and steering systems. JSAE Review, 20, 465-470 https://doi.org/10.1016/S0389-4304(99)00040-5
  16. Hayama, R. and Nishizaki, K. (2000). The vehicle stability control responsibility improvement using steer-bywire. Proc. IEEE Intelligent Vehicles Symp., 596-601
  17. Hinrichs, N., Oestreich, M. and Popp, K. (1997). Dynamics of oscillators with impact and friction. Chaos, Solitons & Fractals, 8, 535-558 https://doi.org/10.1016/S0960-0779(96)00121-X
  18. Hosaka, M. and Murakami, T. (2004). Yaw rate control of electric vehicle using steer-by-wire system. IEEE 8th Int. Workshop, Advance Motion Control, 31-34
  19. Hunt, E. R. (1991). Stabilizing high-period orbits in a chaotic system: The diode resonator. Physical Review Letters, 67, 1953-1955 https://doi.org/10.1103/PhysRevLett.67.1953
  20. Lai, Y. C., Ding, M. and Grebogi, C. (1993). Controlling hamiltonian chaos. Physical Review, E 67, 86-92
  21. Liaw, Y. M. and Tung, P. C. (1998). Application of the differential geometric method to control a noisy chaotic system via dither smoothing. Physics Letters, A 239, 51-58 https://doi.org/10.1016/S0375-9601(97)00919-5
  22. Muller, P. (1995). Calculation of Lyapunov exponents for dynamical systems with discontinuities. Chaos, Solitons & Fractals, 5, 1671-1681 https://doi.org/10.1016/0960-0779(94)00170-U
  23. Ono, E., Hosoe, S., Tuan, H. D. and Doi, S. (1998). Bifurcation in vehicle dynamics and robust front wheel steering control. IEEE Trans. Control Systems Technology, 6, 412-420 https://doi.org/10.1109/87.668041
  24. Ott, E., Grebogi, C. and Yorke, J. A. (1990). Controlling chaos. Physical Letters, 64, 1196-1199 https://doi.org/10.1103/PhysRevLett.64.1196
  25. Sano, S., Furukawa, Y. and Siraishi, S. (1986). Four wheel steering system with rear wheel steer angle controlled as function of steering wheel angle. Proc. Int. Cong. and Exposition, SAE Paper No. 860625
  26. Segawa, M., Nakano, S., Nishihara, O. and Kumamoto, H. (2001). Vehicle stability control strategy for steer by wire system. JSAE Review, 22, 383-388 https://doi.org/10.1016/S0389-4304(01)00144-8
  27. Setlur, P., Dawson, D., Wagner, J. and Fang, Y. (2002). Nonlinear tracking controller design for steer-by-wire automotive systems. Proc. American Control Conf. Anchorage, 280-285
  28. Shibahata, Y., Irie, N., Itoh, H. and Nakamura, K. (1986). The development of an experimental four-wheel-steering vehicle. Proc. Int. Congress and Exposition, SAE Paper No. 860623
  29. Shimada, I. and Nagashima, T. (1979). A numerical approach to ergodic problems of dissipative dynamical systems. Progress of Theoretical Physics, 61, 1605-1616 https://doi.org/10.1143/PTP.61.1605
  30. Stefanski, A. (2000). Estimation of the largest Lyapunov exponent in systems with impact. Chaos, Solitons & Fractals, 11, 2443-2451 https://doi.org/10.1016/S0960-0779(00)00029-1
  31. Takiguchi, T., Yasuda, N., Furutani, S., Kanazawa, H. and Inoue, H. (1986). Improvement of vehicle dynamics by vehicle-speed-sensing four-wheel steering system. Proc. Int. Congress and Exposition, SAE Paper No. 860624
  32. Tung, P. C. and Chen, S. C. (1993). Experimental and analytical studies of the sinusoidal dither signal in a dc motor system. Dynamics and Control, 3, 53-69 https://doi.org/10.1007/BF01968359
  33. Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica, D 16, 285-317 https://doi.org/10.1016/0167-2789(85)90011-9
  34. Yih, P. and Gerdes, J. C. (2005). Modification of vehicle handling characteristics via steer-by-wire. IEEE Trans. Control Systems Technology, 13, 965-976 https://doi.org/10.1109/TCST.2005.854320
  35. You, S. S. and Jeong, S. K. (2002). Controller design and analysis for automatic steering of passenger cars. Mechatronics, 12, 427-446 https://doi.org/10.1016/S0957-4158(01)00005-8