This investigation confirms and controls chaotic motion in a permanent magnet synchronous motor (PMSM) system in electric vehicles. Complex nonlinear behaviors may be observed over a range of parameter values in the bifurcation diagram. The method of the Lyapunov exponent is adopted to identify the onset of chaotic motion and verify the analysis. Finally, a technique for effectively controlling a chaotic PMSM system will be offered. It involves applying an external input, called a dither signal, to the system. Some simulation results are presented to demonstrate the feasibility of the developed approach.
Ataei M., Kiyoumarsi A. and Ghorbani B. ( 2010) Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement. Physics Letter A374: 4226-4230.
2.
Benettin G., Galgani L., Giorgilli A. and Strelcyn JM ( 1980a) Lyapunov exponents for smooth dynamical systems and Hamiltonian systems; a method for computing all of them. Part I: theory. Meccanica15: 9-20.
3.
Benettin G., Galgani L., Giorgilli A. and Strelcyn JM ( 1980b) Lyapunov exponents for smooth dynamical systems and Hamiltonian systems; a method for computing all of them. Part II: numerical application . Meccanica15: 21-30.
4.
Chan CC and Chau KT ( 1997) An overview of power electronics in electric vehicles . IEEE Transactions on Industrial Electronics44: 3-13.
5.
Chang SC and Chen SC ( 2006) Dither signals with particular application to the control of windscreen wiper blades. International Journal of Solids and Structures43: 6998-7013.
6.
Chang SC and Lin HP ( 2005) Nonlinear dynamics and chaos control for an electromagnetic system. Journal of Sound and Vibration279: 327-344.
Feeny BF and Moon FC ( 2000) Quenching stick-slip chaos with dither. Journal of Sound and Vibration273: 173-180.
9.
Fuh CC and Tung PC ( 1997) Experimental and analytical study of dither signals in a class of chaotic systems. Physics Letter A229: 228-234.
10.
Gan J., Chau KT, Chan CC and Jiang Z. ( 2000) A new surface-inset, permanent-magnet, brushless DC motor drive for electric vehicles. IEEE Transactions on Magnetics36: 3810-3818.
11.
Ge X. and Huang J. ( 2005) Chaos control of permanent magnet synchronous motor. In: Proceedings of the Eighth International Conference on Electrical Machines and Systems, Nanjing, China, September 27-29, vol. 1, pp.484-488.
12.
Harb AM ( 2004) Nonlinear chaos control in a permanent magnet reluctance machine. Chaos, Solitons and Fractals19: 1217-1224.
13.
Jiaqun X., Renyuan T. and Minggao O. ( 2008) Improved direct torque control of permanent magnet synchronous motor in electric vehicle drive. In: IEEE Vehicle Power and Propulsion Conference, Harbin, China, September 3-5, pp.1-4.
14.
Jing Z., Yu C. and Chen G. ( 2004) Complex dynamics in a permanent-magnet synchronous motor model. Chaos, Solitons and Fractals22: 831-848.
15.
Kaplan JL and Yorke JA ( 1979) Chaotic Behavior of Multidimensional Difference Equations. Lecture Notes in Mathematics. New York: Springer-Verlag, pp.228-237.
16.
Li Z., Park JB, Joo YH, Zhang B. and Chen G. ( 2002) Bifurcation and chaos in a permanent-magnet synchronous motor. IEEE Transactions on Circuits and Systems I: Fundament Theory and Applications49: 383-387.
17.
Li Z., Zhang B. and Mao Z. ( 2000) Analysis of the chaotic phenomena in permanent-magnet synchronous motors based on Poincare map. In: Proceedings of the 3rd World Congress on Intelligent Control and Automation , Hefei, China, June 28-July 02, vol. 5, pp.3255-3258.
18.
Li Z., Zhang B., Tian L. and Mao Z. ( 1999) Strange attractors in permanent-magnet synchronous motors . In: Proceedings of the IEEE International Conference on Power Electronics and Drive Systems, Hong Kong, July 27-29, vol. 1, pp.150-155.
19.
Liaw YM and Tung PC ( 1998) Application of the differential geometric method to control a noisy chaotic system via dither smoothing. Physics Letters A239: 51-58.
20.
Liu D., Ren HP and Liu XY ( 2004) Chaos control in permanent magnet synchronous motors. In: Proceedings of the International Symposium on Circuits and Systems, Vancouver, Canada, May 23-26, vol. 4, pp.732-735.
21.
Ren H. and Liu D. ( 2006) Nonlinear feedback control of chaos in permanent magnet synchronous motor. IEEE Transactions on Circuits and Systems II: Express Briefs53: 45-50.
22.
Shimada I. and Nagashima T. ( 1979) A numerical approach to ergodic problems of dissipative dynamical systems. Progress of Theoretical Physics61: 1605-1616.
23.
Tung PC and Chen SC ( 1993) Experimental and analytical studies of the sinusoidal dither signal in a DC motor system. Dynamics and Control3: 53-69.
24.
Wolf A., Swift JB, Swinney HL and Vastano JA ( 1985) Determining Lyapunov exponent from a time series. Physica D16: 285-317.
25.
Zhang B., Li Z. and Mao ZY ( 2002) Entrainment and migration control of permanent-magnet synchronous motor system [in Chinese]. Control Theory and Applications19: 53-56.
