In most situations, the high performance of permanent magnet synchronous motors (PMSMs) depends on an absence of chaos; consequently, suppressing chaos becomes quite important. Therefore, this study confirms the chaotic motion and then applies synchronization to a chaotic PMSM system to control chaos. Rich dynamics of the PMSM system are studied using a bifurcation diagram, phase portraits, a Poincaré map, frequency spectra and Lyapunov exponents. First, the largest Lyapunov exponent is estimated using synchronization to identify periodic and chaotic motions. Next, complex nonlinear behaviors are thoroughly observed throughout a range of parameter values in the bifurcation diagram. Finally, a proposed continuous feedback control method based on synchronization characteristics eliminated chaotic oscillations. Numerical simulations are utilized to verify the feasibility and efficiency of the proposed control technique.
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," Meccanica15, 9-20.
2.
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,"Meccanica15, 21-30.
3.
Chan, C.-C. and Chau, K.-T., 1997, "An overview of power electronics in electric vehicles ," IEEE Transactions on Industrial Electronics44, 3-13.
4.
Chang, S.-C., 2006, "Application of synchronization and continuous control to a chaotic automotive wiper system," in Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering vol. 220, pp. 1119-1130.
5.
Chua, K.-T. and Chen, J.-H., 2003, "Modeling analysis and experimentation of chaos in switched reluctance drive system," IEEE Transactions on Circuits and Systems - I: Fundament Theory and Applications50, 712-716.
6.
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, September 27-29, vol. 1, pp. 484-488.
7.
Harb, A.-M., 2004, "Nonlinear chaos control in a permanent magnet reluctance machine," Chaos, Solitons and Fractals19, 1217-1224.
8.
Hemati, N., 1994, "Strange attractors in brushless DC motor," IEEE Transactions on Circuits and Systems - I: Fundament Theory and Applications41, 40.
9.
Jing, Z., Yu, C., and Chen, G., 2004, "Complex dynamics in a permanent-magnet synchronous motor model," Chaos, Solitons and Fractals22, 831-848.
10.
Kapitaniak, T., 1995, "Continuous control and synchronization in chaotic systems," Chaos, Solitons and Fractals6, 237-244.
11.
Kuroe, Y. and Hayashi, S., 1989, "Analysis of bifurcation in power electronic induction motor drive system," in Proceedings of the IEEE Power Electronics Specialists Conference, Milwaukee, WI , June 26-29, pp. 923- 930.
12.
Li, Z., Park, J.-B., Joo, Y.-H., Zhang, B., and Chen, G., 2002a, "Bifurcation and chaos in a permanent-magnet synchronous motor," IEEE Transactions on Circuits and Systems - I: Fundament Theory and Applications49, 383-387.
13.
Li, Z., Zhang, B., Tian, L., Mao, Z., and Pong, M.-H., 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.
14.
Li, Z., Zhang, B., and Mao, Z., 2000, "Analysis of the chaotic phenomena in permanent-magnet synchronous motors based on Poincaré map," in Proceedings of the 3 rd World Congress on Intelligent Control and Automation , Hefei, P.R. China, June 28-July 2, pp. 3255-3258.
15.
Li, Z., Zhang, B., and Mao, Z.-Y., 2002b, "Entrainment and migration control of permanent-magnet synchronous motor system," (in Chinese), Control Theory and Applications19, 53-56.
16.
Liu, D., Ren, H.-P., and Liu, X.-Y., 2004, "Chaos control in permanent magnet synchronous motors ," in IEEE Proceedings of the International Symposium on Circuit and Systems, Vancouver, Canada, May 23-26, vol. 4, 732-735.
17.
Pyragas, K., 1992, "Continuous control of chaos by self-controlling feedback ," Physics Letters A170, 421-428.
18.
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.
19.
Stefanski, A., 2000, "Estimation of the largest Lyapunov exponent in systems with impacts," Chaos, Solitons and Fractals11, 2443-2451.
20.
Wolf, A., Swift, J.-B., Swinney, H.-L., and Vastano, J.-A., 1985, "Determining Lyapunov exponent from a time series," Physica D16, 285-317.
