Synchronization and controlling chaos in a permanent magnet synchronous motor. (English) Zbl 1336.70038

Chang, Shun-Chang

J. Vib. Control 16, No. 12, 1881-1894 (2010).

Summary: 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.

MSC:

70K55	Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
70K50	Bifurcations and instability for nonlinear problems in mechanics
70Q05	Control of mechanical systems
78A55	Technical applications of optics and electromagnetic theory

Keywords:

bifurcation; chaotic motion; Lyapunov exponent; permanent magnet synchronous motor; synchronization

References:

[1]	DOI: 10.1007/BF02128236 · Zbl 0488.70015
[2]	Benettin, G., Meccanica 15 pp 21– (1980)
[3]	Chan, C.-C., IEEE Transactions on Industrial Electronics 44 pp 3– (1997)
[4]	Chang, S.-C., Proceedings of the Institution of Mechanical Engineers, Part D
[5]	Chua, K.-T., IEEE Transactions on Circuits and Systems - I: Fundament Theory and Applications 50 pp 712– (2003)
[6]	Ge, X., Proceedings of the Eighth International Conference on Electrical Machines and Systems
[7]	Harb, A.-M., Solitons and Fractals 19 pp 1217– (2004) · Zbl 1072.78512
[8]	Hemati, N., IEEE Transactions on Circuits and Systems - I: Fundament Theory and Applications 41 pp 40– (1994)
[9]	Jing, Z., Solitons and Fractals 22 pp 831– (2004) · Zbl 1129.70329
[10]	Kapitaniak, T., Solitons and Fractals 6 pp 237– (1995) · Zbl 0976.93504
[11]	Kuroe, Y., Proceedings of the IEEE Power Electronics Specialists Conference
[12]	Li, Z., IEEE Transactions on Circuits and Systems - I: Fundament Theory and Applications 49 pp 383– (2002)
[13]	Li, Z., Proceedings of the IEEE International Conference on Power Electronics and Drive Systems
[14]	Li, Z., Proceedings of the 3 rd World Congress on Intelligent Control and Automation
[15]	Li, Z., Control Theory and Applications 19 pp 53– (2002)
[16]	Liu, D., IEEE Proceedings of the International Symposium on Circuit and Systems
[17]	DOI: 10.1016/0375-9601(92)90745-8
[18]	Ren, H., IEEE Transactions on Circuits and Systems - II: Express Briefs 53 pp 45– (2006)
[19]	Stefanski, A., Solitons and Fractals 11 pp 2443– (2000) · Zbl 0963.70018
[20]	DOI: 10.1016/0167-2789(85)90011-9 · Zbl 0585.58037