Abstract
Of the many technologies being explored to address sustainability and environmental issues, electric cars are considered to be the most promising alternative to vehicles powered by IC engines. This paper studies the instability control of electric vehicles propelled by permanent magnet synchronous motors (PMSMs). The nonlinear characteristics of a surface-mounted PMSM model are studied under three different assumed driving conditions. To mitigate undesirable dynamic instabilities including hyperchaotic responses that are frequented at low and high speeds, so as to extend the operating range of the PMSM system, a novel control scheme that exerts simultaneous control in both the time and frequency domains is developed and subsequently validated. The control approach has its foundation established in discrete wavelet transformation and adaptive control. Its physical implementation consists of an adaptive controller and an adaptive filter both implemented in the wavelet domain. Numerical results demonstrate the effectiveness of the controller design in restoring PMSM instability with low-amplitude limit-cycle in response to a properly specified reference signal.
Similar content being viewed by others
References
Sandalow DB (2009) Plug-in electric vehicles: what role for Washington? Brookings Institution Press, Washington
Sperling D, Gordon D, Schwarzenegger A (2010) Two billion cars: driving toward sustainability. Oxford University Press, Oxford
Vu NTT, Choi HH, Jung JW (2012) Certainty equivalence adaptive speed controller for permanent magnet synchronous motor. Mechatronics 22(6):811–818
Pillay P, Krishnan R (1991) Application characteristics of permanent magnet synchronous and brushless DC motors for servo drives. IEEE Trans Ind Appl 27(5):986–996
Harb AM (2004) Nonlinear chaos control in a permanent magnet reluctance machine. Chaos Solitons Fract 19(5):1217–1224
Ren H, Liu D (2006) Nonlinear feedback control of chaos in permanent magnet synchronous motor. IEEE Trans Circuits Syst II Express Briefs 53(1):45–50
Ren H, Liu D, Li J (2003) Delay feedback control of chaos in permanent magnet synchronous motor. Proc China Soc Electron Eng 23(6):175–178 (In Chinese)
Guan H, Zhao Y, Sun Q, Liu Y, Zhang T (2010) Anticontrol of chaos for a class of stable smooth-air-gap PMSM systems via delayed feedback control. In: 2010 2nd international conference on industrial and information systems, vol. 2, pp 121–124
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst 15(1):116–132
Wu Z-G, Shi P, Su H, Chu J (2014) Sampled-data fuzzy control of chaotic systems based on a T–S fuzzy model. IEEE Trans Fuzzy Syst 22(1):153–163
Nazzal JM, Natsheh AN (2007) Chaos control using sliding-mode theory. Chaos Solitons Fract 33(2):695–702
Yau H-T, Yan J-J (2004) Design of sliding mode controller for Lorenz chaotic system with nonlinear input. Chaos Solitons Fract 19(4):891–898
Xiaohui Y, Liu X, Liu H, Xu S (2013) Fuzzy sliding-mode control of chaos in permanent magnet synchronous motor. Int J Digit Content Technol Appl 7(1):526–535
Choi HH (2012) Adaptive control of a chaotic permanent magnet synchronous motor. Nonlinear Dyn 69(3):1311–1322
Chun-Lai L, Si-Min Y, Xiao-Shu L (2012) Fractional-order permanent magnet synchronous motor and its adaptive chaotic control. Chin Phys B 21(10):100506
Ge X, Huang J (2005) Chaos control of permanent magnet synchronous motor. In: Proceedings of the eighth international conference on electrical machines and systems, vol. 1, pp 484–488
Chang S, Lin B, Lue Y (2011) Dither signal effects on quenching chaos of a permanent magnet synchronous motor in electric vehicles. J Vib Control 17(12):1912–1918
Wei Q, Wang X (2012) Chaos controlling of permanent magnet synchronous motor base on dither signal. J Vib Control 19(16):2541–2550
Andrievskii BR, Fradkov AL (2003) Control of chaos: methods and applications. I. Methods. Autom Remote Control 64(5):673–713
Liu M-K, Suh CS (2012) Simultaneous time-frequency control of bifurcation and chaos. Commun Nonlinear Sci Numer Simul 17(6):2539–2550
Suh CS, Liu M-K (2013) Control of cutting vibration and instability: a time-frequency approach for precision micro and nano machining. Wiley, London
Li Z, Zhang B, Tian L, Mao Z, Pong MH (1999) Strange attractor in permanent-magnet synchronous motors. In: Proceedings of the IEEE international conference on power electronics and drive systems, vo. 1, pp 150–155
Hemati N (1994) Strange attractors in brushless DC motors. IEEE Trans Circuits Syst I Fundam Theory Appl 41(1):40–45
Li Z, Park JB, Joo YH, Zhang B, Chen G (2002) Bifurcation and chaos in a permanent-magnet synchronous motor. IEEE Trans Circuits Syst I Fundam Theory Appl 49(3):383–387
Gao Y, Chau KT (2002) Chaotification of permanent-magnet synchronous motor drives using time-delay feedback. In: IEEE 28th annual conference of the industrial electronics society, vol. 1, pp 762–766
Goedtel A, da Silva IN, Serni PJA (2007) Load torque identification in induction motor using neural networks technique. Electr Power Syst Res 77(1):35–45
Polikar R (1999) The story of wavelets. In: IMACS/IEEE CSCC’99 proceedings, pp 5481–5486
Kuo SM, Morgan DR (1996) Active noise control systems: algorithms and DSP implementations. Wiley, London
Jensen A, la Cour-Harbo A (2001) Ripples in mathematics. Spring, Berlin
Attallah S (2000) The wavelet transform-domain LMS algorithm: a more practical approach. IEEE Trans Circuits Syst II Analog Digit Signal Process 47(3):209–213
Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N-C, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond A 454:903–995
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, X., Suh, C.S. Nonlinear time-frequency control of PM synchronous motor instability applicable to electric vehicle application. Int. J. Dynam. Control 4, 400–412 (2016). https://doi.org/10.1007/s40435-014-0145-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40435-014-0145-y