Abstract
In this paper, the global exponential stabilization for the chaotic brushless DC motor (BLDCM) is considered. Based on Lyapunov-like Theorem with differential and integral inequalities, a single and linear feedback control is proposed to realize the global stabilization of BLDCM with exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. Computer simulation results show that the proposed method is effective.
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Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)
Wei, D., Luo, X., Zhang, B.: Synchronization of brushless DC motors based on LaSalle invariance principle. Nonlinear Dyn. 69, 1733–1738 (2012)
Maetani, T., Isomura, Y., Watanabe, A., Iimori, K., Morimoto, S.: Suppressing bearing voltage in an inverter-fed ungrounded brushless DC motor. IEEE Trans. Ind. Electron. 60, 4861–4868 (2013)
Hemati, N., Leu, M.C.: A complete model characterization of brushless DC motors. IEEE Trans. Ind. Appl. 28, 172–180 (1992)
Hemati, N.: Strange attractors in brushless DC motor. IEEE Trans. Circ. Syst. I 41, 40–45 (1994)
Chau, K.T., Chen, J.H., Chan, C.C.: Dynamic bifurcation in DC drives. In: 28th Annual IEEE Power Electronics Specialists Conference, St. Louis, MO, USA, pp. 1330–13 36 (1997)
Chen, J.H., Chau, K.T., Chan, C.C.: Analysis of chaos in current-mode-controlled dc drive systems. IEEE Trans. Ind. Electron. 47, 67–76 (2000)
Ge, Z.M., Chang, C.M., Chen, Y.S.: Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order system. Chaos Solitons Fractals 27, 1298–1315 (2006)
Ren, H.P., Chen, G.: Control Chaos in Brushless DC Motor via Piecewise Quadratic State Feedback. ICIC Part II. LNCS 3645, pp. 149–158. Springer, Heidelberg (2005)
Ge, Z.M., Chang, C.M.: Chaos synchronization and parameters identification of single time scale brushless DC motors. Chaos Solitons Fractals 20, 883–903 (2004)
Dadras, S., Motallebzadeh, F., Motallebzadeh, F., Ozgoli, S., Momeni, H.R.: Control of chaotic uncertain brushless DC motors. In: IEEE International Conference on Control and Automation, Christchurch, New Zealand, 9–11 December 2009
Poursamad, A., Markazi, A.H.D.: Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems. Chaos Solitons Fractals 42, 3100–3109 (2009)
Meng, Z., Sun, C., An, Y., Yang, H., Hu, Q.: Controlling chaos for BLDC thruster motor in deepwater robot based on fuzzy control. In: 2007 IEEE International Conference on Control and Automation, Guangzhou, China (2007)
Attaianese, C., Perfetto, A., Tomasso, G.: Robust position control of DC drives by means of H-\(\infty \) controllers. Electri. Power Appl. 146, 391–396 (1999)
Sun, Y.J., Hsieh, J.G.: Global exponential stabilization for a class of uncertain nonlinear systems with time-varying delay arguments and input deadzone nonlinearities. J. Franklin Inst. 332, 619–631 (1995)
Hiena, L.V., Phat, V.N.: Exponential stability and stabilization of a class of uncertain linear time-delay systems. J. Franklin Inst. 346, 611–625 (2009)
Sun, Y.J., Lien, C.H., Hsieh, J.G.: Global exponential stabilization for a class of uncertain nonlinear systems with control constraint. IEEE Trans. Autom. Control 43, 674–677 (1998)
Sun, Y.J., Wu, Y.B., Wang, C.C.: Robust stabilization for a class of nonlinear systems via a single input control applicable to chaotic systems and its circuit implementation. Chaos 23, 023127 (2013)
Wang, X., Li, S., Xu, D.: Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nonlinear Dyn. 64, 65–75 (2011)
Zhang, Z., Zhang, T., Huang, S., Xiao, P.: New global exponential stability result to a general Cohen-Grossberg neural networks with multiple delays. Nonlinear Dyn. 67, 2419–2432 (2012)
Acknowledgments
This work is supported by the Key Program of the National Natural Science Foundation of PRC under Grant no. 50937001 and the National Natural Science Foundation of PR China under Grant nos. 61263021, 11262004, 11065003, and 10947011.
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Wei, D.Q., Wan, L., Luo, X.S. et al. Global exponential stabilization for chaotic brushless DC motors with a single input. Nonlinear Dyn 77, 209–212 (2014). https://doi.org/10.1007/s11071-014-1284-6
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DOI: https://doi.org/10.1007/s11071-014-1284-6