Chaos control of single time-scale brushless DC motor with sliding mode control method

In this paper, the sliding mode control (SMC) scheme of single time-scale brushless DC motor (BLDCM) is investigated. The SMC method consists of 2 sections. To simplify the directive of the stability of the controlled single time-scale BLDCM in the sliding mode, first a special type of PI switching surface is adopted. Second, the SMC controller is obtained to guarantee the occurrence of the PI switching surface. The effectiveness of the theoretical analysis is evaluated by numerical simulations. Thus, the numerical results are used to show the verification and trustworthiness of the proposed method.

Chaos control of single time-scale brushless DC motor with sliding mode control method

In this paper, the sliding mode control (SMC) scheme of single time-scale brushless DC motor (BLDCM) is investigated. The SMC method consists of 2 sections. To simplify the directive of the stability of the controlled single time-scale BLDCM in the sliding mode, first a special type of PI switching surface is adopted. Second, the SMC controller is obtained to guarantee the occurrence of the PI switching surface. The effectiveness of the theoretical analysis is evaluated by numerical simulations. Thus, the numerical results are used to show the verification and trustworthiness of the proposed method.

___

  • S.H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, New York, Perseus Books Group, 1994.
  • X. Wu, G. Chen, J. Cai, “Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control”, Physica D: Nonlinear Phenomena, Vol. 229, pp. 52–80, 2007.
  • G. Jiang, W.K.S. Tang, “A global chaos synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach”, International Journal of Bifurcation and Chaos, Vol. 12, pp. 2239–2253, 2002. J.P. Cai, X.F. Wu, S.H. Chen, “Synchronization criteria for non-autonomous chaotic systems via sinusoidal state error feedback control”, Physica Scripta, Vol. 75, pp. 397–387, 2007.
  • X.F. Wu, M.H. Wang, “Robust synchronization of chaotic Lur’e systems via replacing variables control”, International Journal of Bifurcation and Chaos, Vol. 16, pp. 3421–3433, 2006.
  • Z. Liu, Y. Chen, “Global chaos synchronization of the brushless DC motor systems via variable substitution control”, International Workshop on Chaos-Fractals Theories and Applications, pp. 21–24, 2009.
  • J.J. Yan, M.L. Hung, J.S. Lin, T.L. Liao, “Controlling chaos of a chaotic nonlinear gyro using variable structure control”, Mechanical Systems and Signal Processing, Vol. 21, pp. 2515–2522, 2007.
  • X. Yu, “Variable structure control approach for controlling chaos”, Chaos, Solutions and Fractals, Vol. 8, pp. 1577–1586, 1997.
  • M. Chen, D. Zhou, Y. Shang, “Nonlinear feedback control of Lorenz system”, Chaos, Solutions and Fractals, Vol. 21, pp. 295–304, 2004.
  • R.A. Tang, Y.L. Liu, J.K. Xue, “An extended active control for chaos synchronization”, Physics Letters A, Vol. 373, pp. 1449–1454, 2009.
  • D.Q. Wei, X.S. Luo, B.H. Wang, J.Q. Fang, “Robust adaptive dynamic surface control of chaos in permanent magnet synchronous motor”, Physics Letters A, Vol. 363, pp. 71–77, 2007.
  • N. Hemati, “Strange attractors in brushless DC motors”, IEEE Transactions on Circuits and Systems I, Vol. 41, pp. 40–45, 1994.
  • Z.M. Ge, C.M. Chang, “Chaos synchronization and parameters identification of single time scale brushless DC motors”, Chaos, Solutions and Fractals, Vol. 20, pp. 883–903, 2004.
  • N. Hemati, “Dynamic analysis of brushless motors based on compact representations of motion”, Conference Record of the IEEE Industry Applications Society Annual Meeting, Vol. 1, pp. 51–58, 1993.
  • Z.M. Ge, C.M. Chang, Y.S. Chen, “Anti-control of chaos of single time-scale brushless DC motor”, Royal Society of London Transactions Series A, Vol. 364, pp. 2449–2462, 2006.
  • G. Ablay, “Sliding mode control of uncertain unified chaotic systems”, Nonlinear Analysis: Hybrid Systems, Vol. 3, pp. 531–53, 2009.
  • A.M. Harb, A.N. Natsheh, “On sliding-mode control of chaotic systems”, International Journal of Modelling and Simulation, Vol. 29, pp. 89–95, 2009.
  • M. Li, C.X. Liu, “Sliding mode control of a new chaotic system”, Chinese Physics B, Vol. 19, pp. 100504-1–100504-3, 20
  • D. Chen, W. Zhang, “Sliding mode control of uncertain neutral stochastic systems with multiple delays”, Mathematical Problems in Engineering, Vol. 2008, Article ID 761342, 2008.
  • M. Roopaei, B.R. Sahraei, T.C. Lin, “Adaptive sliding mode control in a novel class of chaotic systems”, Communications in Nonlinear Science and Numerical Simulation, Vol. 15, pp. 4158–4170, 2010.
  • G. Shahgholian, A. Rajabi, B. Karimi, “Analysis and design of PSS for multi-machine power system based on sliding mode control theory”, International Review of Electrical Engineering, Vol. 5, pp. 2241–2250, 2010.
  • H. Salarieh, A. Alasty, “Control of stochastic chaos using sliding mode method”, Journal of Computational and Applied Mathematics, Vol. 225, pp. 135–145, 2009.
  • ˙I. Eker, “Sliding mode control with PID sliding surface and experimental application to an electromechanical plant”, ISA Transactions, Vol. 45, pp. 109–118, 2006.
  • W. Perruquetti, J.P. Barbot, Sliding Mode Control in Engineering, New York, Marcel Dekker, 2002.
  • V.I. Utkin, Sliding Modes and Their Application in Variable Structure Systems, Moscow, Mir Editors, 1978.
Turkish Journal of Electrical Engineering and Computer Science-Cover
  • ISSN: 1300-0632
  • Yayın Aralığı: Yılda 6 Sayı
  • Yayıncı: TÜBİTAK