A Backstepping Control of LSM Drive Systems Using Adaptive Modified Recurrent Laguerre OPNNUO

  • Lin, Chih-Hong
  • Received : 2015.07.18
  • Accepted : 2015.11.05
  • Published : 2016.03.20


The good control performance of permanent magnet linear synchronous motor (LSM) drive systems is difficult to achieve using linear controllers because of uncertainty effects, such as fictitious forces. A backstepping control system using adaptive modified recurrent Laguerre orthogonal polynomial neural network uncertainty observer (OPNNUO) is proposed to increase the robustness of LSM drive systems. First, a field-oriented mechanism is applied to formulate a dynamic equation for an LSM drive system. Second, a backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. As the LSM drive system is prone to nonlinear and time-varying uncertainties, an adaptive modified recurrent Laguerre OPNNUO is proposed to estimate lumped uncertainties and thereby enhance the robustness of the LSM drive system. The on-line parameter training methodology of the modified recurrent Laguerre OPNN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre OPNN are derived to accelerate parameter convergence. Finally, the effectiveness of the proposed control system is verified by experimental results.


Backstepping control;Laguerre orthogonal polynomial neural network;Permanent magnet linear synchronous motor


  1. I. Boldea and S. A. Nasar, Linear Electric Actuators and Generators, London: Cambridge University Press, 1997.
  2. G. Bartolini, A. Ferrara, L. Giacomini, and E. Usai, “Peoperties of a combined adaptive/second-order sliding mode control algorithm for some classes of uncertain nonlinear systems,” IEEE Trans. Autom. Contr., Vol. 45, No. 7, pp. 1334-1341, Jul. 2000.
  3. T. Egami and T. Tsuchiya, “Disturbance suppression control with preview action of linear DC brushless motor,” IEEE Trans. Ind. Electron., Vol. 42, No. 5, pp. 494-500, Oct. 1995.
  4. M. Sanada, S. Morimoto, and Y. Takeda, “Interior permanent magnet linear synchronous motor for high-performance drives,” IEEE Trans. Ind. Appl., Vol. 33, No. 5, pp. 966-972, Jul./Aug. 1997.
  5. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controller for feedback linearizable system,” IEEE Trans. Autom. Contr., Vol. 36, No. 11, pp. 1241-1253, Nov. 1991.
  6. M. N. Eskander, “Minimization of losses in permanent magnet synchronous motors using neural network,” Journal of Power Electronics, Vol. 2, No. 3, pp 220-229, Jul. 2002.
  7. A. F. Payam, M. N. Hashemnia, and J. Faiz, “Robust DTC control of doubly-fed induction machines based on input-output feedback linearization using recurrent neural networks,” Journal of Power Electronics, Vol. 11, No. 5, pp. 719-725, Sep. 2011.
  8. C. H. Lin, “A PMSM driven electric scooter system with V-belt continuously variable transmission using novel hybrid modified recurrent Legendre neural network control,” Journal of Power Electronics, Vol. 14, No. 5, pp 220-229, Sep. 2014.
  9. C. H. Lin, "Novel adaptive recurrent Legendre neural network control for PMSM servo-drive electric scooter," J. Dynamic Systems, Measurement, and Control- Transactions of the ASME, Vol. 137 / 011010-1, 12 pages, 2015.
  10. J. C. Patra, P. K. Meher, and G. Chakraborty, “Development of Laguerre neural-network-based intelligent sensors for wireless sensor networks,” IEEE Trans. Instrum. Meas., Vol. 60, No. 3, pp. 725-734, Mar.2011.
  11. C. H. Lin, “Dynamic control of V-belt continuously variable transmission-driven electric scooter using hybrid modified recurrent Legendre neural network control system,” Nonlinear Dynamics, Vol. 79, No. 2, pp. 787-808, 2015.
  12. C. H. Lin, "Hybrid recurrent Laguerre-orthogonalpolynomial NN control system applied in V-belt continuously variable transmission system using particle swarm optimization," Mathematical Problems in Engineering, Vol. 2015, Article ID 106707, 17 pages, 2015.
  13. J. C. Patra, C. Bornand and P. K. Meher, "Laguerre neural network-based smart sensors for wireless sensor networks," IEEE Instrumentation and Measurement Technology Conference, pp. 832-837, 2009.
  14. J. J. E. Slotine and W. Li, Applied Nonlinear Control, Englewood Cliffs, NJ: Prentice-Hall, 1991.
  15. J. Astrom and B. Wittenmark, Adaptive Control, New York: Addison-Wesley, 1995.
  16. C. C. Ku and K. Y. Lee, “Diagonal recurrent neural networks for dynamic system control,” IEEE Trans. Neural Netw., Vol. 6, No. 1, pp.144-156, Jan. 1995.
  17. C. H. Lin, “Recurrent modified Elman neural network control of PM synchronous generator system using wind turbine emulator of PM synchronous servo motor drive,” Intl. J. Electrical Power and Energy Systems, Vol. 52, pp. 143-160, Nov. 2013.
  18. F. L. Lewis, J. Campos and R. Selmic, Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities. SIAM Frontiers in Applied Mathematics, 2002.
  19. T. Hagglund and K. J. Astrom, “Revisiting the Ziegler-Nichols tuning rules for PI control – Part II: The frequency response method,” Asian J. Control, Vol. 6, No. 4, pp. 469-482, Dec. 2004.
  20. F. J. Lin and C. H. Lin, “On-line gain-tuning IP controller using RFNN,” IEEE Trans. Aerosp. Electron. Syst., Vol. 37, No. 2, pp. 655-670, Apr. 2001.
  21. K. J. Astrom and T. Hagglund, PID Controller: Theory, Design, and Tuning, North Carolina: Instrument Society of America, Research Triangle Park, 1995
  22. T. Hagglund and K. J. Astrom, “Revisiting the Ziegler-Nichols tuning rules for PI control,” Asian J. Control, Vol. 4, No. 4, pp. 364-380, Dec. 2002.

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