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Dynamic control of V-belt continuously variable transmission-driven electric scooter using hybrid modified recurrent legendre neural network control system

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Abstract

Because of unknown nonlinear and time-varying characteristics of V-belt continuously variable transmission (CVT)-driven electric scooter by using permanent magnet synchronous motor (PMSM) servo drive system, all gains tuning process for linear controller is a very time-consuming task. A hybrid modified recurrent Legendre neural network (NN) control system, which consists of an inspector control, a hybrid modified recurrent Legendre NN control and a recouped control with estimation law, is proposed for controlling the V-belt CVT-driven electric scooter under the occurrence of the nonlinear load disturbances and the variation of parameters to acquire better control performance. Moreover, the online parameters tuning method of the modified recurrent Legendre NN is based on Lyapunov stability theorem and gradient descent method. Furthermore, the two optimal learning rates of the hybrid modified recurrent Legendre NN control system are derived according to discrete Lyapunov function to enhance convergence speed. The proposed control scheme is capable of responding to system’s nonlinear and time-varying behaviors due to online learning ability. Finally, some experimental results are verified to show that the effectiveness of the proposed hybrid modified recurrent Legendre NN control system controlled the V-belt CVT-driven electric scooter by using PMSM servo drive system.

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References

  1. Novotny, D.W., Lipo, T.A.: Vector Control and Dynamics of AC Drives. Oxford University Press, New York (1996)

    Google Scholar 

  2. Krishnan, R.: Electric Motor Drives: Modeling, Analysis, and Control. Prentice Hall, New Jersey (2001)

    Google Scholar 

  3. Lin, F.J.: Real-time IP position controller design with torque feedforward control for PM synchronous motor. IEEE Trans. Ind. Electron. 4, 398–407 (1997)

    Google Scholar 

  4. Tseng, C.Y., Chen, L.W., Lin, Y.T., Li, J.Y.: A hybrid dynamic simulation model for urban scooters with a mechanical-type CVT. In: IEEE International Conference on Automation and Logistics, pp. 519–519, Qingdao, China (2008)

  5. Guzzella, L., Schmid, A.M.: Feedback linearization of spark-ignition engines with continuously variable transmissions. IEEE Trans. Control Syst. Technol. 3, 54–58 (1995)

    Article  Google Scholar 

  6. Kim, W., Vachtsevanos, G.: Fuzzy logic ratio control for a CVT hydraulic module. In: Proceedings of the IEEE Symposium on Intelligent Control, pp. 151–156, Rio, Greece (2000)

  7. Srivastava, N., Haque, I.: A review on belt and chain continuously variable transmissions (CVT): dynamics and control. Mech. Mach. Theory 44, 19–41 (2009)

    Article  MATH  Google Scholar 

  8. Ziegler, J.G., Nichols, N.B.: Optimum settings for automatic controllers. Trans. ASME 64, 759–768 (1942)

    Google Scholar 

  9. Astrom, K.J., Hagglund, T.: PID Controller: Theory, Design, and Tuning. Instrument Society of America Research Triangle Park, North Carolina (1995)

    Google Scholar 

  10. Hagglund, T., Astrom, K.J.: Revisiting the Ziegler–Nichols tuning rules for PI control. Asian J. Control 4, 364–380 (2002)

    Article  Google Scholar 

  11. Hagglund, T., Astrom, K.J.: Revisiting the Ziegler–Nichols tuning rules for PI control—part II: the frequency response method. Asian J. Control 6, 469–482 (2004)

    Article  Google Scholar 

  12. Wen, G.X., Liu, Y.J., Tong, S.C., Li, X.L.: Adaptive neural output feedback control of nonlinear discrete-time systems. Nonlinear Dyn. 65, 65–75 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Zou, A.M., Kumar, K.D.: Neural network-based adaptive output feedback formation control for multi-agent systems. Nonlinear Dyn. 70, 1283–1296 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  14. Sun, G., Wang, D., Li, T., Peng, Z., Wang, H.: Single neural network approximation based adaptive control for a class of uncertain strict-feedback nonlinear systems. Nonlinear Dyn. 72, 175–184 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wang, H., Chen, B., Lin, C.: Adaptive neural tracking control for a class of perturbed pure-feedback. Nonlinear Dyn. 72, 207–220 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lakshmanan, S., Park, J.H., Rakkiyappan, R., Jung, H.Y.: State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach. Nonlinear Dyn. 73, 509–520 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  17. Pao, Y.H.: Adaptive Pattern Recognition and Neural Networks. Addison-Wesley, Boston (1989)

    MATH  Google Scholar 

  18. Pao, Y.H., Philips, S.M.: The functional link net and learning optimal control. Neurocomputing 9, 149–164 (1995)

    Article  MATH  Google Scholar 

  19. Patra, J.C., Pal, R.N., Chatterji, B.N., Panda, G.: Identification of nonlinear dynamic systems using functional link artificial neural networks. IEEE Trans. Syst. Man Cybern. B 29, 254–262 (1999)

    Article  Google Scholar 

  20. Dehuri, S., Cho, S.B.: A comprehensive survey on functional link neural networks and an adaptive PSOBP learning for CFLNN. Neural Comput. Appl. 19, 187–205 (2010)

    Article  Google Scholar 

  21. Yang, S.S., Tseng, C.S.: An orthogonal neural network for function approximation. IEEE Trans. Syst. Man Cybern. B 26, 779–785 (1996)

    Article  Google Scholar 

  22. Patra, J.C., Chin, W.C., Meher, P.K., Chakraborty, G.: Legendre-FLANN-based nonlinear channel equalization in wireless communication systems. In: Proceedings of the IEEE International Conference on Systems. Man, Cybernetics, pp. 1826–1831 (2008)

  23. Patra, J.C., Meher, P.K., Chakraborty, G.: Nonlinear channel equalization for wireless communication systems using Legendre neural networks. Signal Process. 89, 2251–2262 (2009)

    Article  MATH  Google Scholar 

  24. Patra, J.C., Bornand, C.: Nonlinear dynamic system identification using Legendre neural network. In: Proceedings of the International Joint Conference on Neural Networks, pp. 1–7 (2010)

  25. Liu, F., Wang, J.: Fluctuation prediction of stock market index by Legendre neural network with random time strength function. Neurocomputing 83, 12–21 (2012)

    Article  Google Scholar 

  26. Das, K.K., Satapathy, J.K.: Novel algorithms based on Legendre neural network for nonlinear active noise control with nonlinear secondary path. Int. J. Comput. Sci. Inf. Technol. 3, 5036–5039 (2012)

    Google Scholar 

  27. Chow, T.W.S., Fang, Y.: A recurrent neural-network-based real-time learning control strategy applying to nonlinear systems with unknown dynamics. IEEE Trans. Ind. Electron. 45, 151–161 (1998)

    Article  MathSciNet  Google Scholar 

  28. Brdys, M.A., Kulawski, G.J.: Dynamic neural controllers for induction motor. IEEE Trans. Neural Netw. 10, 340–355 (1999)

    Article  Google Scholar 

  29. Li, X.D., Ho, J.K.L., Chow, T.W.S.: Approximation of dynamical time-variant systems by continuous-time recurrent neural networks. IEEE Trans. Circuits Syst. II 52, 656–660 (2005)

    MathSciNet  Google Scholar 

  30. Balasubramaniam, P., Lakshmanan, S., Jeeva Sathya Theesar, S.: State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60, 661–675 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  31. Li, N., Hu, J., Hu, J., Li, L.: Exponential state estimation for delayed recurrent neural networks with sampled-data. Nonlinear Dyn. 69, 555–564 (2012)

    Article  MATH  Google Scholar 

  32. Balasubramaniam, P., Vembarasan, V.: Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback. Nonlinear Dyn. 70, 667–691 (2012)

  33. Yoo, S.J., Park, J.B., Choi, Y.H.: Stable predictive control of Chaotic systems using self-recurrent wavelet neural network. Int. J. Autom. Control Syst. 3, 43–55 (2005)

    Google Scholar 

  34. Lu, C.H.: Design and application of stable predictive controller using recurrent wavelet neural networks. IEEE Trans. Ind. Electron. 56, 3733–3742 (2009)

    Article  Google Scholar 

  35. Lin, C.H.: Dynamic control for permanent magnet synchronous generator system using novel modified recurrent wavelet neural network. Nonlinear Dyn. 77, 1261–1284 (2014). doi:10.1007/s11071-014-1376-3

    Article  Google Scholar 

  36. Lin, C.H., Lin, C.P.: The hybrid RFNN control for a PMSM drive system using rotor flux estimator. Int. J. Power Electron. 4, 33–48 (2012)

    Article  Google Scholar 

  37. Lin, C.H. Chiang, P.H., Tseng, C.S., Lin, Y.L., Lee, M.Y.: Hybrid recurrent fuzzy neural network control for permanent magnet synchronous motor applied in electric scooter. In: 6th International Power Electronics Conference, pp. 1371–1376 (2010)

  38. Lin, C.H.: Hybrid recurrent wavelet neural network control of PMSM servo-drive system for electric scooter. Int. J. Autom. Control Syst. 12, 177–187 (2014)

    Article  Google Scholar 

  39. Lin, C.H., Lin, C.P.: Hybrid modified Elman NN controller design on permanent magnet synchronous motor driven electric scooter. Trans. Can. Soc. Mech. Eng. 37, 1127–1145 (2013)

    Google Scholar 

  40. Tseng, C.Y., Lue, Y.F., Lin, Y.T., Siao, J.C., Tsai, C.H., Fu, L.M.: Dynamic simulation model for hybrid electric scooters. In: IEEE International Symposium on Industrial Electronics, pp. 1464–1469 (2009)

  41. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  42. Astrom, K.J., Wittenmark, B.: Adaptive Control. Addison-Wesley, New York (1995)

    Google Scholar 

  43. Ku, C.C., Lee, K.Y.: Diagonal recurrent neural networks for dynamic system control. IEEE Trans. Neural Netw. 6, 144–156 (1995)

    Article  Google Scholar 

  44. Lin, C.H.: Recurrent modified Elman neural network control of PM synchronous generator system using wind turbine emulator of PM synchronous servo motor drive. Intl. J. Electr. Power Energy Syst. 52, 143–160 (2013)

    Article  Google Scholar 

  45. Lewis, F.L., Campos, J., Selmic, R.: Neuro-fuzzy control of industrial systems with actuator nonlinearities. SIAM Frontiers Appl. Math. 139–150 (2002). doi:10.1137/1.9780898717563

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Acknowledgments

The author would like to acknowledge the financial support of the Ministry of Science and Technology in Taiwan, R.O.C., through its Grant MOST 103-2221-E-239-016.

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Authors and Affiliations

  1. Department of Electrical Engineering, National United University, No. 1, Lienda, Kung-Jing Li, Miaoli, 36003, Taiwan

    Chih-Hong Lin

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  1. Chih-Hong Lin
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Correspondence to Chih-Hong Lin.

Additional information

1. The hybrid modified recurrent Legendre NN is designed to control speed of the PMSM.

2. A PMSM is designed to drive electric scooter with V-belt CVT.

3. Online tuning parameters of the modified recurrent Legendre NN with two optimal learning rates are developed.

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Lin, CH. Dynamic control of V-belt continuously variable transmission-driven electric scooter using hybrid modified recurrent legendre neural network control system. Nonlinear Dyn 79, 787–808 (2015). https://doi.org/10.1007/s11071-014-1703-8

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  • DOI: https://doi.org/10.1007/s11071-014-1703-8

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