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Composite recurrent Laguerre orthogonal polynomials neural network dynamic control for continuously variable transmission system using altered particle swarm optimization

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Abstract

The composite recurrent Laguerre orthogonal polynomials neural network (NN) control system using altered particle swarm optimization (PSO) is developed for controlling the V-belt continuously variable transmission (CVT) system driven by permanent magnet synchronous motor to obtain better control performance. The simplified dynamic and kinematic models of a V-belt CVT system are derived by law of conservation. The control system consists of an inspector control, a recurrent Laguerre orthogonal polynomials NN control with adaptation law, and a recouped control with estimation law. Moreover, the adaptation law of online parameters in the recurrent Laguerre orthogonal polynomials NN is originated from Lyapunov stability theorem. Additionally, two optimal learning rates of the parameters by means of altered PSO are posed in order to achieve better convergence. At last, comparative studies shown by experimental results are illustrated to demonstrate the control performance of the proposed control scheme.

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References

  1. 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)

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

  3. 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 

  4. 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)

  5. Carbone, G., Mangialardi, L., Bonsen, B., Tursi, C., Veenhuizen, P.A.: CVT dynamics: theory and experiments. Mech. Mach. Theory 42, 409–428 (2007)

    Article  Google Scholar 

  6. Carbone, G., Mangialardi, L., Mantriota, G.: The influence of pulley deformations on the shifting mechanisms of MVB-CVT. ASME J. Mech. Des. 127, 103–113 (2005)

    Article  Google Scholar 

  7. Srivastava, N., Haque, I.: Transient dynamics of metal V-belt CVT: effects of bandpack slip and friction characteristic. Mech. Mach. Theory 43, 457–479 (2008)

    Article  Google Scholar 

  8. 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  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  11. 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 

  12. Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical system using neural networks. IEEE Trans. Neural Netw. 1, 4–27 (1990)

    Article  Google Scholar 

  13. Sastry, P.S., Santharam, G., Unnikrishnan, K.P.: Memory neural networks for identification and control of dynamical systems. IEEE Trans. Neural Netw. 5, 306–319 (1994)

    Article  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  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  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  MathSciNet  Google Scholar 

  17. Ge, S.S., Hang, C.C., Zhang, T.: Adaptive neural network control of nonlinear systems by state and output feedback. IEEE Trans. Syst. Man. Cybern. 29, 818–828 (1999)

    Article  Google Scholar 

  18. Ge, S.S., Wang, J.: Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems. IEEE Trans. Neural Netw. 13, 1409–1419 (2002)

    Article  Google Scholar 

  19. Polycarpou, M.M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41, 447–451 (2002)

  20. Liu, Y.J., Chen, C.L., Wen, G.X., Tong, S.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 7, 1162–1167 (2011)

    Google Scholar 

  21. Liu, Y.J., Tang, L., Tong, S., Chen, C.L.: Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems. IEEE Trans. Neural Netw. Learn. Syst. (2015) doi:10.1109/TNNLS.2014.2330336

  22. Liu, Y.J., Tong, S.: Adaptive NN tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input. IEEE Trans. Syst. Man. Cybern. (2015). doi:10.1109/TCYB.2014.2329495

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

    Google Scholar 

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

    Article  Google Scholar 

  25. 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 

  26. Aadaleesan, P., Miglan, N., Sharma, R., Saha, P.: Nonlinear system identification using Wiener type Laguerre-wavelet network model. Chem. Eng. Sci. 63, 3932–3941 (2008)

  27. Mahmoodi, S.J., Poshtan, J., Jahed-Motlagh, M.R., Montazeri, A.: Nonlinear model predictive control of a pH neutralization process based on Wiener–Laguerre model. Chem. Eng. J. 146, 328–337 (2009)

    Article  Google Scholar 

  28. Zou, A., Xiao, X.: An asynchronous encryption arithmetic based on Laguerre Chaotic neural networks. In: IEEE WRI Global Congress on Intelligent Systems, pp. 36–39, Xiamen, China (2009)

  29. Patra, J.C., Bornand, C., Meher, P.K.: Laguerre neural network-based smart sensors for wireless sensor networks. In: IEEE Instrumentation and Measurement Technology Conference, pp. 832–837, Singapore (2009)

  30. Patra, J.C., Meher, P.K., Chakraborty, G.: Development of Laguerre neural-network-based intelligent sensors for wireless sensor networks. IEEE Trans. Instrum. Meas. 60, 725–734 (2011)

    Article  Google Scholar 

  31. 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 

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

    Article  Google Scholar 

  33. 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 

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

    Article  Google Scholar 

  35. 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)

    Article  MathSciNet  Google Scholar 

  36. Duan, L., Huang, L., Guo, Z.: Stability and almost periodicity for delayed high-order Hopfield neural networks with discontinuous activations. Nonlinear Dyn. 77, 1469–1484 (2014)

    Article  MathSciNet  Google Scholar 

  37. Duan, L., Huang, L.: Global dissipativity of mixed time-varying delayed neural networks with discontinuous activations. Commun. Nonlinear Sci. Numer. Simul. 19, 4122–4134 (2014)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  39. Lin, C.H.: A novel hybrid recurrent wavelet neural network control of PMSM servo-drive system for electric scooter. Turk. J. Electr. Eng. Comput. Sci. 22, 1056–1175 (2014)

    Article  Google Scholar 

  40. 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 

  41. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)

  42. Goldberg, D.: The Design of Innovation: Lessons from and for Competent Genetic Algorithms. Kluwer, Norwell (2002)

    Book  Google Scholar 

  43. Clerc, M., Kennedy, J.: The particle swarm-explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans. Evol. Comput. 6, 58–73 (2002)

    Article  Google Scholar 

  44. Carvalho, A.B., de Pozo, A., Vergilio, S.R.: A symbolic fault-prediction model based on multi objective particle swarm optimization. J. Syst. Softw. 83, 868–882 (2010)

    Article  Google Scholar 

  45. Li, Q., Chen, W., Wang, Y., Liu, S., Jia, J.: Parameter identification for PEM fuel-cell mechanism model based on effective informed adaptive particle swarm optimization. IEEE Trans. Ind. Electron. 58, 2410–2419 (2011)

    Article  Google Scholar 

  46. Cheng, C.T., Liao, S.L., Tang, Z.T., Zhao, M.Y.: Comparison of particle swarm optimization and dynamic programming for large scale hydro unit load dispatch. Energy Convers. Manag. 50(12), 3007–3014 (2009)

    Article  Google Scholar 

  47. Liao, Y.X., She, J.H., Wu, M.: Integrated hybrid-PSO and fuzzy-NN decoupling control for temperature of reheating furnace. IEEE Trans. Ind. Electron. 56, 2704–2714 (2009)

    Article  Google Scholar 

  48. Zitzler, E., Deb, K., Thiele, L.: Comparison of multi objective evolutionary algorithms: empirical results. Evol. Comput. 8, 173–195 (2000)

    Article  Google Scholar 

  49. Eberhart, R.C., Shi, Y.: Comparison between genetic algorithms and particle swarm optimization. Lect. Notes Comput. Sci. 1447, 611–616 (1998)

    Article  Google Scholar 

  50. Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the Congress on Evolutionary Computation, pp. 84–88, La Jolla, CA (2000)

  51. Gao, H., Xu, W.: A new particle swarm algorithm and its globally convergent modifications. IEEE Trans. Syst. Man Cybern. Part B Cybern. 41, 1334–1351 (2011)

    Article  Google Scholar 

  52. Sun, T.Y., Liu, C.C., Tsai, S.J., Hsieh, S.T., Li, K.Y.: Cluster guide particle swarm optimization (CGPSO) for underdetermined blind source separation with advanced conditions. IEEE Trans. Evol. Comput. 15, 798–811 (2011)

    Article  Google Scholar 

  53. Zhang, Y., Xiong, X., Zhang, Q.D.: An improved self-adaptive PSO algorithm with detection function for multimodal function optimization problems. Math. Probl. Eng. 2013 (2013), Article ID 716952

  54. Jothi Swaroopan, N.M., Somasundaram, P.: Fuzzified PSO algorithm for OPF with FACTS devices in interconnected power systems. Lect. Notes Comput. Sci. 6466, 468–480 (2010)

    Article  Google Scholar 

  55. 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)

  56. Lin, C.H., Lin, C.P.: The hybrid RFNN control for a PMSM drive system using rotor flux estimator. Int. J. Electr. Power Energy Syst. 51, 213–223 (2013)

    Article  Google Scholar 

  57. 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 

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

  59. Lin, C.H.: 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). doi:10.1007/s11071-014-1703-8

  60. Lin, C.H.: Novel adaptive recurrent Legendre neural network control for PMSM servo-drive electric scooter. AME-J. Dyn. Syst. Meas. Control 137 (2015)

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  64. 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 

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

    Google Scholar 

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

    Google Scholar 

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Acknowledgments

The author gratefully acknowledges financial support from Ministry of Science and Technology Grant MOST 103-2221-E-239-016 in Taiwan, R.O.C.

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Correspondence to Chih-Hong Lin.

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(1) The composite recurrent Laguerre orthogonal polynomials NN control system using altered PSO is designed to control a PM synchronous motor-driven V-belt CVT.

(2) Online tuning parameters of the recurrent Laguerre orthogonal polynomials NN-based Lyapunov stability theorem are developed.

(3) Two optimal learning rates of parameters in the recurrent Laguerre orthogonal polynomials NN using altered PSO are posed.

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Lin, CH. Composite recurrent Laguerre orthogonal polynomials neural network dynamic control for continuously variable transmission system using altered particle swarm optimization. Nonlinear Dyn 81, 1219–1245 (2015). https://doi.org/10.1007/s11071-015-2064-7

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