Skip to main content
Log in

RETRACTED ARTICLE: Hybrid recurrent Laguerre-orthogonal-polynomials neural network control with modified particle swarm optimization application for V-belt continuously variable transmission system

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

This article was retracted on 28 January 2021

This article has been updated

Abstract

A V-belt continuously variable transmission system driven by a permanent magnet synchronous motor has much unknown nonlinear and time-varying characteristics. In order to capture the system’s nonlinear and dynamic behavior, a hybrid recurrent Laguerre-orthogonal-polynomials neural network (NN) control system with modified particle swarm optimization (PSO) is proposed for achieving online better learning capacity and faster convergence to enhance system robustness. The hybrid recurrent Laguerre-orthogonal-polynomials NN control system can perform inspected control, recurrent Laguerre-orthogonal-polynomials NN control, which involves an adaptive law, and recouped control, which involves an estimated law. Moreover, the adaptive law of online parameters in the recurrent Laguerre-orthogonal-polynomials NN is derived by means of Lyapunov stability theorem. Furthermore, two optimal learning rates of the online parameters in the recurrent Laguerre-orthogonal-polynomials NN by means of modified PSO are applied to achieve online better learning capacity and faster convergence. Finally, to show the effectiveness of the proposed control scheme, comparative studies are demonstrated by experimental results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Change history

References

  1. Akbari R, Ziarati K (2011) A rank based particle swarm optimization algorithm with dynamic adaptation. J Comput Appl Math 235:2694–2714

    Article  MathSciNet  Google Scholar 

  2. Patra JC et al (2009) Laguerre neural network-based smart sensors for wireless sensor networks. In: Proceedings of the IEEE instrumentation and measurement technology conference, Singapore, pp 832–837

  3. Tseng CY et al (2009) Dynamic simulation model for hybrid electric scooters. In: IEEE international symposium on industrial electronics, Seoul, Korea, pp 1464–1469

  4. Lin CH et al (2010) Hybrid recurrent fuzzy neural network control for permanent magnet synchronous motor applied in electric scooter. In: 6th international power electronics conference, Sapporo, Japan, pp 1371–1376

  5. Angeline PJ (1998) Evolutionary optimization verses particle swarm optimization: philosophy and the performance difference. Lect Notes Comput Sci 1447:600–610

    Google Scholar 

  6. Astrom KJ, Hagglund T (1995) PID controller: theory, design, and tuning. Instrument Society of America, Research Triangle Park, NC, USA

  7. Astrom KJ, Wittenmark B (1995) Adaptive control. Addison-Wesley, New York

    MATH  Google Scholar 

  8. Brdys MA, Kulawski GJ (1999) Dynamic neural controllers for induction motor. IEEE Trans Neural Netw 10:340–355

    Article  Google Scholar 

  9. Carbone G et al (2005) The influence of pulley deformations on the shifting mechanisms of MVB-CVT. ASME J Mech Design 127:103–113

    Article  Google Scholar 

  10. Carbone G et al (2007) CVT dynamics: theory and experiments. Mech Mach Theory 42:409–428

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. del Valle Y et al (2008) Particle swarm optimization: basic concepts, variants and applications in power systems. IEEE Trans Evol Comput 12:171–195

    Article  Google Scholar 

  15. Eberhart RC, Shi Y (1998) Comparison between genetic algorithms and particle swarm optimization. In: Proceedings of the 7th international conference evolutionary programming VII, Diego, California, USA, pp 611–616

  16. Eberhart RC, Shi Y (2000) Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the congress on evolutionary computation, La Jolla, California, USA, pp 84–88

  17. Goldberg D (2002) The design of innovation: lessons from and for competent genetic algorithms. Kluwer, Norwell

    Book  Google Scholar 

  18. Grino R et al (2000) Nonlinear system identification using additive dynamic neural networks-two on-line approaches. IEEE Trans Circuits Syst I 47:150–165

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  22. He X et al (2013) Pulse neural network-based adaptive iterative learning control for uncertain robots. Neural Comput Appl 23:1885–1890

    Article  Google Scholar 

  23. Hsu CF (2013) Hermite-neural-network-based adaptive control for a coupled nonlinear chaotic system. Neural Comput Appl 24:421–433

    Article  Google Scholar 

  24. Ismail A et al (2014) An optimised product-unit neural network with a novel PSO–BP hybrid training algorithm: applications to load–deformation analysis of axially loaded piles. J Eng Appl Artif Intell 26:2305–2314

    Article  Google Scholar 

  25. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, Perth, WA, USA, pp 1942–1948

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

  27. Krishnan R (2001) Electric motor drives: modeling, analysis, and control. Prentice Hall, New Jersey

    Google Scholar 

  28. Li XD et al (2005) Approximation of dynamical time-variant systems by continuous-time recurrent neural networks. IEEE Trans Circuits Syst II 52:656–660

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  31. Lin CH (2014) A novel hybrid recurrent wavelet neural network control of PMSM servo-drive system for electric scooter. Turkish J Electr Eng Comput Sci 22:1056–1075

    Article  Google Scholar 

  32. Lin CH (2015) Novel adaptive recurrent Legendre neural network control for PMSM servo-drive electric scooter. ASME J Dyn Syst Meas Control 137(1). doi:10.1115/1.4027507

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

    Article  Google Scholar 

  34. Lin CM et al (2014) Intelligent control system design for UAV using a recurrent wavelet neural network. Neural Comput Appl 24:487–496

    Article  Google Scholar 

  35. Monjezi M et al (2013) Evaluation and prediction of blast-induced ground vibration at Shur River Dam, Iran, by artificial neural network. Neural Comput Appl 22:1637–1643

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Novotny DW, Lipo TA (1996) Vector control and dynamics of AC drives. Oxford University Press, New York

    Google Scholar 

  38. Pao YH (1989) Adaptive pattern recognition and neural networks. Addison-Wesley, Boston

    MATH  Google Scholar 

  39. Pao YH, Philips SM (1995) The functional link net and learning optimal control. Neurocomputing 9:149–164

    Article  Google Scholar 

  40. Patra JC et al (1999) Identification of nonlinear dynamic systems using functional link artificial neural networks. IEEE Trans Syst Man Cybern B 29:254–262

    Article  Google Scholar 

  41. Patra JC et al (2011) Development of Laguerre neural-network-based intelligent sensors for wireless sensor networks. IEEE Trans Instrum Meas 60:725–734

    Article  Google Scholar 

  42. Sastry PS et al (1994) Memory neural networks for identification and control of dynamical systems. IEEE Trans Neural Networks 5:306–319

    Article  Google Scholar 

  43. Sattler H, (1999) Efficiency of metal chain and V-belt CVT. In: Proceedings of the international conference on continuously variable power transmissions, Eindhoven, Netherlands, pp 99–104

  44. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE international conference on evolutionary computation, Anchorage, Alaska, USA, pp 69–73

  45. Slotine JJE, Li W (1991) Applied nonlinear control. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

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

    Article  Google Scholar 

  47. Sun TY et al (2011) Cluster guide particle swarm optimization (CGPSO) for underdetermined blind source separation with advanced conditions. IEEE Trans Evol Comput 15:798–811

    Article  Google Scholar 

  48. Tseng, CY et al (2008) A hybrid dynamic simulation model for urban scooters with a mechanical-type CVT. In: IEEE international conference on automation and logistics, Qingdao, China, pp 515–519

  49. Zhang Y et al (2011) A particle swarm optimization based on dynamic parameter modification. Appl Mech Mater 40–41:201–205

    Article  Google Scholar 

  50. Ziegler JG, Nichols NB (1942) Optimum settings for automatic controllers. Trans ASME 64:59–768

    Google Scholar 

  51. Zitzler E et al (2000) Comparison of multi objective evolutionary algorithms: empirical results. Evol Comput 8:173–195

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chih-Hong Lin.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, CH. RETRACTED ARTICLE: Hybrid recurrent Laguerre-orthogonal-polynomials neural network control with modified particle swarm optimization application for V-belt continuously variable transmission system. Neural Comput & Applic 28, 245–264 (2017). https://doi.org/10.1007/s00521-015-2053-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-2053-2

Keywords

Navigation