Intelligent Sliding-Mode Position Control Using Recurrent Wavelet Fuzzy Neural Network for Electrical Power Steering System

Abstract

A digital signal processor (DSP)-based intelligent sliding-mode control (SMC) is proposed for the position control of a six-phase permanent magnet synchronous motor (PMSM) drive system installed in an electric power steering (EPS) system in this study. First, the dynamic mathematical model of the EPS system is derived by the Lagrangian dynamics. Since the EPS system is a nonlinear and time-varying system, the control accuracy is very sensitive to the parameter variations and external disturbances. Therefore, a SMC is developed for the position control of the EPS system. However, the upper bound of the uncertainties is difficult to obtain in advance and the choice of switching control gain in SMC is vital but time-consuming and may cause undesired chattering phenomenon. Hence, an intelligent SMC with a novel recurrent wavelet fuzzy neural network (ISMC-RWFNN) is proposed, in which a recurrent wavelet fuzzy neural network (RWFNN) is adopted as an uncertainty estimator to overcome the aforementioned disadvantage of SMC. Moreover, a robust compensator is employed to reduce the estimation error. In addition, the adaptive learning algorithms for the online training of the RWFNN are derived using the Lyapunov theorem and Taylor series. Finally, the proposed ISMC-RWFNN to control the position of a six-phase PMSM drive system for the EPS system is implemented in a 32-bit floating-point DSP, and some experimental results are provided to verify its effectiveness.

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References

  1. 1.

    Cetin, E., Adli, M.A., Barkana, D.E., Kucuk, H.: Implementation and development of an adaptive steering-control system. IEEE Trans. Veh. Technol. 59(1), 75–83 (2010)

    Article  Google Scholar 

  2. 2.

    Chen, X., Yang, T., Chen, X., Zhou, K.: A generic model-based advanced control of electric power-assisted steering systems. IEEE Trans. Control Syst. Technol. 16(6), 1289–1300 (2008)

    Article  Google Scholar 

  3. 3.

    Marouf, A., Djemaï, M., Sentouh, C., Pudlo, P.: A new control strategy of an electric-power-assisted steering system. IEEE Trans. Veh. Technol. 61(8), 3574–3589 (2012)

    Article  Google Scholar 

  4. 4.

    Parmar, M., Hung, J.Y.: A sensorless optimal control system for an automotive electric power assist steering system. IEEE Trans. Ind. Electron. 51(2), 290–298 (2004)

    Article  Google Scholar 

  5. 5.

    Lin, F.J., Hung, Y.C., Ruan, K.C.: An intelligent second-order sliding-mode control for an electric power steering system using a wavelet fuzzy neural network. IEEE Trans. Fuzzy Syst. 22(6), 1598–1611 (2014)

    Article  Google Scholar 

  6. 6.

    Hung, Y.C., Lin, F.J., Hung, J.C., Chang, J.K., Ruan, K.C.: Wavelet fuzzy neural network with asymmetric membership function controller for electric power steering system via improved differential evolution. IEEE Trans. Power Electron. 30(4), 2350–2362 (2015)

    Article  Google Scholar 

  7. 7.

    Kim, W., Son, Y.S., Chung, C.C.: Torque-overlay-based robust steering wheel angle control of electrical power steering for a lane-keeping system of automated vehicles. IEEE Trans. Veh. Technol. 65(6), 4379–4392 (2016)

    Article  Google Scholar 

  8. 8.

    Lee, D., Kim, K.S., Kim, S.: Controller design of an electric power steering system. IEEE Trans. Control Syst. Technol. PP(99), 1–8 (2017)

    Google Scholar 

  9. 9.

    Nam, K., Fujimoto, H., Hori, Y.: Lateral stability control of in-wheel-motor-driven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Trans. Veh. Technol. 61(5), 1972–1985 (2012)

    Article  Google Scholar 

  10. 10.

    Utkin, V.I.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control 22(2), 212–222 (1977)

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

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

    Google Scholar 

  12. 12.

    Mercorelli, P.: A two-stage sliding-mode high-gain observer to reduce uncertainties and disturbances effects for sensorless control in automotive applications. IEEE Trans. Ind. Electron. 62(9), 5929–5940 (2015)

    Article  Google Scholar 

  13. 13.

    Wai, R.J., Shih, L.C.: Design of voltage tracking control for DC–DC boost converter via total sliding-mode technique. IEEE Trans. Ind. Electron. 58(6), 2502–2511 (2011)

    Article  Google Scholar 

  14. 14.

    Lin, F.J., Hung, Y.C., Tsai, M.T.: Fault tolerant control for six-phase PMSM drive system via intelligent complementary sliding mode control using TSKFNN-AMF. IEEE Trans. Ind. Electron. 60(12), 5747–5762 (2013)

    Article  Google Scholar 

  15. 15.

    Ko, C.N.: Identification of chaotic system using fuzzy neural networks with time-varying learning algorithm. Int. J. Fuzzy Syst. 14(4), 540–548 (2012)

    Google Scholar 

  16. 16.

    Er, M.J., Liu, F., Li, M.B.: Self-constructing fuzzy neural networks with extended Kalman filter. Int. J. Fuzzy Syst. 12(1), 66–72 (2010)

    Google Scholar 

  17. 17.

    Sahoo, A., Xu, H., Jagannathan, S.: Adaptive neural network-based event-triggered control of single-input single-output nonlinear discrete-time systems. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 151–164 (2016)

    MathSciNet  Article  Google Scholar 

  18. 18.

    Wang, W.Y., Li, I.H., Li, S.C., Tsai, M.S., Su, S.F.: A dynamic hierarchical fuzzy neural network for a general continuous function. Int. J. Fuzzy Syst. 11(2), 130–136 (2009)

    Google Scholar 

  19. 19.

    Chen, S.Y., Hung, Y.H., Gong, S.S.: Speed control of vane-type air motor servo system using proportional integral derivative based fuzzy neural network. Int. J. Fuzzy Syst. 18(6), 553–564 (2016)

    MathSciNet  Google Scholar 

  20. 20.

    Wai, R.J.: Hybrid fuzzy neural-network control for nonlinear motor-toggle servomechanism. IEEE Trans. Control Syst. Technol. 10(4), 519–532 (2002)

    Article  Google Scholar 

  21. 21.

    Li, Y., Wei, H.L., Billings, S.A.: Identification of time-varying systems using multi-wavelet basis functions. IEEE Trans. Control Syst. Technol. 19(3), 656–663 (2011)

    Article  Google Scholar 

  22. 22.

    Catalão, J.P.S., Pousinho, H.M.I., Mendes, V.M.F.: Hybrid wavelet-PSO-ANFIS approach for short-term electricity prices forecasting. IEEE Trans. Power Syst. 26(1), 137–144 (2011)

    Article  Google Scholar 

  23. 23.

    Lu, C.H.: Wavelet fuzzy neural networks for identification and predictive control of dynamic systems. IEEE Trans. Ind. Electron. 58(7), 3046–3058 (2011)

    Article  Google Scholar 

  24. 24.

    Shahriari-kahkeshi, M., Sheikholeslam, F.: Adaptive fuzzy wavelet network for robust fault detection and diagnosis in non-linear systems. IET Control Theory Appl. 8(15), 1487–1498 (2014)

    Article  Google Scholar 

  25. 25.

    Park, S.H., Han, S.I.: Robust-tracking control for robot manipulator with deadzone and friction using backstepping and RFNN controller. IET Control Theory Appl. 5(12), 1397–1417 (2011)

    MathSciNet  Article  Google Scholar 

  26. 26.

    Lin, F.J., Sun, I.F., Yang, K.J., Chang, J.K.: Recurrent fuzzy neural cerebellar model articulation network fault-tolerant control of six-phase permanent magnet synchronous motor position servo drive. IEEE Trans. Fuzzy Syst. 24(1), 153–167 (2016)

    Article  Google Scholar 

  27. 27.

    Lin, Y.Y., Chang, J.Y., Lin, C.T.: Identification and prediction of dynamic systems using an interactively recurrent self-evolving fuzzy neural network. IEEE Trans. Neural Netw. Learn. Syst. 24(2), 310–321 (2013)

    Article  Google Scholar 

  28. 28.

    Mai, T., Wang, Y.: Adaptive force/motion control system based on recurrent fuzzy wavelet CMAC neural networks for condenser cleaning crawler-type mobile manipulator robot. IEEE Trans. Control Syst. Technol. 22(5), 1973–1982 (2014)

    Article  Google Scholar 

  29. 29.

    Ganjefar, S., Tofighi, M.: Single-hidden-layer fuzzy recurrent wavelet neural network: applications to function approximation and system identification. Inf. Sci. 294, 269–285 (2015)

    MathSciNet  Article  MATH  Google Scholar 

  30. 30.

    Lin, F.J., Chen, S.Y., Shyu, K.K.: Robust dynamic sliding-mode control using adaptive RENN for magnetic levitation system. IEEE Trans. Neural Netw. 20(6), 938–951 (2009)

    Article  Google Scholar 

  31. 31.

    Chen, S.Y., Lin, F.J.: Robust nonsingular terminal sliding-mode control for nonlinear magnetic bearing system. IEEE Trans. Control Syst. Technol. 19(3), 636–643 (2011)

    Article  Google Scholar 

  32. 32.

    El-Sousy, F.F.M.: Adaptive dynamic sliding-mode control system using recurrent RBFN for high-performance induction motor servo drive. IEEE Trans. Ind. Inf. 9(4), 1922–1936 (2013)

    Article  Google Scholar 

  33. 33.

    Lin, F.J., Chou, P.H.: Robust Fuzzy-neural-network sliding-mode control for two-axis motion control system. IEEE Trans. Ind. Electron. 53(4), 1209–1225 (2006)

    Article  Google Scholar 

  34. 34.

    Wang, L.X.: A course in Fuzzy Systems and Control. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

  35. 35.

    Lin, F.J., Lee, C.C.: Adaptive backstepping control for linear induction motor drive to track periodic references. IEE Proc. Electr. Power Appl. 147(6), 449–458 (2000)

    Article  Google Scholar 

  36. 36.

    Lin, F.J., Chang, C.K., Huang, P.K.: FPGA-based adaptive backstepping sliding-mode control for linear induction motor drive. IEEE Trans. Power Electron. 22(4), 1222–1231 (2007)

    Article  Google Scholar 

  37. 37.

    Lin, F.J., Wai, R.J.: Hybrid control using recurrent fuzzy neural network for linear induction motor servo drive. IEEE Trans. Fuzzy Syst. 9(1), 102–115 (2001)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the financial supports of Ministry of Science and Technology of Taiwan through its Grant No. MOST 104-2221-E-008-040-MY3.

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Correspondence to Faa-Jeng Lin.

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Lin, FJ., Chen, SG. & Sun, IF. Intelligent Sliding-Mode Position Control Using Recurrent Wavelet Fuzzy Neural Network for Electrical Power Steering System. Int. J. Fuzzy Syst. 19, 1344–1361 (2017). https://doi.org/10.1007/s40815-017-0342-x

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Keywords

  • Sliding-mode control
  • Six-phase permanent synchronous motor
  • Electric power steering system
  • Recurrent wavelet fuzzy neural network
  • Taylor series expansion