Skip to main content
SpringerLink
Log in

Chaos RBF dynamics surface control of brushless DC motor with time delay based on tangent barrier Lyapunov function

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Non-dimensional mathematical model of brushless DC motor (BLDCM) system is presented here. BLDCM is known to produce chaotic phenomenon under certain conditions. This paper fuses dynamic surface control, radial basis function neural network, and adaptive technology to control the BLDCM, which overcomes the repetitive differentiation of the nonlinear terms of backstepping and the boundedness hypothesis of control gain pre-determined. The tangent barrier Lyapunov function is also used for time-delay nonlinear system with parametric uncertainties. Simulation results under different conditions indicate that the proposed method works well to suppress chaos and effects of parameter variation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Ditto, W.L., Spano, M.L., Savage, H.T., Rauseo, S.N., Heagy, J., Ott, E.: Experimental observation of a strange nonchaotic attractor. Phys. Rev. Lett. 65, 533–536 (1990)

    Article  Google Scholar 

  2. Wang, Z., Chau, K.T.: Anti-control of chaos of a permanent magnet DC motor system for vibratory compactors. Chaos Solitons Fractals 36, 694–708 (2008)

    Article  Google Scholar 

  3. Li, D., Wang, S.L., Zhang, X.H., Yang, D.: Fuzzy impulsive control of chaos in permanent magnet synchronous motors with parameter uncertainties. Acta Phys. Sin. 58, 1432–1440 (2009)

    MathSciNet  Google Scholar 

  4. Hernandez-Guzman, V.M., Santibanez, V., Zavala-Rio, A.: A saturated PD controller for robots equipped with brushless DC-motors. Robotica 28, 405–411 (2010)

    Article  Google Scholar 

  5. Huang, X.Y., Goodman, A., Gerada, C., Fang, Y.T., Lu, Q.F.: Design of a five-phase brushless DC motor for a safety critical aerospace application. IEEE Trans. Ind. Electron. 59, 3532–3541 (2012)

    Article  Google Scholar 

  6. Feng, Y., Yu, X.H., Man, Z.H.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38, 2159–2167 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Estrada, A., Fridman, L.: Quasi-continuous HOSM control for systems with unmatched perturbations. Automatica 46, 1916–1919 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Alasty, A., Salarieh, H.: Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers. Chaos Solitons Fractals 26, 379–392 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Paula, A.S.D., Savi, M.A.: A multi-parameter chaos control method based on OGY approach. Chaos Solitons Fractals 40, 1376–1390 (2009)

    Article  MATH  Google Scholar 

  10. Zhang, C.M., Liu, H.P., Chen, S.J., Wang, F.J.: Application of neural network for permanent magnet synchronous motor direct torque control. J. Syst. Eng. Electron. 19, 555–561 (2008)

    Article  Google Scholar 

  11. Elmas, C., Ustun, O., Sayan, H.H.: A neuro-fuzzy controller for speed control of a permanent magnet synchronous motor drive. Expert Syst. Appl. 34, 657–664 (2008)

    Article  Google Scholar 

  12. Ge, Z.M., Cheng, J.W., Chen, Y.S.: Chaos anticontrol and synchronization of three time scales brushless DC motor system. Chaos Solitons Fractals 22, 1165–1182 (2004)

    Article  MATH  Google Scholar 

  13. Ge, Z.M., Chang, C.M., Chen, Y.S.: Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems. Chaos Solitons Fractals 27, 1298–1315 (2006)

  14. Ngo, K.B., Mahony, R., Jiang, Z.P.: Integrator backstepping using barrier functions for systems with multiple state constraints. In: Proc 44th IEEE Conf. on Decision and Control, and the European Control Conf., 8306–8312 (2005)

  15. Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45, 918–927 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Luo, X., Wu, X., Guan, X.: Adaptive backstepping control for unmatched nonlinear system against actuator dead-zone fault. IET Control Theory Appl. 4, 879–888 (2010)

    Article  MathSciNet  Google Scholar 

  17. Wu, X.L., Wu, X.J., Luo, X.Y., Zhu, Q.M., Guan, X.P.: Neural network-based adaptive tracking control for nonlinearly parameterized systems with unknown input nonlinearities. Neurocomputing 82, 127–142 (2012)

    Article  Google Scholar 

  18. Wei, D.Q., Luo, X.S., Wang, B.H., Fang, J.Q.: Robust adaptive dynamic surface control of chaos in permanent magnet synchronous motor. Phys. Lett. A 363, 71–77 (2007)

    Article  Google Scholar 

  19. Zhang, X.Y., Lin, Y.: A robust adaptive dynamic surface control for nonlinear systems with hysteresis input. Acta Autom. Sin. 36, 1264–1271 (2010)

    Google Scholar 

  20. Ma, H., Deshmukh, V., Butcher, E., Averina, V.: Delayed state feedback and chaos control for time-periodic systems via a symbolic approach. Commun. Nonlinear Sci. Numer. Simul. 10, 479–497 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wu, X.J., Wu, X.L., Luo, X.Y., Guan, X.P.: Dynamic surface control for a class of state-constrained non-linear systems with uncertain time delays. IET Control Theory Appl. 6, 1948–1957 (2012)

    Article  MathSciNet  Google Scholar 

  22. Li, Y.M., Ren, C.E., Tong, S.C.: Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer. Nonlinear Dyn. 67, 1175–1191 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Li, Y., Tong, S.C., Li, Y.M.: Observer-based adaptive fuzzy backstepping dynamic surface control design and stability analysis for MIMO stochastic nonlinear systems. Nonlinear Dyn. 69, 1333–1349 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ge, Z.M., Cheng, J.W.: Chaos synchronization and parameter identification of three time scales brushless DC motor system. Chaos Solitons Fractals 24, 597–616 (2005)

    Article  MATH  Google Scholar 

  25. Michael Steele, J.: The Cauchy–Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities, Chapter 1. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51375506), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100191110008), China Postdoctoral Science Foundation funded project (Grant No. 2013M542258) and the Par-Eu Scholars Program Special Foundation of Chongqing.

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing,  400044, China

    Shaohua Luo, Jiaxu Wang, Songli Wu & Ke Xiao

  2. College of Mechanical Engineering, Hunan University of Arts and Science, Hunan,  415000, China

    Shaohua Luo & Songli Wu

Authors
  1. Shaohua Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiaxu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Songli Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ke Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaohua Luo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, S., Wang, J., Wu, S. et al. Chaos RBF dynamics surface control of brushless DC motor with time delay based on tangent barrier Lyapunov function. Nonlinear Dyn 78, 1193–1204 (2014). https://doi.org/10.1007/s11071-014-1507-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1507-x

Keywords

Search

Navigation