Skip to main content

Advertisement

SpringerLink
Log in

Finite-time sampled-data control of permanent magnet synchronous motor systems

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

Abstract

This paper investigates the problem of finite-time sampled-data control for permanent magnet synchronous motor system (PMSMS) with input time-varying delay. First, a novel state space equation of PMSMS is obtained by choosing suitable state variables to the system attribute of PMSMS model. Then, based on the obtained state space model, the problem of finite-time sampled-data control design is addressed for uncertain PMSMS. By implementing a proper novel Lyapunov–Krasovskii functional together with linear matrix inequality optimization technique and Wirtinger-based integral inequality approach, a new set of delay-dependent sufficient condition is derived which guarantees the robust finite-time stability of the closed-loop PMSMS. Based on the obtained condition, an explicit expression for the desired controller can be established in terms of matrix inequalities. Finally, the effectiveness of developed control technique is validated via simulation results.

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

Similar content being viewed by others

References

  1. Ai, Z., Zong, G.: Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems. Appl. Math. Comput. 245, 462–473 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, Q., Ren, X., Na, J.: Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors. ISA Trans. 58, 262–269 (2015)

    Article  Google Scholar 

  3. Deng, Z., Nian, X.: Robust control of permanent magnet synchronous motors. IEEE J. Autom. Sin. 2, 143–150 (2015)

  4. Ge, C., Zhang, W., Li, W., Sun, X.: Improved stability criteria for synchronization of chaotic Lur’e systems using sampled-data control. Neurocomputing 151, 215–222 (2015)

    Article  Google Scholar 

  5. Guo, H., Xu, J., Kuang, X.: A novel fault tolerant permanent magnet synchronous motor with improved optimal torque control for aerospace application. Chin. J. Aeronaut. 28, 535–544 (2015)

    Article  Google Scholar 

  6. Hao, X., Peng, B., Chen, Y., Xie, G.: Transient thermal model of a permanent magnet synchronous planar motor considering spreading thermal resistance. Appl. Therm. Eng. 81, 1–9 (2015)

    Article  Google Scholar 

  7. Kwon, O.M., Park, M.J., Park, Ju H., Lee, S.M., Cha, E.J.: Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality. J. Franklin Inst. 351, 5386–5398 (2014)

    Article  MathSciNet  Google Scholar 

  8. Li, S., Xia, C., Zhou, X.: Disturbance rejection control method for permanent magnet synchronous motor speed-regulation system. Mechatronics 22, 706–714 (2012)

    Article  Google Scholar 

  9. Li, H., Sun, X., Shi, P., Lam, H.K.: Control design of interval type-2 fuzzy systems with actuator fault: sampled-data control approach. Inf. Sci. 302, 1–13 (2015)

    Article  Google Scholar 

  10. Lee, T.S., Lin, C.H., Lin, F.J.: An adaptive \(H_\infty \) controller design for permanent magnet synchronous motor drives. Control Eng. Pract. 13, 425–439 (2005)

    Article  Google Scholar 

  11. Liu, Y., Hu, L.S., Shi, P.: A novel approach on stabilization for linear systems with time-varying input delay. Appl. Math. Comput. 218, 5937–5947 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, X., Han, Y.: Finite time control for MIMO nonlinear system based on higher-order sliding mode. ISA Trans. 53, 1838–1846 (2014)

    Article  Google Scholar 

  13. Li, X., Lin, X., Li, S., Zou, Y.: Finite-time stability of switched nonlinear systems with finite-time unstable subsystems. J. Franklin Inst. 352, 1192–1214 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, H.X., Li, S.H.: Speed control for PMSM servo system using predictive functional control and extended state observer. IEEE Trans. Ind. Electron. 59, 1171–1183 (2012)

    Article  Google Scholar 

  15. Moulay, E., Dambrine, M., Yeganefar, N., Perruquetti, W.: Finite-time stability and stabilization of time-delay systems. Syst. Control Lett. 57, 561–566 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Meng, Q., Shen, Y.: Finite-time \(H_\infty \) control for linear continuous system with norm-bounded disturbance. Commun. Nonlinear Sci. Numer. Simul. 14, 1043–1049 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Park, M.J., Kwon, O.M., Park, Ju H., Lee, S.M., Cha, E.J.: Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica 55, 204–208 (2015)

    Article  MathSciNet  Google Scholar 

  18. Ren, J.J., Liu, Y.C., Wang, N., Liu, S.Y.: Sensorless control of ship propulsion interior permanent magnet synchronous motor based on a new sliding mode observer. ISA Trans. 54, 15–26 (2015)

    Article  Google Scholar 

  19. Ren, H., Liu, D., Li, J.: Delay feedback control of chaos in permanent magnet synchronous motor. Proc. Chin. Soc. Elect. Eng. 23, 175–178 (2003)

    Google Scholar 

  20. Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49, 2860–2866 (2013)

    Article  MathSciNet  Google Scholar 

  21. Sakthivel, R., Selvaraj, P., Mathiyalagan, K., Park, Ju H.: Robust fault-tolerant \({\cal H}_\infty \) control for offshore steel jacket platforms via sampled-data approach. J. Franklin Inst. 352, 2259–2279 (2015)

    Article  MathSciNet  Google Scholar 

  22. Sakthivel, R., Selvi, S., Mathiyalagan, K.: Fault-tolerant sampled-data control of flexible spacecraft with probabilistic time delays. Nonlinear Dyn. 79, 1835–1846 (2015)

    Article  MATH  Google Scholar 

  23. Sakthivel, R., Arunkumar, A., Mathiyalagan, K.: Robust sampled-data \(H_\infty \) control for mechanical systems. Complexity 20, 19–29 (2014)

    Article  MathSciNet  Google Scholar 

  24. Stojanovic, S.B., Debeljkovic, D.L., Antic, D.S.: The application of different Lyapunov-like functionals and some aggregate norm approximations of the delayed states for finite-time stability analysis of linear discrete time-delay systems. J. Franklin Inst. 351, 3914–3931 (2014)

  25. Zhang, Y., Shi, P., Nguang, S.K., Zhang, J., Karimi, H.R.: Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps. Neurocomputing 140, 1–7 (2014)

    Article  Google Scholar 

  26. Liu, H., Zhou, G.: Finite-time sampled-data control for switching T–S fuzzy systems. Neurocomputing 166, 294–300 (2015)

    Article  Google Scholar 

  27. Lee, L., Liu, Y., Liang, J., Cai, X.: Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems. ISA Trans. 57, 172–178 (2015)

    Article  Google Scholar 

  28. Xu, Z.D., Shen, Y.P., Guo, Y.Q.: Semi-active control of structures incorporated with magnetorheological dampers using neural networks. Smart Mater. Struct. 12, 80–87 (2003)

    Article  Google Scholar 

  29. Xu, Z.D.: Fuzzy control method for earthquake mitigation structures with magnetorheological dampers. J. Intell. Mater. Syst. 17, 871–881 (2006)

    Article  Google Scholar 

  30. Yu, J., Shi, P., Yu, H., Chen, B., Lin, C.: Approximation-based discrete-time adaptive position tracking control for interior permanent magnet synchronous motors. IEEE Trans. Cybern. 45, 1363–1371 (2015)

    Article  Google Scholar 

  31. Yu, J., Shi, P., Dong, W., Chen, B., Lin, C.: Neural network-based adaptive dynamic surface control for permanent magnet synchronous motors. IEEE Trans. Neural Netw. Learn. Syst. 26, 640–645 (2015)

    Article  MathSciNet  Google Scholar 

  32. 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 

  33. Zhang, B., Pi, Y., Luo, Y.: Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor. ISA Trans. 51, 649–656 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sri Ramakrishna Institute of Technology, Coimbatore, 641010, India

    R. Sakthivel & B. Kaviarasan

  2. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    R. Sakthivel

  3. Department of Mathematics, Anna University Regional Campus, Coimbatore, 641046, India

    Srimanta Santra

  4. Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749, Republic of Korea

    Ju H. Park

Authors
  1. R. Sakthivel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Srimanta Santra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Kaviarasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ju H. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to R. Sakthivel or Ju H. Park.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sakthivel, R., Santra, S., Kaviarasan, B. et al. Finite-time sampled-data control of permanent magnet synchronous motor systems. Nonlinear Dyn 86, 2081–2092 (2016). https://doi.org/10.1007/s11071-016-3017-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-3017-5

Keywords

Search

Navigation