DOI QR코드

DOI QR Code

Sampled-data Fuzzy Tracking Control of Nonlinear Control Systems

비선형 제어 시스템의 샘플치 퍼지 추적 제어

  • Kim, Han Sol (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Park, Jin Bae (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Joo, Young Hoon (Department of Control and Robotics Engineering, Kunsan National University)
  • Received : 2016.12.01
  • Accepted : 2016.12.05
  • Published : 2017.01.01

Abstract

In this paper, we propose a method of designing the sampled-data tracking controller for nonlinear systems expressed by the Takagi-Sugeno (T-S) fuzzy model. A sufficient condition that asymptotically stabilizes the state error between the linear reference model and the T-S fuzzy model is derived in terms of linear matrix inequalities. To this end, error dynamics are constructed, and the exact discretization method and the Lyapunov stability theory are employed in this paper. Finally, we validate the proposed method through the simulation example.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. T. Chen, B. Francis, Optimal sampled-data control systems, Springer, London, 1995.
  2. X. L. Zhu, B. Chen, D. Yue, and Y. Wang, "An improved input delay approach to stabilization of fuzzy systems under variable sampling," IEEE Trans. Fuzzy Syst., vol. 20, no. 2, pp. 330-341, 2012. https://doi.org/10.1109/TFUZZ.2011.2174242
  3. G. B. Koo, J. B. Park, and Y. H. Joo, "LMI condition for sampled-data fuzzy control of nonlinear systems," Elec. Lett., vol. 51, no. 1, pp. 29-31, 2015. https://doi.org/10.1049/el.2014.3669
  4. D. W. Kim and H. J. Lee, "Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: Exact discrete-time design approach," Fuzzy Sets and Syst., vol. 201, pp. 20-39, 2012. https://doi.org/10.1016/j.fss.2011.12.017
  5. D.W. Kim, H.J. Lee, M. Tomizuka, "Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach," IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 251-260, 2010. https://doi.org/10.1109/TFUZZ.2010.2040184
  6. D. W. Kim, J. B. Park, and Y. H. Joo, "Effective digital implementation of fuzzy control systems based on approximate discrete-time models," Automatica, vol. 43, pp. 1671-1683, 2007. https://doi.org/10.1016/j.automatica.2007.01.025
  7. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Fuzzy Syst., vol. SMC-15, no. 1, pp. 116-132, 1985.
  8. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM, Pennsylvania, 1994.
  9. H. K. Lam and L. D. Seneviratne, "Tracking control of sampled-data fuzzy-model-based control systems," IET Cont. Theory Appl., vol. 3, no. 1, pp. 56-67, 2009. https://doi.org/10.1049/iet-cta:20070466
  10. G. B. Koo, J. B. Park, and Y. H. Joo, "Exponential mean-square stabilisation for non-linear systems: sampled-data fuzzy control approach," IET Cont. Theory Appl., vol. 18, no. 6, pp. 2765-2774, 2012.
  11. G. B. Koo, J. B. Park, Y. H. Joo, "Decentralized fuzzy observer-based output-feedback control for nonlinear large-scale systems: an LMI approach", IEEE Transactions on Fuzzy Systems 22 (2), 406-419, 2014, 2014 https://doi.org/10.1109/TFUZZ.2013.2259497
  12. D. H. Lee, J. B. Park, Y. H. Joo, K. C. Lin, C. H. Ham, "Robust $H{\infty}$ control for uncertain nonlinear active magnetic bearing systems via Takagi-Sugeno fuzzy models", International Journal of Control, Automation and Systems 8 (3), 636-646, 2010 https://doi.org/10.1007/s12555-010-0317-2