Skip to main content

Advertisement

SpringerLink
Log in

Robust fuzzy control and evolutionary fuzzy identification of singularly perturbed nonlinear systems with parameter uncertainty

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

This paper presents an H ∞ robust fuzzy control strategy which stabilizes singularly perturbed (SP) nonlinear systems with bounded uncertainties and guarantees disturbance attenuation bounds for all admissible uncertainties. The modified Takagi–Sugeno (T–S) fuzzy linear models are used to describe the SP nonlinear systems. By the proposed fuzzy control strategy, the number and type of membership functions in the fuzzy control rules are not necessarily the same as those in the fuzzy models. A sufficient condition for the existence of the H ∞ robust fuzzy controllers is then presented in terms of a novel linear matrix inequalities (LMIs) form which takes full consideration of modeling error and uncertainties in system parameters. This condition provides extra design parameters with more flexibility in control gain selection. Furthermore, we propose a compound search strategy composed of island genetic algorithms concatenated with the simplex method to identify the uncertain SP nonlinear systems for the fuzzy control design, and to solve the LMI problem. Finally, design example of the proposed H ∞ robust fuzzy controller for an uncertain SP nonlinear system is presented.

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

Similar content being viewed by others

References

  1. Tseng CS and Chen BS (2001). H ∞ decentralized fuzzy model reference tracking control design for nonlinear interconnected systems. IEEE Trans Fuzzy Syst 9: 795–809

    Article  Google Scholar 

  2. Assawinchaichote W and Nguang SK (2006). Fuzzy H ∞ output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach. IEEE Trans Fuzzy Syst 14: 361–371

    Article  Google Scholar 

  3. Lee KR, Jeung ET and Park HB (2001). Robust fuzzy H ∞ control for uncertain nonlinear systems via state feedback: an LMI approach. Fuzzy Sets Syst 120: 123–134

    Article  MATH  MathSciNet  Google Scholar 

  4. Tanaka K, Ikeda T and Wang HO (1998). Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans Fuzzy Syst 6: 250–265

    Article  Google Scholar 

  5. Li TS and Lin KJ (2004). Stabilization of singularly perturbed fuzzy systems. IEEE Trans Fuzzy Syst 12: 579–595

    Article  Google Scholar 

  6. Assawinchaichote W and Nguang SK (2004). H ∞ filtering for fuzzy singularly perturbed systems with pole placement constraints: an LMI approach. IEEE Trans. Signal Process Speech Signal Process 52: 1659–1667

    MathSciNet  Google Scholar 

  7. Malki HA, Misir D, Feigenspan D and Guanrong C (1997). Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Trans Control Syst Technol 5: 371–378

    Article  Google Scholar 

  8. Chang YZ and Daniel RW (1992). On the adaptive control of flexible joint robots. Automatica 28: 969–974

    Article  MATH  MathSciNet  Google Scholar 

  9. Thompson MT (2000). Electrodynamic magnetic suspension-models, scaling laws and experimental results. IEEE Trans Educ 43: 336–341

    Article  Google Scholar 

  10. Shao ZH (2004). Robust stability of two-time-scale systems with nonlinear uncertainties. IEEE Trans Autom Control 49: 258–261

    Article  Google Scholar 

  11. Kokotovic PV, Khalil HK and O’Reilly J (1986). Singularly perturbation methods in control: analysis and design. Academic, New York

    Google Scholar 

  12. Liu H, Sun F and Sun Z (2005). Stability analysis and synthesis of fuzzy singularly perturbed systems. IEEE Trans Fuzzy Syst 13: 273–284

    Article  Google Scholar 

  13. Tong S and Li HH (2002). Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets Syst 131: 165–184

    Article  MATH  MathSciNet  Google Scholar 

  14. Chang YZ, Chang J and Huang CK (1999). Parallel genetic algorithms for a neurocontrol problem. Int Joint Conf Neural Netw 6: 4151–4155

    Google Scholar 

  15. Nelder JA and Mead R (1965). A simplex method for function minimization. Comput J 7: 308–313

    Google Scholar 

  16. Chen BS, Tseng CS and Uang HJ (1999). Robustness design of nonlinear dynamic systems via fuzzy linear control. IEEE Trans Fuzzy Syst 7: 571–585

    Article  Google Scholar 

  17. LaSalle JP (1960). Some extensions of Lyapunov’s second method. IRE Trans Circuit Theory 7: 520–527

    MathSciNet  Google Scholar 

  18. Gahinet P, Nemirovski A, Laub A and Chilali M (1995). LMI Control Toolbox. The Math Works, Natick

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, 33302, Taiwan

    Yau-Zen Chang

  2. Department of Electrical Engineering, Chang Gung University, Tao-Yuan, 33302, Taiwan

    Zhi-Ren Tsai & Jye Lee

  3. Department of Electronic Engineering, Jinwen University of Science and Technology, Taipei, 23154, Taiwan

    Jiing-Dong Hwang

Authors
  1. Yau-Zen Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Ren Tsai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiing-Dong Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jye Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiing-Dong Hwang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, YZ., Tsai, ZR., Hwang, JD. et al. Robust fuzzy control and evolutionary fuzzy identification of singularly perturbed nonlinear systems with parameter uncertainty. Electr Eng 90, 379–393 (2008). https://doi.org/10.1007/s00202-007-0085-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-007-0085-z

Keywords

Search

Navigation