JACIII Vol.19 No.3 pp. 439-446
doi: 10.20965/jaciii.2015.p0439


Polynomial Controller Design Using Disturbance Observer

Hugang Han* and Hak-Keung Lam**

*Prefectural University of Hiroshima
1-1-71 Ujina-Higashi, Minami-ku, Hiroshima 734-8558, Japan
**King’s College London
WC2R 2LS London, United Kingdom

August 4, 2014
March 3, 2015
Online released:
May 20, 2015
May 20, 2015
polynomial fuzzy model, disturbance observer, asymptotically stable, lumpted disturbane, stability analysis

Disturbance observer-based control provides a promising approach to handle system disturbance and improve robustness. In this paper, a new fuzzy disturbance observer (FDO) is proposed into the SOS-based approach, where the polynomial fuzzy model is used to develop the system controller. Compared with other works published so far, the FDO mainly features two things: 1) the estimation error between the FDO and disturbance shrinks asymptotically to zero if the disturbance has a constant steady-state value; 2) parameters involved in the FDO is adjusted on the basis of the polynomial fuzzy model which is basically nonlinear. Finally, computer simulations are provided to illustrate the effectiveness of the proposed approach.

  1. [1]  T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst., Man, Cybern., Vol.15, pp. 116-132, 1985.
  2. [2]  K. Tanaka and H. O. Wang, “Fuzzy Control System Design and Analysis – A Linear Matrix Inequality Approach,” Wiley, New York, 2001.
  3. [3]  K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, “A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems,” IEEE Trans. Fuzzy Syst., Vol.17, No.4, pp. 911-922, 2009.
  4. [4]  S. Prajna, A. Papachristodoulou, and P. A. Parrilo, “Introducing SOSTOOLS: A general purpose sum of squares programming solver,” in Proc. 41st IEEE Conf. Decision Control, 2002.
  5. [5]  B. Yao, M. A. Majed, and M. Tomizuka, “High-performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments,” IEEE/ASME Trans. Mechatronics, Vol.2, No.2, pp. 63-76, 1997.
  6. [6]  W.-H. Chen, “Disturbance observer based control for nonlinear systems,” IEEE/ASME Trans. Mechatronics, Vol.9, No.4, pp. 706-710, 2004.
  7. [7]  J. Yang, W.-H. Chen, and S. Li, “Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties,” IET Control Theory Appl., Vol.5, Iss.18, pp. 2053-2062, 2011.
  8. [8]  E. Kim, “A fuzzy disturbance observer and its application to control,” IEEE Trans. Fuzzy Syst., Vol.10, No.1, pp. 77-84, 2002.
  9. [9]  E. Kim and S. Lee, “Output feedback tracking control of MIMO systems using a fuzzy disturbance observer and its application to the speed control of a PM synchronous motor,” IEEE Trans. Fuzzy Syst., Vol.13, No.6, pp. 725-741, 2005.
  10. [10]  H. Han, “Adaptive fuzzy controller for a class of uncertain nonlinear systems,” J. of Japan Society for Fuzzy Theory and Intelligence Informatics, Vol.21, No.4, pp. 577-586, 2009.
  11. [11]  H. Han and T. Koshiro, “Adaptive T-S fuzzy controller using fuzzy approximators,” Proc. of 2010 IEEE World Congress on Computational Intelligence, Barcelona, Spain, 2010.
  12. [12]  Y.-Y. Cao and P. M. Frank, “Robust H disturbance attenuation for a class of uncertain discrete-time fuzzy systems,” IEEE Trans. on Fuzzy Systems, Vol. 8, No, 4, pp. 406-415, 2000.
  13. [13]  L.-X. Wang and J. M. Mendal, “Fuzzy basis functions, universal approximation, and orthogonal least-squares learning,” IEEE Trans. Neural Networks, Vol.3, pp. 807-814, 1992.
  14. [14]  D. Soffker, T.-J. Yu, and P. C. Muller, “State estimation of dynamical systems with nonlinearities by using proportional-integral observer,” Int. J. Syst. Sci., Vol.26, No.9, pp. 1571-1582, 1995.
  15. [15]  D. Soffker and P. C. Muller, “Detection of cracks in turbo rotors – a new observer based method,” ASME J. of Dynamic Systems, Measurement and Control, No.3, pp. 518-524, 1993.

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