Non Linear Disturbance Accommodation Fuzzy Control

Slim Abdelbari; Jelel Ezzine

doi:10.20965/jaciii.2008.p0165

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JACIII Vol.12 No.2 pp. 165-171

doi: 10.20965/jaciii.2008.p0165

(2008)

Paper:

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Non Linear Disturbance Accommodation Fuzzy Control

Slim Abdelbari and Jelel Ezzine

Signals and Systems Laboratory, ENIT, Tunisia

Received:

July 20, 2005

Accepted:

June 4, 2007

Published:

March 20, 2008

Keywords:

Takagi-Sugeno fuzzy systems, chaotic systems, DAC theory, fuzzy observer, LMIs.

Abstract

This paper deals with the problem of chaotic disturbances accommodation when these are generated by known non linear dynamics. In order to accomplish this goal, Takagi-Sugeno fuzzy models are called for as they offer the advantage of having virtually a linear rule consequent to approximate non linear systems. A control law inspired from the known disturbance accommodation control theory (DAC theory) is used to make the effects of disturbances vanish or attenuated while the considered linear plant is stabilized at the same time. An illustrative example is provided.

Cite this article as:

S. Abdelbari and J. Ezzine, “Non Linear Disturbance Accommodation Fuzzy Control,” J. Adv. Comput. Intell. Intell. Inform., Vol.12, No.2, pp. 165-171, 2008.

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References

[1] J. Castro and M. Delgado, “Fuzzy Systems with Defuzzification are Universal Approximators,”, IEEE Trans. Syst., Man, Cybern., 26, pp. 149-152, 1996.
[2] T. Hung, M. Sugeno, R. Tong, and R. R. Yager, “Theoretical Aspects Of Fuzzy Control,” John Wiley and Sons Editions, 1995.
[3] J. J. Buckley, “Sugeno Type Controllers are Universal Controllers,” Fuzzy Sets and Systems, 53, pp. 299-303, 1993.
[4] C. Lee, “Fuzzy Logic in control systems: Fuzzy Logic Controller, Part I,” IEEE Trans. Syst., Man, Cybern., 20, pp. 408-418, August 1990.
[5] N. Li, S. Yuan, Y. G. Xi, and S. S. Ge, “Stability Analysis Of TS Fuzzy System Based on Observer,” Int. Journal of Fuzzy System, 15, March 2003.
[6] X.-J. Ma, Z.-Q. Sun, and Y.-Y. He, “Analysis and design of fuzzy Controller and fuzzy Observer,” IEEE Trans. Fuzzy Syst., 6, February 1998.
[7] K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy Regulator and Fuzzy Observer: Relaxed Stability Conditions and LMI-Based Designs,” IEEE Trans. Fuzzy Syst., 6, May 1998.
[8] H. O. Wang, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of Nonlinear systems:Stability and design issues,” IEEE Trans. Fuzzy Syst., 4, February 1996.
[9] H. Han, “Adaptive Fuzzy Controller for a Class of Nonlinear Systems,” Int. J. Innovative Computing, Information and Control, 1, 2005.
[10] H. Yang, “Subspace-Based Adaptive Predictive Control for a Class of Nonlinear Systems,” Int. J. Innovative Computing, Information and Control, 1, March 2005.
[11] Z. Li, J. B. Park, Y. H. Joo, and G. Chen, “Anticontrol of Chaos for Discrete TS Fuzzy Systems,” IEEE Trans. Circuits Syst. I, 49, February 2002.
[12] B. R. Andrievskii and A. L. Fradkov, “Control of Chaos: Methods and Applications,” Automation and Remote Control, 64, 2003.
[13] C.-S. chiu, T.-S. Chiang, and P. Liu, “LMI-Based Fuzzy Chaotic Synchronization and Communications,” IEEE Trans. Fuzzy Syst., 9, pp. 539-553, August 1998.
[14] C. D. Jhonson, “Theory of Disturbance Accommodating Controllers,” Academic Press, 1976.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. Castro and M. Delgado, “Fuzzy Systems with Defuzzification are Universal Approximators,”, IEEE Trans. Syst., Man, Cybern., 26, pp. 149-152, 1996.

[2] [2] T. Hung, M. Sugeno, R. Tong, and R. R. Yager, “Theoretical Aspects Of Fuzzy Control,” John Wiley and Sons Editions, 1995.

[3] [3] J. J. Buckley, “Sugeno Type Controllers are Universal Controllers,” Fuzzy Sets and Systems, 53, pp. 299-303, 1993.

[4] [4] C. Lee, “Fuzzy Logic in control systems: Fuzzy Logic Controller, Part I,” IEEE Trans. Syst., Man, Cybern., 20, pp. 408-418, August 1990.

[5] [5] N. Li, S. Yuan, Y. G. Xi, and S. S. Ge, “Stability Analysis Of TS Fuzzy System Based on Observer,” Int. Journal of Fuzzy System, 15, March 2003.

[6] [6] X.-J. Ma, Z.-Q. Sun, and Y.-Y. He, “Analysis and design of fuzzy Controller and fuzzy Observer,” IEEE Trans. Fuzzy Syst., 6, February 1998.

[7] [7] K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy Regulator and Fuzzy Observer: Relaxed Stability Conditions and LMI-Based Designs,” IEEE Trans. Fuzzy Syst., 6, May 1998.

[8] [8] H. O. Wang, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of Nonlinear systems:Stability and design issues,” IEEE Trans. Fuzzy Syst., 4, February 1996.

[9] [9] H. Han, “Adaptive Fuzzy Controller for a Class of Nonlinear Systems,” Int. J. Innovative Computing, Information and Control, 1, 2005.

[10] [10] H. Yang, “Subspace-Based Adaptive Predictive Control for a Class of Nonlinear Systems,” Int. J. Innovative Computing, Information and Control, 1, March 2005.

[11] [11] Z. Li, J. B. Park, Y. H. Joo, and G. Chen, “Anticontrol of Chaos for Discrete TS Fuzzy Systems,” IEEE Trans. Circuits Syst. I, 49, February 2002.

[12] [12] B. R. Andrievskii and A. L. Fradkov, “Control of Chaos: Methods and Applications,” Automation and Remote Control, 64, 2003.

[13] [13] C.-S. chiu, T.-S. Chiang, and P. Liu, “LMI-Based Fuzzy Chaotic Synchronization and Communications,” IEEE Trans. Fuzzy Syst., 9, pp. 539-553, August 1998.

[14] [14] C. D. Jhonson, “Theory of Disturbance Accommodating Controllers,” Academic Press, 1976.