Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems

  • Hafedh Abid Institut supérieure des études technologiques de Sfax Laboratoire d’Automatique, Génie Informatique et Signal Cité Scientifique, BP 48, 59651 Villeneuve d’Ascq, France
  • Mohamed Chtourou Unité de Commande Intelligente, design et optimisation des Systèmes complexes(ICOS) ENIS, B.P. W, 3038 sfax, Tunisie
  • Ahmed Toumi 3Unité de Procédés Industriels Unité de Commande Automatique (UCPI) ENIS,B.P. W, 3038 sfax, Tunisie

Abstract

In this work we are interested to discrete robust fuzzy sliding mode control. The discrete SISO nonlinear uncertain system is presented by the Takgi- Sugeno type fuzzy model state. We recall the principle of the sliding mode control theory then we combine the fuzzy systems with the sliding mode control technique to compute at each sampling time the control law. The control law comports two terms: equivalent control law and switching control law which has a high frequency. The uncertainty is replaced by its upper bound. Inverted pendulum and mass spring dumper are used to check performance of the proposed fuzzy robust sliding mode control scheme.

References

[1] Michio Sugeno "On Stability of fuzzy Systems expressed by rules with singleton consequents, (IEEE Transaction on Fuzzy Systems,Vol 7 N 2 Feb 1999).
http://dx.doi.org/10.1109/91.755401

[2] T.Takagi and M.Sugeno, Fuzzy identification of systems and its applications to modeling and control IEEE trans syst. Man,Cybern. Vol15. 116-132 Jan/Feb1985.
http://dx.doi.org/10.1109/TSMC.1985.6313399

[3] W.Chang, J.Bae Park, Y.Hoan Joob and G.chen Design of robust fuzzy model-based controller with sliding mode control for SISO non-linear systems Fuzzy Sets and Systems 125 (2002) pp 1-22.
http://dx.doi.org/10.1016/S0165-0114(01)00038-0

[4] Hafedh Abid Mohamed Chtourou et Ahmed Toumi, A Sliding Mode Based Robust Fuzzy Controller For a Class of Uncertain Systems SSD05, Mrach 2005 Sousse Tunisia.

[5] Y. dote and R.G..hoft, Microprocessor based sliding mode controller for dc motor drives presented at the Industrial Application. SOC. Annu. Meeting, Cincinnati, OH, 1980.

[6] D. Milosavljevic, General conditions for the existence of a quasi-sliding mode on the switching hyperplane in Discrete Variable Systems Automat. Remote Contr., vol. 46, pp(307-314) 1985.

[7] S. Z. Sarpturk, Y Istefanopulos, and O. Kaynak, On the stability of Discrete-time sliding mode control systems IEEE Trans. Automat. Contr., vol. 32, N 10, pp(930-932) 1987..

[8] K. Furuta, Sliding Mode Control of a discrete system", Systems and Control Letter, Volume 14, pp145-152.
http://dx.doi.org/10.1016/0167-6911(90)90030-X

[9] Weibing Gao, Yufu Wang and Abdollah Homaifa, Discrete-Time Variable Structure Control Systems IEEE Transactions on Industrial, Electronics, volume 42, N 2, April 1995, pp(117-122).

[10] Weibing Gao., and Hung, J.C., Variable structure control of nonlinear systems: a new approach IEEE Transactions on Industrial Electronics, 40, 45, 1993
http://dx.doi.org/10.1109/41.184820

[11] H. Lee, E. Kim, H.J. Kang et M. Park, A new sliding-mode control with fuzzy boundary layer Fuzzy Sets and Systems 120 (2001), pp. 135-143
http://dx.doi.org/10.1016/S0165-0114(99)00072-X

[12] Utkin, V. I, Sliding Modes and their Application in Variable Structure Systems (Moscow: Nauka) 1974 (in Russian, and also, 1978, Mir, in English).

[13] Utkin, V. I, Variable structure systems with sliding mode" IEEE Transactions on Automatic Control, Vol. AC-22, No. 2, pp 212-222, April., (1977).

[14] Yu, X. H., Man, Z. H. and Wu, B. L Design of fuzzy sliding-mode control systems, Fuzzy Sets and Systems, 95, pp.295-306. ., (1998)
http://dx.doi.org/10.1016/S0165-0114(96)00278-3

[15] Ting, C. S., Li, T. H. S, and Kung, F. C., An approach to systematic design of the fuzzy control system Fuzzy Sets and Systems, 77, pp. 151-166. (1996).
http://dx.doi.org/10.1016/0165-0114(95)00075-5

[16] Slotine, J. J. E. and Li.W., Applied nonlinear control, Prentice Hall, Englewood Cliffs, NJ.(1991),

[17] Kazuo Tanaka, Takayuki Ikeda and Hua O.Wang, Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stability, H¥ Control Theory, and linear Matrix Inequalities IEEE Trans on Fuzzy System, Vol 4 N 1 Feb 1996.
http://dx.doi.org/10.1109/91.481840

[18] Mehrdad Hojati and Saeed Gazor Hybrid Adaptive Fuzzy Identification and Control nonlinear SystemsIEEE Transactions ON Fuzzy Systems vol 10, N 2. April 2002 pp 198-210.
Published
2008-03-01
How to Cite
ABID, Hafedh; CHTOUROU, Mohamed; TOUMI, Ahmed. Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 3, n. 1, p. 6-20, mar. 2008. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/2370>. Date accessed: 05 july 2020. doi: https://doi.org/10.15837/ijccc.2008.1.2370.

Keywords

Nonlinear systems, Sliding mode, T-S fuzzy systems, Reaching law