DIRECT ADAPTIVE FUZZY PI SLIDING MODE CONTROL OF SYSTEMS WITH UNKNOWN BUT BOUNDED DISTURBANCES

Document Type: Research Paper

Authors

DEPARTMENT OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING, FERDOWSI UNIVERSITY OF MASHHAD, MASHHAD, IRAN

Abstract

An asymptotically stable direct adaptive fuzzy PI sliding mode
controller is proposed for a class of nonlinear uncertain systems. In contrast to
other existing approaches of handling disturbances, the proposed approach
does not require this bound to be known, only requiring that it exists.
Moreover, a PI control structure is used to attenuate chattering. The approach
is applied to stabilize an open-loop unstable nonlinear system as well as
the Duffing forced-oscillation chaotic nonlinear system amid significant
disturbances. Analysis of simulations reveals the effectiveness of the proposed
method in terms of a significant reduction in chattering while maintaining
asymptotic convergence.

Keywords


[1] M.-R. Akbarzadeh-T. and R. Shahnazi, Direct adaptive fuzzy PI sliding mode control for a
class of uncertain nonlinear systems, In Proceeding of IEEE International Conference on
Systems, Man and Cybernetics, (2005), 2566-2571.
[2] K. J. Astrom and B. Wittenmark, Adaptive control, second Edition, Addison-Wesley Pub
Co, Newyork, December (1994).
[3] Y. Byungkook and H. Woonchul, Adaptive fuzzy sliding mode control of nonlinear systems,
IEEE Transaction Fuzzy systems, 6 (2) (1998).
[4] Z. M. Chen, J. G. Zhang, Z. C. Zhang and J. C. Zeng, Adaptive fuzzy sliding mode control
for uncertain nonlinear systems, In Proceeding of the Second International Conference
on Machine Learning and Cybernetics, Xian, 2-5 November (2003).
[5] Y. Guo and P. Y. Woo, Adaptive fuzzy sliding mode control for robotic manipulators, In
Proceeding of 42nd Conference on Decision and Control, Maui, Hawaii USA,
December (2003).
[6] H.G. Han and C. Y. Su, Further results on adaptive control of a class of nonlinear systems
with fuzzy logic, In Proceedings of IEEE Conference on Fuzzy Systems, Seoul, Korea,
(1999), 1309-1314.
[7] H. F. Ho, Y. K. Wong and A. B. Rad, Adaptive fuzzy sliding mode control design: Lyapunov
approach, In Proceeding of 5th Asian Control Conference, 3 (2004), 1502- 1507.
[8] H. K. Khalil. Nonlinear systems, Prentice-Hall Inc., second edition, (1996).
[9] Y. K. Kim and G. J. Jeon, Error reduction of sliding mode control using sigmoid-type
nonlinear interpolation in the boundary layer, International Journal of Control, and
Systems, 2 (4) (2004), 523-529.
[10] C. C. Lee, Fuzzy logic in control systems: fuzzy logic controller, part I and part II, IEEE
Transactions on Systems, Man, and Cybernetics, 20 (1990), 404-435.
[11] K. S. Narenda and A. M. Annaswamy, Stable adaptive systems, Prentice-Hall Inc., (1989).

[12] R. Shahnazi and M.-R. Akbarzadeh-T., Robust PI adaptive fuzzy control for a class of
uncertain nonlinear systems, In Proceeding of IEEE International Conference on
Systems, Man and Cybernetics, (2005), 2548-2553.
[13] J. J. Slotine and W. Li, Applied nonlinear control, Prentice Hall, Inc.: Englewood Cliffs,
New Jersy, (1991).
[14] C. Y. Su and Y. Stepanenko, Adaptive control of a class of nonlinear systems with fuzzy
logic, IEEE Transactions on Fuzzy Systems, 2 (2) (1994), 285-294.
[15] C. W. Tao, M.L. Chan and T. T. Lee, Adaptive fuzzy sliding mode controller for linear
systems with mismatched time-varying uncertainties, IEEE Transaction on Systems Man
and Cybernetics, Part B: Cybernetics, 33 (2)(2003).
[16] V. I. Utkin, Sliding modes and their application in variable structure systems, Moscow,
Russia: Mir, (1978).
[17] J. Wang, S. S. Get and T. H. Lee, Adaptive fuzzy sliding mode control of a class of nonlinear
systems, In Proceedings of the 3rd Asian Control Conference, Shanghai, July 4-7,
(2000).
[18] L. X. Wang, A course in fuzzy systems and control, Prentice Hall., New Jersy, August
(1996).
[19] L. X. Wang, Adaptive fuzzy systems and control: design and stability analysis, Prentice Hall,
Englewood Cliffs, NJ., (1994).
[20] L. X. Wang, Stable adaptive fuzzy control of nonlinear systems, IEEE Transaction on
Fuzzy systems, 1 (2) (1993).