TS Fuzzy Controller to Stochastic Systems

Authors: Joabe Silva, Ginalber Serra

Abstract:

This paper proposes the analysis and design of robust fuzzy control to Stochastic Parametrics Uncertaint Linear systems. This system type to be controlled is partitioned into several linear sub-models, in terms of transfer function, forming a convex polytope, similar to LPV (Linear Parameters Varying) system. Once defined the linear sub-models of the plant, these are organized into fuzzy Takagi- Sugeno (TS) structure. From the Parallel Distributed Compensation (PDC) strategy, a mathematical formulation is defined in the frequency domain, based on the gain and phase margins specifications, to obtain robust PI sub-controllers in accordance to the Takagi- Sugeno fuzzy model of the plant. The main results of the paper are based on the robust stability conditions with the proposal of one Axiom and two Theorems.

Keywords: Fuzzy Systems; Robust Stability, Stochastic Control, Stochastic Process

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071680

References:

[1] K. J. Astrom and T. Hagglund. Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica, 20:645-651, 1984.
[2] S. ┬©Cetin and O. Demir. Fuzzy pid controller with coupled rules for a nonlinear quarter car model. In Proceedings of World Academy of Science, Engineering and Technology, volume 31, pages 238-241, Jul. 2008.
[3] M.J. Castro-Sitiriche, A. Rubaai, and A.R. Ofoli. Design and implementation of parallel fuzzy pid controller for high-performance brushless motor drives: An integrated environment for rapid control prototyping. IEEE Transactions on Industry Applications, 44(7):1090-1098, 2008.
[4] X. Cheng, Z. Lei, and Y. Junqiu. Fuzzy pid controller for wind turbines. In Second International Conference on Intelligent Networks and Intelligent Systems, pages 74-77, 2009.
[5] G.F. Franklin, J. D. Powell, and A.E. Baeini. Feedback control of dynamic systems. Addison-Wesley, 1986.
[6] R. Gao, K. Ohtsubo, and H. Kajiwara. Lpv design for a space vehicle attitude control benchmark problem. In SICE Annual Conference in Fukui, pages 1461-1464, 2003.
[7] P. Gaspar, Z. Szabo, and J. Bokor. Design of reconfigurable and faulttolerant suspension systems based on lpv methods. In 47th IEEE Conference on Decision and Control - CDC, pages 5384-5389, 2008.
[8] A.M. Ibrahim. Fuzzy Logic for Embedded Systems Applications. Elsevier Science, USA, 2003.
[9] H. Kajiwara, P. Apkarian, and P. Gahinet. Lpv techniques for control of an inverted pendulum. IEEE Control Systems Magazine, pages 44-54, 1999.
[10] B. Lu, F. Wu, and S. Kim. Switching lpv control of an f-16 aircraft via controller state reset. IEEE Transactions on Control Systems Technology, 14(2):267-277, 2006.
[11] E. Mamdani and S. Assilian. An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies, 7(1):1-13, 1975.
[12] J. Park, C. Oh, H. Bang, and M. Tahk. An experimental study on attitude control of spacecraft using fuzzy controller. Dept. of Aerospace Engineering, Korea. Advanced Institute of Science and Technology, 2007.
[13] P. Pelladra, P. Apkarian, and H. Tuan. Missile autopilot design via a multi-channel lft/lpv control method. International Journal Robust and Nonlinear Control, 12(1):1-20, 2009.
[14] A.I. Petros and J. Sun. Robust Adaptive Control. PTR Prentice-Hall, 1996.
[15] G.L.O. Serra and C.P. Boturra. Genetic approach for neural scheduling of multiobjective fuzzy pi controllers. In International Symposium on Evolving Fuzzy Systems, pages 274-279, sept. 2006.
[16] J.S. Shamma and M. Athans. Stability and robustness of slowly timevarying linear systems. In 26th IEEE Conference on Decision and Control, volume 26, pages 434-439, dec. 1987.
[17] J.A. Silva, G.L.O. Serra, and C.C.T. Ferreira. Development method for a robust pid fuzzy controller of lpv systems. In Proceedings of IEEE International Conference on Fuzzy Systems - FUZZY IEEE 2009, pages 826-830, 2009.
[18] T. Takagi and M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. In Proceedings of the IEEE Transactions on Systems, Man and Cybernetics, volume 15, pages 116- 132, 1985.
[19] K. Tanaka and M. Sugeno. Concept of stability margin of fuzzy systems and design of robust fuzzy controller. In 2nd IEEE International Conference on Fuzzy Systems, volume 1, pages 29-34, 1993.
[20] H.O. Wang, K. Tanaka, and M. Griffin. Parallel distributed compensation of nonlinear systems by takagi-sugeno fuzzy model. In 5th IEEE International Conference on Fuzzy Systems, volume 2, pages 531-538, 1995.
[21] H. Ying, W. Siler, and J. Buckley. Fuzzy control theory: a nonlinear case. Automatica, 26:513-520, 1990.
[22] L. A. Zadeh. Fuzzy Sets, volume 8. Information and Control, 1965.