DIRECT MODEL REFERENCE TAKAGI–SUGENO FUZZY CONTROL OF SISO NONLINEAR SYSTEMS DESIGN BY MEMBERSHIP FUNCTION

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Volume 6 (1), June 2023, Pages 19-29

Foad Hosseini¹, Meshkat Sadat Hosseini²

¹ Semnan University, Semnan, Iran, This email address is being protected from spambots. You need JavaScript enabled to view it.

² Shahed University, Tehran, Iran, This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract

What is discussed in this article is to find a way for membership functions optimally. In most scholars, these functions are constant and have a limited number. Therefore, in some cases, this limitation reduces control performance improvement. One of the best solutions is finding these functions in a differential form. This article used the Takagi-Sugeno function as a fuzzy detector to identify and control a nonlinear SISO system by direct adaptive reference model control. Using this method with Lyapunov for the stability of the control system makes output fuzzy linguistic variables optimally. Then simultaneously using these values, membership functions can be defined in differential form. Therefore, there is no other limitation in the variance and midpoint.

Keywords:

Fuzzy Control, Model Reference Adaptive Control, Takagi-Sugeno (T-S) Fuzzy Model, Membership Function, Fuzzy Inference Engine

DOI: https://doi.org/10.32010/26166127.2023.6.1.19.29

Reference 

Åström, K.J. and Wittenmark, B. (2013). Adaptive control. Courier Corporation.

Bridges, M.M., Dawson, D.M. and Abdallah, C.T. (1995). Control of rigid‐link, flexible‐joint robots: a survey of backstepping approaches. Journal of Field Robotics, 12(3), pp.199-216.

Cho, Y.W., Park, C.W. and Park, M. (2002). An indirect model reference adaptive fuzzy control for SISO Takagi–Sugeno model. Fuzzy Sets and Systems, 131(2), pp.197–215.

Green, A. and Sasiadek, J.Z. (2005). Adaptive control of a flexible robot using fuzzy logic. Journal of Guidance, Control, and Dynamics, 28(1), pp.36-42.

Huang, A.C. and Chen, Y.C. (2004). Adaptive sliding control for the single-link flexible-joint robot with mismatched uncertainties. IEEE Transactions on Control Systems Technology, 12(5), pp.770–775.

Khanesar, M.A. and Hosseini, M. (2017, July). Guaranteed cost adaptive sliding mode fuzzy control systems. In Fuzzy Systems (FUZZ-IEEE), 2017 IEEE International Conference on (pp. 1–5). IEEE.

Khanesar, M.A., Kaynak, O. and Teshnehlab, M. (2011). Direct model reference Takagi–Sugeno fuzzy control of SISO nonlinear systems. IEEE Transactions on fuzzy systems, 19(5), pp.914-924.

Liu, Y.J., Tong, S. and Chen, C.P. (2013). Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Transactions on Fuzzy Systems, 21(2), pp.275–288.

Madani, T. and Benallegue, A. (2006), October. Backstepping control for a quadrotor helicopter. In Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on (pp. 3255-3260). IEEE.

Malki, H.A., Misir, D., Feigenspan, D. and Chen, G. (1997). Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Transactions on Control Systems Technology, 5(3), pp.371-378.

Unbehauen, H. D. (Ed.). (2009). Control Systems, Robotics and Automation –Volume VI: Modeling and System Identification-III. EOLSS Publications.

Zimmermann, H.J. (1996). Fuzzy control. In Fuzzy Set Theory - and Its Applications (pp. 203-240). Springer, Dordrecht.