Autosoft Journal

Online Manuscript Access


BIBO Stability Analysis of TSK Fuzzy PI/PD Control Systems


Authors



Abstract

In this paper, we determine the sufficient conditions in which nonlinear feedback systems using Takagi-Sugeno-Kang (TSK) fuzzy PI/PD controllers become bounded-input bounded-output (BIBO) stable. To determine BIBO stability conditions, we apply the small-gain theorem to the systems. Compared to previous results, BIBO stability conditions in this study are determined for controllers that are developed using more relaxed input fuzzy sets. In addition, the procedures used to determine sufficient conditions are simple because region-based input2013output relationship analysis is not required. Finally, the derived conditions are less conservative than those determined in previous studies. MATLAB simulations are performed to validate the results of this study.


Keywords


Pages

Total Pages: 14
Pages: 645-658

DOI
10.1080/10798587.2015.1015243


Manuscript ViewPdf Subscription required to access this document

Obtain access this manuscript in one of the following ways


Already subscribed?

Need information on obtaining a subscription? Personal and institutional subscriptions are available.

Already an author? Have access via email address?


Published

Volume: 21
Issue: 4
Year: 2015

Cite this document


References

Guanrong Chen, and Hao Ying. "Stability Analysis of Nonlinear Fuzzy PI Control Systems." Third International Conference on Industrial Fuzzy Control and Intelligent Systems n. pag. Crossref. Web. https://doi.org/10.1109/IFIS.1993.324200

Ding, Y., H. Ying, and S. Shao. "Structure and Stability Analysis of a Takagi-Sugeno Fuzzy PI Controller with Application to Tissue Hyperthermia Therapy." Soft Computing - A Fusion of Foundations, Methodologies and Applications 2.4 (1999): 183-190. Crossref. Web. https://doi.org/10.1007/s005000050051

Ding, Y. "Typical Takagi-Sugeno PI and PD Fuzzy Controllers: Analytical Structures and Stability Analysis." Information Sciences 151 (2003): 245-262. Crossref. Web. https://doi.org/10.1016/S0020-0255(02)00302-X

Feng, G. "A Survey on Analysis and Design of Model-Based Fuzzy Control Systems." IEEE Transactions on Fuzzy Systems 14.5 (2006): 676-697. Crossref. Web. https://doi.org/10.1109/TFUZZ.2006.883415

Bao-Gang Hu, G.K.I. Mann, and R.G. Gosine. "A Systematic Study of Fuzzy PID Controllers-Function-Based Evaluation Approach." IEEE Transactions on Fuzzy Systems 9.5 (2001): 699-712. Crossref. Web. https://doi.org/10.1109/91.963756

Khalil, H. K. (2002). Chapter 5. Input–Output stability. In Nonlinear systems (3rd ed., pp. 195–221). Upper Saddle River, NJ: Prentice Hall.

Kim J. A study on full-scale fuzzy proportional-integral-derivative controllers

Kim, J., Choi, O. K. & Lee, J. S. (2012, June). Design and stability analysis of TSK-type full-scale fuzzy PID controllers. In IEEE international conference on fuzzy systems (pp. 1–8). Brisbane.

Kumar, Vineet, A. P. Mittal, and R. Singh. "Stability Analysis of Parallel Fuzzy P + Fuzzy I + Fuzzy D Control Systems." International Journal of Automation and Computing 10.2 (2013): 91-98. Crossref. Web. https://doi.org/10.1007/s11633-013-0701-5

Kumar V. International Journal of Innovative Computing, Information & Control

The MathWorks, Inc. Fuzzy Logic Toolbox User”s Guide

Mohan, B.M. "Fuzzy Pid Control Via Modified Takagi-Sugeno Rules." Intelligent Automation & Soft Computing 17.2 (2011): 165-174. Crossref. Web. https://doi.org/10.1080/10798587.2011.10643139

Mohan, B.M., and J.M. Reddy. "Mathematical Model of a Takagi-Sugeno PI/PD Controller." 2010 5th International Conference on Industrial and Information Systems (2010): n. pag. Crossref. Web. https://doi.org/10.1109/ICIINFS.2010.5578631

Reddy B. A. International Journal of Soft Computing and Engineering

Sugeno, M, and G.T Kang. "Structure Identification of Fuzzy Model." Fuzzy Sets and Systems 28.1 (1988): 15-33. Crossref. Web. https://doi.org/10.1016/0165-0114(88)90113-3

Takagi, Tomohiro, and Michio Sugeno. "Fuzzy Identification of Systems and Its Applications to Modeling and Control." IEEE Transactions on Systems, Man, and Cybernetics SMC-15.1 (1985): 116-132. Crossref. Web. https://doi.org/10.1109/TSMC.1985.6313399

Wang, L. X. (1997). A course in fuzzy systems and control. Englewood Cliffs, NJ: Prentice Hall.

Yame, J.J. "Conventional Structure of a Simple Class of Takagi-Sugeno PI-Type Controllers." Proceedings of the 41st IEEE Conference on Decision and Control, 2002. n. pag. Crossref. Web. https://doi.org/10.1109/CDC.2002.1184489

Hao Ying. "Constructing Nonlinear Variable Gain Controllers via the Takagi-Sugeno Fuzzy Control." IEEE Transactions on Fuzzy Systems 6.2 (1998): 226-234. Crossref. Web. https://doi.org/10.1109/91.669021

Ying, Hao. "The Takagi-Sugeno Fuzzy Controllers Using the Simplified Linear Control Rules Are Nonlinear Variable Gain Controllers." Automatica 34.2 (1998): 157-167. Crossref. Web. https://doi.org/10.1016/S0005-1098(97)00173-8

Ying, H. "Theory and Application of a Novel Fuzzy PID Controller Using a Simplified Takagi-Sugeno Rule Scheme." Information Sciences 123.3-4 (2000): 281-293. Crossref. Web. https://doi.org/10.1016/S0020-0255(99)00133-4

Zadeh, L.A. "Fuzzy Sets." Information and Control 8.3 (1965): 338-353. Crossref. Web. https://doi.org/10.1016/S0019-9958(65)90241-X

JOURNAL INFORMATION


ISSN PRINT: 1079-8587
ISSN ONLINE: 2326-005X
DOI PREFIX: 10.31209
10.1080/10798587 with T&F
IMPACT FACTOR: 0.652 (2017/2018)
Journal: 1995-Present




CONTACT INFORMATION


TSI Press
18015 Bullis Hill
San Antonio, TX 78258 USA
PH: 210 479 1022
FAX: 210 479 1048
EMAIL: tsiepress@gmail.com
WEB: http://www.wacong.org/tsi/