Volume 9, Issue 3 (March 2022), Pages: 159-164
----------------------------------------------
Original Research Paper
Title: A Takagi-Sugeno model approach for robust fuzzy control design for trajectory tracking of non-linear systems
Author(s): Sulaiman Alkaik *, Mourad Kchaw, Ahmed Al-Shammari
Affiliation(s):
College of Engineering, University of Hail, Hail, Saudi Arabia
Full Text - PDF XML
* Corresponding Author.
Corresponding author's ORCID profile: https://orcid.org/0000-0002-9040-0694
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2022.03.018
Abstract:
This article investigates the robust fuzzy tracking control design for a class of uncertain nonlinear systems using the Takagi–Sugeno (TS) fuzzy models. The main purpose of this study is to design state feedback and observer-based controllers such that the closed-loop system is asymptotically stable. Based on the Lyapunov theory, sufficient conditions are derived such that the closed-loop system is robustly stable. The linear matrix inequality LMI approach is used to obtain the state-feedback and observer gains. The effectiveness of the proposed design approach is provided via numerical simulations for a pendulum system.
© 2022 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: T-S fuzzy systems, State feedback, Observer, Robust control, Uncertainty, LMI
Article History: Received 11 November 2021, Received in revised form 22 January 2022, Accepted 23 January 2022
Acknowledgment
No Acknowledgment.
Compliance with ethical standards
Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Citation:
Alkaik S, Kchaw M, and Al-Shammari A (2022). A Takagi-Sugeno model approach for robust fuzzy control design for trajectory tracking of non-linear systems. International Journal of Advanced and Applied Sciences, 9(3): 159-164
Permanent Link to this page
Figures
Fig. 1 Fig. 2
Tables
No Table
----------------------------------------------
References (15)
- Cao YY and Frank PM (2000). Robust H∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Transactions on Fuzzy Systems, 8(4): 406-415. https://doi.org/10.1109/91.868947 [Google Scholar]
- Ding B, Sun H, and Yang P (2006). Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi–Sugeno's form. Automatica, 42(3): 503-508. https://doi.org/10.1016/j.automatica.2005.11.005 [Google Scholar]
- Fang CH, Liu YS, Kau SW, Hong L, and Lee CH (2006). A new LMI-based approach to relaxed quadratic stabilization of TS fuzzy control systems. IEEE Transactions on Fuzzy Systems, 14(3): 386-397. https://doi.org/10.1109/TFUZZ.2006.876331 [Google Scholar]
- Kim E and Lee H (2000). New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Transactions on Fuzzy Systems, 8(5): 523-534. https://doi.org/10.1109/91.873576 [Google Scholar]
- Lin C, Wang QG, and Lee TH (2005). Improvement on observer-based H∞ control for T–S fuzzy systems. Automatica, 41(9): 1651-1656. https://doi.org/10.1016/j.automatica.2005.04.004 [Google Scholar]
- Lo JC and Lin ML (2004). Observer-based robust H∞ control for fuzzy systems using two-step procedure. IEEE Transactions on Fuzzy Systems, 12(3): 350-359. https://doi.org/10.1109/TFUZZ.2004.825992 [Google Scholar]
- Petersen IR (1987). A stabilization algorithm for a class of uncertain linear systems. Systems and Control Letters, 8(4): 351-357. https://doi.org/10.1016/0167-6911(87)90102-2 [Google Scholar]
- Takagi T and Sugeno M (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1): 116-132. https://doi.org/10.1109/TSMC.1985.6313399 [Google Scholar]
- Tanaka K, Ikeda T, and Wang HO (1996). Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities. IEEE Transactions on Fuzzy Systems, 4(1): 1-13. https://doi.org/10.1109/91.481840 [Google Scholar]
- Tseng CS, Chen BS, and Uang HJ (2001). Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model. IEEE Transactions on Fuzzy Systems, 9(3): 381-392. https://doi.org/10.1109/91.928735 [Google Scholar]
- Tuan HD, Apkarian P, Narikiyo T, and Kanota M (2004). New fuzzy control model and dynamic output feedback parallel distributed compensation. IEEE Transactions on Fuzzy Systems, 12(1): 13-21. https://doi.org/10.1109/TFUZZ.2003.819828 [Google Scholar]
- Wang HO, Tanaka K, and Griffin MF (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Transactions on Fuzzy Systems, 4(1): 14-23. https://doi.org/10.1109/91.481841 [Google Scholar]
- Wang T and Tong S (2006). Decentralized fuzzy model reference H∞ tracking control for nonlinear large-scale systems. In the 6th World Congress on Intelligent Control and Automation, IEEE, Dalian, China, 1: 75-79. https://doi.org/10.1109/WCICA.2006.1712365 [Google Scholar]
- Xiaodong L and Qingling Z (2003). New approaches to H∞ controller designs based on fuzzy observers for TS fuzzy systems via LMI. Automatica, 39(9): 1571-1582. https://doi.org/10.1016/S0005-1098(03)00172-9 [Google Scholar]
- Yoneyama J (2006). Robust H∞ control analysis and synthesis for Takagi–Sugeno general uncertain fuzzy systems. Fuzzy Sets and Systems, 157(16): 2205-2223. https://doi.org/10.1016/j.fss.2006.03.020 [Google Scholar]
|