Control of a hydraulic system by means of a fuzzy approach
DOI:
https://doi.org/10.11121/ijocta.01.2013.00153Keywords:
Takagi Sugeno fuzzy models, stabilization, hydraulic system, LMIsAbstract
Non linear models can be represented conveniently by Takagi-Sugeno fuzzy models when nonlinearities are bounded. This approach uses a collection of linear models which are interpolated by non linear functions. Then the global control law is the interpolation by the same functions of each feedback associated to each linear model. A Lyapunov approach enables to compute these feedback gains. The number of linear models depends directly on the number of nonlinearities the system has. The more models there are, the more difficult it is to guarantee the stability of the closed loop. This paper proposes a method to reduce the number of linear models by assuming a number of nonlinearities considered as uncertainties and to guarantee the global exponential stability of the system. This method is applied on a hydraulic system.Downloads
References
T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Transactions on Systems Man and Cybernetics, 15 (1), 116-132 (1985). CrossRef
J. Lauber, "Moteur à allumage commandé avec EGR : modélisation et commande non linéaires," Ph.D, Université de Valenciennes et du Hainaut-Cambrésis, France, décembre (In French) (2003).
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, "Linear Matrix Inequalities in system and control theory," Studies in Applied Mathematics. SIAM, 1069-1087, Philadelphia PA, June (1994).
J. Yoneyama, M. Nishikawa, H. Katayama and A. Ichikawa, "Output stabilization of Takagi-Sugeno fuzzy fuzzy systems," Fuzzy sets and system, 111, 253-266 (2000). CrossRef
M. Ksontini, F. Delmotte, T-M. Guerra and A. Kamoun, "Disturbance Rejection Using Takagi Sugeno Fuzzy Model Applied to an interconnected tank system," SMC'03, Washington, DC, USA, 3352-3357 (2003).
Y. Morère, " Mise en œuvre d'une loi de commande pour les modèles flous de type Takagi Sugeno," Ph.D, LAMIH, Université de Valenciennes, (in French) (2001).
T. Taniguchi, K. Tanaka, H. Ohtake & H.O. Wang, "Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems," IEEE Trans. on Fuzzy Systems, 9 (4), 525-537 (2001). CrossRef
D. Peaucelle, D. Arzelier, O. Bachelier and J. Bernussou, "A new robust stability condition for real convex polytopic uncertainty, " Systems and Control letters, 40 (1), 21-30 (2000). CrossRef
K. Tanaka, T. Ikeda and H.O. Wang, "Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs,"IEEE Transactions on Fuzzy Systems, 6 (2), 1-16 (1998). CrossRef
A. Sala and C. Ari-ob, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem," Fuzzy sets and system, 158, 2671-2686 (2007). CrossRef
J. T. Pan, T. M. Guerra, S.M. Fei, A. Jaadari, Non Quadratic Stabilization of Continuous TS Fuzzy Models : LMI Solution for a Local Approach, IEEE transaction on Fuzzy systems, 1063-6706 (2011).
F. Delmotte, T.M. Guerra, M. Ksontini "Continuous Takagi-Sugeno's Models: Reduction of the Number of LMI conditions in various fuzzy control design techniques", IEEE Trans. on Fuzzy Systems, 15 (3), 426-438 (2007). CrossRef
X. Liu. and Z. Zhao Qingling, "New approaches to controller designs based on fuzzy observers for TS fuzzy systems via LMIS", Fuzzy sets and system, Automatica (2003).
T.M. Guerra and W. Perruquetti, "Non quadratic stabilisation of discrete Takagi Sugeno fuzzy models," Fuzzy IEEE 2001, Australie, Melbourne, December (2001).
Mitra Usaha Tani. (2020). Retrieved 21 May 2017, from https://www.mitrausahatani.com
X.J. Ma, Z.Q. Sun and Y.Y. He, "Analysis and design of fuzzy controller and fuzzy observer,"IEEE transactions Fuzzy Systems, 6 (1), 41-50 (1998). CrossRef
V. F. Montagner, R. C. L. F. Oliveira, P. L. D. Peres: Convergent LMI Relaxations for Quadratic Stabilizability and Hin Control of Takagi-Sugeno Fuzzy Systems, IEEE T. Fuzzy Systems, 17 (4), 863-873, (2009). CrossRef
S. Cao, N. Rees and G. Feng, "Stability analysis and design for a class of continuous-time fuzzy control systems," International Journal of Control, 64 (6), 1069-1087 (1996). CrossRef
Downloads
Published
How to Cite
Issue
Section
License
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
This work is licensed under a Creative Commons Attribution 4.0 International License.
