Fuzzy Robust H∞ Tracking Control For Wind Generator System: LMI approach


  • Kaoutar Lahmadi Department of physics, LESSI Laboratory, Faculty of Sciences Dhar el Mahraz, University Sidi Mohammed Ben Abdellah, Fez, Morocco
  • Ismail Boumhidi Department of physics, LESSI Laboratory, Faculty of Sciences Dhar el Mahraz, University Sidi Mohammed Ben Abdellah, Fez, Morocco




Wind system, H∞ tracking control, observer-based controller, linear matrix inequality (LMI).


This study concerns the tracking control problem of the wind turbine generator system with uncertainties parameters and external disturbances. Based on T-S fuzzy model, a fuzzy observer-based and a fuzzy robust state feedback output tracking control are developed to reduce the tracking error by minimizing the disturbance level caused by the wind speed. Using a Lyapunov function combined with H∞ tracking criteria and a judicious of the famous Young relation, a sufficient stability condition for the robust fuzzy tracking control formulated in terms of linear matrix inequality, which can be very efficiently solved by using LMI optimization techniques. The simulation results are given to show the performance of the observer-based tracking controller.


(1) (Takagi & Sugeno, 1985) Takagi, T., and Sugeno, M., Fuzzy identification of systems and its application to modelling and control”. IEEE Trans. Syst., Man and Cyber, Vol.1115, pp. 116-132, 1985

(2) ShaochengTong,TaoWang,Han-Xiong Li “Fuzzy robust tracking control for uncertain nonlinear systems “ (2002)

(3) K. Rai Lee, E. Tae Jeung, H. Bae Park"Robust fuzzy H∞control for uncertain nonlinear systems via state feedback: an LMI approach”(2001)

(4) B.Mansouri, N. Manamanni, A.Hamzaoui and J. Zaytoon “Tracking control for uncertain Takagi Sugeno fuzzy systems with external disturbances ”(2005)

(5) S. Bououden, M. Chadli,, S. Filali, A. El Hajjaji “Fuzzy model based multivariable predictive control of a variable speed wind turbine: LMI approach”(2012)

(6) K. Tanaka, and K. O. Wang. Fuzzy Control Systems Design and Analysis: A linear Matrix Inequality Approach.John Wiley & Sons, Inc., 2001

(7) Boyd, S., El Ghaoui, L., Feron, E., &Balakrishnan, V. (1994).

Linearmatrix inequalities in system and control theory. In SIAM Studies in Applied Mathematics: vol. 15. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM)

(8) B. Mansouri, N. Manamanni, K. Guelton, A. Kruszewski, T.M. Guerra “Output feedback LMI tracking control conditions withH1criterion for uncertain and disturbed T–S models”(2008)

(9) N. Harrabi, M. Kharrat, M. Souissi, A. Aitouche “Maximum Power Point Tracking of a Wind Generation System Based on T-S Fuzzy Model”(2015)

(10) C.Tseng, B.Chen, and H.Uang “Fuzzy Tracking Control Design for Nonlinear Dynamic Systems via T–S Fuzzy Model”(2001)

(11) D.Zhang, Q. Han and X. Jia “Tracking Control for Network-Based T-S Fuzzy Systems With Asynchronous Constraints”(2012)

(12) S. Bezzaoucha, B. Marx, D. Maquin, J. Ragot “Model Reference Tracking Control for Nonlinear Systems described by Takagi-Sugeno Structure”(2013)

(13) K. Ben Meziane, I. Boumhidi “An Interval Type-2 Fuzzy Logic PSS with the optimal H ∞ tracking control for multi-machine power system”(2015)

(14) A. Abdelkrim, C. Ghorbel, M. Benrejeb “LMI-based tracking control for Takagi-Sugeno fuzzy model”(2010)

(15) F.Khaber, A.Hamzaoui, K. Zehar “State Feedback Controller Design via Takagi-Sugeno fuzzy Model : A Linear Matrix Inequalities Approach”

(16) J. Zhang, M.Fei, T. Yang and Y. Tan “Robust Fuzzy Tracking Control of Nonlinear Systems with Uncertainty Via T-S Fuzzy Model”(2006)


(18) Chang-Hua Lien“An efficient method to design robust observer-based control of uncertain linear systems ”(2004)

(19) M. Chadli and A. El Hajjaji “Wind energy conversion systems control using T-S fuzzy modeling”(2010




How to Cite

Lahmadi, K., & Boumhidi, I. (2017). Fuzzy Robust H∞ Tracking Control For Wind Generator System: LMI approach. Transactions on Engineering and Computing Sciences, 5(4). https://doi.org/10.14738/tmlai.54.2971



Special Issue : 1st International Conference on Affective computing, Machine Learning and Intelligent Systems