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Shock and Vibration
Volume 2014, Article ID 597827, 12 pages
Research Article

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

1Aeronautical Institute of Technology (ITA), 12 228-900 São José dos Campos, SP, Brazil
2Universidade Estadual Paulista (UNESP), 17 033-360 Bauru, SP, Brazil

Received 14 July 2013; Accepted 10 March 2014; Published 10 June 2014

Academic Editor: Miguel M. Neves

Copyright © 2014 Douglas Domingues Bueno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen’s theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov’s stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.