Abstract
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.
Highlights
The requirement for more accurate tools for predictions of nonlinear effects has motivated many research groups to investigate aeroelastic systems considering nonlinearities
The problem involving freeplay in control surfaces has called attention of various researchers because it can be a cause of limit cycle oscillation (LCO) leading to serious consequences such as fatigue, pilot handling/ride quality, confined manoeuvrings envelope, weapon aiming of military aircraft, and induced flutter
Another motivation to consider control surface freeplay is that the requirements for aircraft design according to military specification can be quite difficult to achieve in practice, increasing the manufacturing and maintenance costs
Summary
The requirement for more accurate tools for predictions of nonlinear effects has motivated many research groups to investigate aeroelastic systems considering nonlinearities. The problem involving freeplay in control surfaces has called attention of various researchers because it can be a cause of limit cycle oscillation (LCO) leading to serious consequences such as fatigue, pilot handling/ride quality, confined manoeuvrings envelope, weapon aiming of military aircraft, and induced flutter. Tang and colleagues published theoretical and experimental results considering an aeroelastic apparatus and the high order Harmonic Balance methods [3]. This method was introduced by Kryloff and Bogoliuboff in 1947 and it has been studied by different researchers as shown in [4,5,6,7,8]. Numerical simulations are performed on the benchmark airfoil problem to demonstrate that LMIs combined with FTS modeling can be used to design controllers for nonlinear aeroelastic problems
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