Abstract:
In this paper, Limit Cycle Oscillations (LCOs) of a Two-Dimensional (2-D) airfoil
with cubic structural nonlinearity in the plunge Degree of Freedom (DOF) are investigated. The
aerodynamic loads are modelled using the unsteady Theodorsen?s theory. Wagner function and
Jones? approximation are used to transform the unsteady aerodynamic loads from frequency
domain into time domain. The aeroelastic differential equations are solved using the routine
ODE45 in MATLAB to get the system response. Both subcritical and supercritical LCOs are
observed in the 3-DOF airfoil with structural nonlinearity in the plunge DOF. Such LCOs are
undesirable phenomena and should be suppressed within the flight envelope. A nonlinear state
feedback controller is designed to minimize the amplitude of LCOs presented in the considered
nonlinear aeroelastic system. The State-Dependent Riccati Equation (SDRE) approach in
combination with Kalman filter technique is used to design a controller for the 2-D airfoil with
trailing edge control surface (flap). The forces and moments produced by this flap?s action are
used to stabilize the system and suppress the existence of LCOs. The efficiency of the proposed
nonlinear controller by the SDRE and Kalman filter in suppressing the existence of subcritical and
supercritical LCOs are verified by the numerical simulation results.