Aeroservoelasticity of an Airfoil with Parametric Uncertainty and Subjected to Atmospheric Gusts

This paper presents the dynamics and adaptive control of an airfoil with structural stiffness and damping uncertainties, which is subjected to atmospheric gusts. The motion of the airfoil is modeled by three degrees of freedom (DOFs), namely, pitch, plunge, and flap. A flat spot or dead-zone-type stiffness is used for modeling the flap hinge free play. The nonlinear dynamics of the system without control and parametric uncertainty, where a cubic stiffness for pitch and a linear stiffness for plunge are considered, is examined. Numerical results show that the airfoil may become unstable via a Hopf bifurcation at a flow velocity well below the linear flutter speed; if the structural damping is not sufficiently high, it may also undergo chaotic motion. It was found that a proportional–derivative controller based on the partial feedback linearized system could effectively alleviate oscillations induced by gusts at flow velocities below and above the linear flutter speed. Next, an uncertain N th-order polynomial stiffness for pitch and uncertain structural damping (modeled by viscous damping) coefficients for all DOFs are assumed. Considering such uncertainties, an adaptive controller with an estimation update law is designed to stabilize the airfoil subjected to gusts. A Lyapunov function is established to prove the stability of the closed-loop system. Simulation results demonstrate the effectiveness of the designed controller.