Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities

Nonlinearities in aircraft mechanisms are inevitable, especially in the control system. It is necessary to investigate the effects of them on the dynamic response and control performance of aeroelastic system. In this paper, based on the state-dependent Riccati equation method, a state feedback suboptimal control law is derived for aeroelastic response and flutter suppression of a three degree-of-freedom typical airfoil section. With the control law designed, nonlinear effects of freeplay in the control surface and time delay between the control input and actuator are investigated by numerical approach. A cubic nonlinearity in pitch degree is adopted to prevent the aeroelastic responses from divergence when the flow velocity exceeds the critical flutter speed. For the system with a freeplay, the responses of both open- and closed-loop systems are determined with Runge-Kutta algorithm in conjunction with Henon's method. This method is used to locate the switching points accurately and efficiently as the system moves from one subdomain into another. The simulation results show that the freeplay leads to a forward phase response and a slight increase of flutter speed of the closed-loop system. The effect of freeplay on the aeroelastic response decreases as the flow velocity increases. The time delay between the control input and actuator may impair control performance and cause high-frequency motion and quasi-periodic vibration.