Passivity-based adaptive control of aeroelastic system with unsteady aerodynamics and wind gust

Abstract

This paper presents two simple output feedback adaptive control laws for the control of a two-dimensional nonlinear aeroelastic system, including unsteady aerodynamics, parameter uncertainties, and wind gust.
The objective is to stabilize the plunge-pitch oscillatory motion by the use of a single trailing-edge control surface. Based on the $G$-passivity theory for nonsquare systems, two adaptive control systems
($\mathcal{C}1$ and $\mathcal{C}2$) are designed. The control law $\mathcal{C}1$ uses the plunge displacement, pitch angle, and their first derivatives for feedback, and the control law $\mathcal{C}2$ is synthesized using only two outputs (pitch angle and pitch rate). For attenuating the effect of gust load and nonlinearities, a switching control signal is designed.
In addition, sigma modification is introduced to prevent parameter divergence. By the Lyapunov analysis, the convergence of the trajectories in a region surrounding the origin is established. Simulation results show that
in the closed-loop system, each adaptive law suppresses the oscillatory responses, despite uncertainties in parameters and gust load. It is seen that the control law $\mathcal{C}1$ gives little smaller settling time, but requires larger flap deflection compared with the control law $\mathcal{C}2$.