Immersion- and Invariance-Based Adaptive Control ofa Nonlinear Aeroelastic System

Abstract

This paper treats the question of adaptive control of prototypical aeroelastic wing sections with structural nonlinearity based on the immersion and invariance approach. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. A single control surface is used for the purpose of control. It is assumed that the model parameters except the sign of coefficient of control input are unknown. A noncertaintyequivalent adaptive control law for the trajectory tracking of the pitch angle is derived. Using Lyapunov analysis, asymptotic convergence of the state variables to the origin is established. Unlike the certainty-equivalent control laws developed in literature for aeroelastic systems, this new control system can accomplish superior tracking performance. A special feature of the designed control system is that, whenever the estimated parameters coincide with their true values, the adaptation stops and the closed-loop system recovers the performance of deterministic closed-loop system. This cannot happen if certainty-equivalent adaptive controllers are used. Furthermore, the trajectory of the closed-loop system, including the noncertainty-equivalent adaptive law, is eventually confined to a manifold in the space of state variables and parameter estimates. Simulation results using the new controller and the conventional certainty-equivalent controller are presented. These results show that the new controller performs better in suppressing oscillatory responses of the wing in the presence of large parameter uncertainties.