ℒ1 adaptive control of an aeroelastic system with unsteady aerodynamics and gust load

Abstract

This paper presents the design of an ℒ1 adaptive control system for the stabilization of a two-dimensional aeroelastic system with structural nonlinearities and unsteady aerodynamics, using a single trailing-edge control surface. This model describes the plunge and pitch motion of a prototypical wing. It is assumed that its parameters are unknown and external disturbances are present. The unsteady aerodynamics are modeled with an approximation to Theodorsen's theory. The system exhibits limit cycle oscillations beyond a critical speed. Based on the ℒ1 adaptive control theory, a control law is developed for the trajectory control of the integral of the pitch angle. The control system includes a state predictor, a projection algorithm-based adaptation law designed based on the Lyapunov method, and a stabilizing control law. For the synthesis of the control law only the pitch angle and its derivative are measured. Simulation results show that in the closed-loop system, the aeroelastic vibrations are suppressed, despite parametric uncertainties and gust loads. Furthermore the performance limits of this ℒ1 adaptive law with respect to the freestream velocity and strength of gust load are examined.