Variable Structure Control of Unsteady Nonlinear Aeroelastic System with Partial State Information

Abstract

This paper treats the question of control of a two-degree-of-freedom unsteady aeroelastic system with partial state information in the presence of uncertainties. The chosen model describes the plunge and pitch motion of a wing and a single trailing-edge control surface is utilized for the purpose of control. Based on the Lyapunov approach, a variable structure control law is derived. For the control law derivation, the system is treated as the interconnection of two subsystems in which the subsystem associated with the unsteady aerodynamics is input-to-state stable. The stability property of this subsystem is exploited to generate a dominating signal for feedback; thereby, the problem of state estimation of the subsystem describing the unsteady dynamics is avoided. In the closed-loop system, the pitch angle trajectory tracks reference trajectory and the state vector converges to the origin. The designed variable structure control system is simple compared to adaptive controllers and is synthesized easily using only the measured states. Moreover, the structure of the controller is independent of the dimension of subsystem associated with the unsteady aerodynamics. This is important because in literature this subsystem of varying order has been considered. Simulation results are presented which show that in the closed-loop system, regulation of the plunge and pitch trajectories are accomplished in spite of the uncertainties in the freestream velocity and elastic axis location.