Aeroelastic Linear Model Reference Adaptive Controllers and Robustness to Gust and Nonlinearity

The paper presents three simple linear model reference adaptive control (MRAC) laws for the output trajectory control of a 2-DOF nonlinear aeroelastic system perturbed by wind gust using a trailing-edge flap. All the wing model parameters (except the sign of high frequency gain) are assumed to be unknown. The objective is to track the output of a reference model by the selected output of the wing model. Unlike the published adaptive aeroelastic control systems, the first MRAC system includes a gradient-based normalized parameter estimation law, which is designed using a bilinear static parametric model (B-SPM). The second adaptive control law is derived using a bilinear state-space parametric model (B-SSPM) of the tracking error dynamics. Each of these two state feedback control systems achieves reference output trajectory tracking. Finally, the MRAC systems designed based on B-SPM and B-SSPM are combined to obtain a new composite model reference control (CMRAC) system for the output trajectory control. Lyapunov method is used to establish signal boundedness and the convergence of the tracking error. Simulation results are presented which show robust performance of the three MRAC laws despite parameter uncertainties, wind gust, and unmodelled structural nonlinearity. Interestingly, by a simple change of the output matrix, trajectory control of the output variable (pitch angle, plunge displacement, or linear combination of pitch angle and plunge displacement) can be accomplished, if the transfer function of the wing section model is minimum-phase.