Composite Adaptive Control and Identification of MIMO Aeroelastic System with Enhanced Parameter Excitation

Abstract

This paper develops a composite adaptive control law for the stabilization and parameter identification of a two-degree-of-freedom aeroelastic system, which is equipped with leading- and trailing-edge flaps. The multiple-input multiple-output (MIMO) model represents the plunge and pitch dynamics of a prototypical wing section. It is assumed that all model parameters, except the signs of the principal minors of the input matrix, are unknown. The composite adaptive control system includes a control module and a composite parameter identifier for the estimation of parameters. The parameter estimation law is synthesized using information on the tracking error, as well as on a model prediction error. In addition, unlike works published in the literature for aeroelastic systems, the novelty of this paper lies in the inclusion of a regressor-dependent matrix integral in the parameter adaptation law. By the Lyapunov analysis, it is shown that the origin of the closed-loop system is stable. Interestingly, the regressor matrix’s integral component contributes a negative semidefinite nonincreasing quadratic function of the parameter error in the derivative of the Lyapunov function. This, in turn, enhances the stability and parameter convergence properties of the closed-loop system. Simulation results show that this composite adaptive control system accomplishes simultaneous suppression of limit cycle oscillations (LCOs) and identification of parameters despite gust input, unmodeled actuator dynamics, and time-varying nonlinearity.