Composite Adaptive Aeroelastic System Control and Multifold Regressor Integrals-based Identification

Abstract

The paper presents a composite adaptive control system for the stabilization and parameter estimation of a multi-input multi-output two degree of freedom aeroelastic system equipped with leading- and trailing-edge control surfaces. The model describes the pitch and plunge motion of a prototypical wing section. The control law consists of a control module and a composite identifier. The novelty of the identifier lies in inclusion of multifold regressor matrix integrals for parameter estimation. Based on the Lyapunov stability analysis, asymptotic convergence of state vector to zero is established. The adaptive system achieves parameter error convergence if a mild initially exciting (IE) condition is satisfied. Interestingly, for the choice of $r$-fold regressor matrix integral, the trajectories of the system converge to $(r+1)$ parameter error-dependent manifolds in an extended state space. Simulation results show the suppression of limit cycle oscillations as well as parameter estimation despite wind gust, and unmodeled actuator dynamics. Furthermore, the results show that parameter error converges faster as the number of regressor integrals increases in the adaptation law.