Nonlinear Control Theory for a Class of Structural Nonlinearities In a Prototypical Wing Section

With the increase in popularity of active materials for control actuation, renewed interest is evident in the derivation of control methodologies for aeroelastic systems. It has been known for some time that prototypical aeroelastic wing sections can exhibit a broad class of pathological response regimes when the system includes certain types of nonlinearities. In this paper, we investigate nonlinear control laws for aeroelastic systems that include polynomial structural nonlinearities, and study the closed loop stability of the system. It is shown that locally asymptotically stable (nonlinear) feedback controllers can be derived for the aeroelastic system using partial feedback linearization techniques. In this case, the stability results are necessarily local in nature and are derived by considering stability of the associated zero dynamics subsystem. It is also demonstrated that globally stable (nonlinear) adaptive control methods can be derived for a class of aeroelastic systems under consideration. Numerical simulations are used to provide empirical validation of some of the results in this paper.

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