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Nonlinear Dynamics and Control for a Structurally Nonlinear Aeroelastic System

This paper studies the stability properties of a class of nonlinear controls derived via feedback linearization techniques for a structurally nonlinear prototypical wing section. In the case in which the wing section has a single trailing edge control surface, the stability of partial feedback linearization to achieve plunge primary control is studied. It is shown that the zero dynamics in this case associated with the closed loop system response is locally asymptotically stable for a range of flow speeds and elastic axis locations. However, there exist locations of the elastic axis and speeds of the flow for which this simple feedback strategy exhibits a wide range of bifurcation phenomena. Both Hopf and pitchfolk bifurcations evolve parametrically in terms of the flow speed and elastic axis location. In the case in which the wing section has two control surfaces, the global stability of adaptive control techniques derived from full feedback linearization is studied. In comparison to partial or full feedback linearization techniques, the adaptive control strategies presented do not require explicit knowledge of the form of the structural nonlinearity.