Adaptive feedback linearization for the control of a typical wing section with structural nonlinearity

Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salle's invariance principle.