Control of a Nonlinear Wing Section Using Leading- and Trailing-Edge Surfaces

Abstract

The control of nonlinear aeroelastic response of a wing section with a continuous stiffening-type structural nonlinearity is examined through analytical and experimental studies. Motivated by the limited effectiveness of using a single, trailing-edge control surface for the suppression of limit-cycle oscillations of a typical wing section, improvements in the control of limit-cycle oscillations are investigated through the use of multiple control surfaces, namely, an additional leading-edge control surface. The control methodology consists of a feedback linearization approach that transforms the system equations of motion via Lie algebraic methods and a model reference adaptive control strategy that augments the closed-loop system to account for inexact cancellation of nonlinear terms due to modeling uncertainty. Specifically, uncertainty in the nonlinear pitch stiffness is examined. It is shown through simulations and experiments that globally stabilizing control may be achieved by using two control surfaces. Nomenclature a = nondimensional distance from midchord to elastic axis position b = semichord of wing section= pitch cam moment of inertia I cg − wing = wing section moment of inertia about the center of gravity I α = total pitch moment of inertia about elastic axis k h = plunge stiffness m T = total mass of pitch-plunge system m wing = mass of wing section m W − tot = total wing section plus mount mass r cg = distance from elastic axis to center of mass s = wing section span U = freestream velocity x α = nondimensional distance from elastic axis to center of mass α = angle of attack β = trailing-edge control surface deflection γ = leading-edge control surface deflection ρ = air density

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