Abstract
Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO). It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.
Highlights
The response of an aeroelastic system is governed by a combination of linear and nonlinear dynamics
0 kα α α where mT is the total mass of the wing and its support structure, mW is the wing mass alone, Iα is the mass moment of inertia about the elastic axis, b is the half chord length, xα rcg/b is the nondimensionalized distance between the center of mass and the elastic axis, ch and cα are the plunge and pitch structural damping coefficients, respectively, L and M are the aerodynamic lift and moment about the elastic axis, and kh and kα are the structural stiffnesses for the plunge and pitch motions, respectively
Linear and nonlinear controls are implemented on a rigid airfoil undergoing pitch and plunge motions
Summary
The response of an aeroelastic system is governed by a combination of linear and nonlinear dynamics. For the pitch-plunge airfoil, Strganac et al 9 used a trailing edge flap to control a twodimensional nonlinear aeroelastic system They showed that linear control strategies may not be appropriate to suppress large-amplitude LCO and proposed a nonlinear controller based on partial feedback linearization to stabilize the LCO above the nominal flutter velocity. Kang 11 developed a mathematical framework for the analysis and control of bifurcations and used an approach based on the normal form to develop a feedback design for delaying and stabilizing bifurcations. His approach involves a preliminary state transformation and center manifold reduction. This methodology involves the following steps: i reduction of the dynamics of the system into a one-dimensional dynamical system using the method of multiple scales and ii designing a nonlinear feedback controller to convert subcritical to supercritical bifurcations and reduce the amplitude of any ensuing LCO
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