Feedback control of vibrations in an extendible cantilever wing

The vibrations of a cantilever wing which may extend or contract during flight are studied. A mathematical model for the coupled bending and torsional vibrations of an extendible wing is developed. It is found that the extending or contracting motion of the wing has a stabilizing or destabilizing effect on the wing vibrations respectively. A Galerkin-type approximation based on an appropriate time-dependent basis for the solution space is used to obtain an approximate finite-dimensional model for simulation studies. A simple implementable nonlinear feedback control for damping the motion-induced vibrations is derived by considering the time rate-of-change of the total vibrational energy of the wing. Simulation studies show that the proposed control law is effective in reducing the peak amplitude of the motion-induced vibrations.