Multiple Attractor Dynamics in Active Flutter Suppression Problem
by
M G Goman
De Montfort University, Leicester, UK
Coauthors: M N Demenkov

An active stabilization of flutter instability was investigated using mathematical model for two degree-of freedom aeroelastic airfoil system with trailing and leading edge flaps. A number of control laws based on LQR, linear eigenstructure assignment and nonlinear dynamic inversion methods have been analysed. The open-loop aeroelastic airfoil system following the onset of linear flutter instability exhibits limit cycle oscillations due to nonlinearities in the torsional and/or bending stiffness. The dynamic properties of the closed-loop system were investigated using a systematic search method for all possible equilibrium solutions and the continuation of limit cycles by application of the numerical continuation package MATCONT. A computational analysis revealed that multiple attractors can coexist in the closed-loop system. These multiple attractors include a stabilized equilibrium, transformed open-loop limit cycle oscillations with large amplitude and asymmetrical equilibria or asymmetrical oscillations with small amplitude, induced by feedback control law. The size of region of attraction of a stabilized equilibrium depends on the size of unstable saddle-type limit cycle and may be dramatically reduced due to onset of additional asymmetrical equilibrium solutions. The computational analysis showed that for a global stabilization of flutter instability a designed control law should annihilate or destabilize the open-loop limit cycle and prevent the onset of asymmetrical equilibria.

Date received: April 9, 2008