Chaotic Motion in a Flexible Rotating Beam and Synchronization

Abstract

A rotating flexible beam undergoing large deformation is known to exhibit chaotic motion for certain parameter values. This work deals with an approach for control of chaos known as chaos synchronization. A nonlinear controller based on the Lyapunov stability theory is developed, and it is shown that such a controller can avoid the sensitive dependence of initial conditions seen in all chaotic systems. The proposed controller ensures that the error between the controlled and the original system, for different initial conditions, asymptotically goes to zero. A numerical example using the parameters of a rotating power generating wind turbine blade is used to illustrate the theoretical approach.