Active Control with the Acceleration Feedback on a Parametrically Excited System

The control of a buckled beam subjected to a parametric excitation is considered. The active control with acceleration feedback is applied to suppress the unaccepted large vibration. A parametrically excited system is considered as an initial model. The acceleration feedback is applied to control erosion of safe basins in the nonlinear system. The mechanism of the evolution of the dynamics is studied analytically by the Melnikov function method. And the evolutions of boundary and nature of safe basins with time delay are presented numerically by the 4th Runge-Kutta and Monte-Carlo methods. It is found that the acceleration feedback can be used as a good approach to increase the safe probability of the structure.