Active nonlinear saturation-based control for suppressing the free vibration of a self-excited plant

A nonlinear saturation-based control strategy for the suppression of the free vibration of a self-excited plant is presented. The self-excitation to have the classical form of that of the van der Pol oscillator is considered. The control technique is implemented by coupling the active absorber with the plant via a specific set of quadratic nonlinearities. The perturbation method of multiple scales is employed to find the first-order approximate solutions to the governing equations. Then a stability analysis is conducted for the response of the system and the performance of the control strategy is investigated. A parametric investigation is carried out to see the effects of changing the damping ratio of the absorber, and the value of the feedback gain on the responses of the plant and the absorber. Finally, the perturbation solutions are verified by numerical integration of the governing differential equations. It is demonstrated that the saturation-based control method is effective in reducing the vibration response of the self-excited plant when the absorber’s frequency is exactly tuned to one-half the natural frequency of the plant.