Frequency domain analysis for suppression of output vibration from periodic disturbance using nonlinearities

A frequency domain approach is proposed to suppress output vibration from periodic exogenous disturbances for SISO systems by using nonlinear feedback. Based on the frequency domain theory of nonlinear Volterra systems, the analytical relationship between system output frequency response and controller parameters is obtained, and a series of associated theoretical results and techniques are discussed for the purpose of nonlinear feedback analysis and design. It is shown that a low degree nonlinear feedback may be sufficient for some control problems. A general procedure is provided for this frequency domain analysis and design. This paper provides a systematic frequency domain approach to exploiting the potential advantage of nonlinearities to achieve a desired frequency domain performance for active/passive vibration control or energy dissipation systems. The new approach is demonstrated through an analysis and design of a nonlinear feedback for a simple vibration control system. By properly introducing a simple nonlinear damping to the system, the performance of the system output response when subject to a periodic disturbance is improved, compared with a linear damping controller.