Repetitive control design for variable instantaneous frequencies signals

Abstract

Vibration disturbances with variable instantaneous frequencies can be found in many industrial applications. Therefore, rejecting vibration disturbances is a key point for accuracy machining. This paper presents a new method for synthesizing repetitive controllers capable of rejecting variable instantaneous frequencies disturbance. The instantaneous frequencies of the disturbance signal are always consisted of multiple-periods characteristics. Therefore, multiple-periodic repetitive control scheme is obtained and multiple-periods are estimated by Hilbert-Huang transform (HHT). HHT is a way to decompose a signal into so-called intrinsic mode functions, and obtain instantaneous frequency data. It is designed to work well for data that is non-stationary and non-linear. Control performance and stability of the proposed repetitive controller with a multi-periodic disturbance are analyzed and its control scheme can be obtained. The decay rate of the rejecting error due to the multiple-periodic disturbance inputs is related to the peak value of a defined regeneration spectrum function. The control performance of the present method is evaluated in an experimental disturbance rejecting control system. Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.