|Repetitive Control Design for Variable Instantaneous Frequencies Signals
International Journal of Control, Automation, and Systems, vol. 15, no. 2, pp.689-697, 2017
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."
Disturbance rejecting control, multiple-period, regeneration spectrum, repetitive controller.
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