Patent ID: 7904495

Claim:
A repetitive controller with negative feedback and feedforward, the repetitive controller including: a first adder, a second adder, and a time delay circuit for imparting a time delay, wherein the first adder receives an input periodic signal inputted into the controller for compensation and also receives a feedback signal, wherein the first adder outputs a first output signal corresponding to a subtraction of the feedback signal from the input periodic signal, wherein the second adder receives the first output signal and a feedforward signal, wherein the second adder outputs a controller output signal, the controller output signal corresponding to a subtraction of the feedforward signal from the first output signal and the controller output signal corresponding to the input periodic signal after being compensated by the repetitive controller, wherein the feedforward signal corresponds to the first output signal delayed by the time delay circuit, wherein the feedback signal corresponds to the first output signal delayed by the time delay circuit, wherein the controller further applies a gain factor of K, wherein the feedforward signal corresponds to the first output signal delayed by the time delay circuit and modified by the gain factor of K, wherein the feedback signal corresponds to the first output signal delayed by the time delay circuit and modified by the gain factor of K, wherein the application of the gain factor of K adds damping to the repetitive controller by slightly shifting all poles and zeros of a transfer function of the repetitive controller to a location on an s-plane that is left of an imaginary axis of the s-plane, such that a peak amplitude becomes bounded and, in effect, the gain factor of K is applied, and wherein resonant peaks of the transfer function as displayed in a Bode plot reach a maximum magnitude of (1+K)/(1−K), and notches of the transfer function as displayed in the Bode plot reach a minimum magnitude of (1−K)/(1+K) when 0<K<1.