The Optimal Design of Repetitive Controllers Based on Inverse Frequency Response

This paper presents a complete design of non-causal finite impulse response and infinite

impulse response compensators for repetitive control. The concept of repetitive

controllers involves imitating the inverse frequency response of the feedback control

system by minimizing the amplitude of error propagation from one period to the

next in the frequency domain. The finite impulse response compensator design has

already been presented in our previous work. However, it was not complete since

some parameters, such as the number of causal gains and total number of gains were

still left open for the designers to select. This work provides a reasonable suggestion

on how to choose parameters based on the steepest descent method. In addition, an

infinite impulse response compensator is further developed based on the designed

finite impulse response design. The gains of the infinite impulse response compensator

are adjusted by aiming to minimize the cost function using the steepest descent.

As can be observed from the results, the infinite impulse response compensator developed

from the finite impulse response compensator cannot overcome the original

finite impulse response compensator since its learning performance is relatively slow

and the extra gains added to the denominator increase memory usage when executing.