  Iterative Learning Control (ILC) is useful in spacecraft application for
repeated high precision scanning maneuvers. Repetitive Control (RC) produces
effective active vibration isolation based on frequency response. This paper
considers ILC designed from frequency response, comparing two methods recently
developed. One adapts for ILC the FIR filter design in RC that mimics the
systems steady state frequency response inverse, creating a filter designed for
all frequencies from zero to Nyquist. Adjustment of gains must near the
beginning of the matrix need to be made because FIR gains are truncated there.
The other approach uses a circulant matrix obtained from the Toeplitz matrix of
Markov parameters. It is shown to give steady state frequency response for the
discrete frequencies that can be seen in the number of time steps in the ILC
tracking problem. The main aim is to compare their performance and ease of use.
A second aim is to learn from successful ILC designs to enhances stability
robustness of the two methods. Finally, the use of an ILC frequency cutoff is
studied as an alternative method to eliminate instability of the control action
in the converged zero tracking error solution of many ILC problems.
