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Feedback control systems do not do what you ask. The concept of bandwidth isdefined to tell what components of a command are reasonably well handled.Iterative Learning Control (ILC) seeks to converge to zero error following anygiven finite time desired trajectory as iterations progress. The approach canbe used to achieve high precision tracking in spacecraft sensors performingrepeated highly accurate sensor scanning. ILC asks for zero error for a finitetime tracking maneuver, containing initial transients each iteration. Thepurpose of this paper is to create a method of designing ILC compensators basedon steady state frequency response, and have the ILC converge to zero error inspite of transients and bandwidth. In this work the inverse of the circulantmatrix of Markov parameters is used as a learning gain matrix. One can showthat this matrix gives the steady state frequency response of the system at thefinite number of frequencies observable in the finite data sequence of aniteration or run. Methods are used to adjust the steady state frequencyresponse gains to address the transient part of the error signal. Numericalsimulations compare the design approach to common time domain ILC designapproaches, and one observes much faster convergence.

Modifying and optimizing the inverse of the frequency response circulant matrix as an iterative learning control compensator