Steady State Frequency Response Design of Finite Time Iterative Learning Control

Steady state frequency response is a major design approach in control theory, and is normally used to obtain reasonable response to commands up to a chosen or obtainable bandwidth. By contrast, iterative learning control (ILC) aims to converge to zero error at all time steps of a finite time tracking task, using an iterative update of the command to a control system. It asks for zero error during the transient as well as steady state response phases. This paper develops a rigorous design approach to apply frequency response to the ILC problem. The gains in an FIR compensator from repetitive control are used to fill the ILC learning gain matrix. The compensator mimics the inverse frequency response. This paper does not ask for zero error for one or more initial times steps, in oder to address a well posed problem that is not trying to converge to an unstable command input. It is seen that by adjusting just one gain in the upper left corner of the learning matrix, the ILC can be stabilized in spite of the length of time involving transients. This makes a very simple design process. One can also adjust two gains in the first row, or better a two-by-two block, but further adjustment seems of limited benefit. The frequency based ILC design developed here is compared to existing ILC design methods, and shown to be vastly superior in convergence rate. It also has the advantage that the ILC can be designed directly from frequency response test data without creating a mathematical model.