ON DESIGNING FINITE TIME ITERATIVE LEARNING CONTROL BASED ON STEADY STATE FREQUENCY RESPONSE

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 steady state frequency response. This paper considers the finite time ILC problem addressed using steady state frequency response, comparing two methods recently developed. One adapts for ILC the FIR filter design in RC that mimics the system’s steady state frequency response inverse, creating a filter designed for all frequencies from zero to Nyquist. Adjustment of gains 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, but not for intermediate frequencies. The main aim of the paper is to compare the performance of each approach, and compare the ease of use. The inverse of the frequency response is used in RC to avoid the usually unstable inverse of the discrete time transfer function. Here the use in ILC has the same property, but must also eliminate error during the initial transient phase. The performance and the robustness to model parameter error do not seem to have any significant difference. Both methods can work well converging to zero tracking error. The main distinction is that the adjustment by steepest descent of a small number of gains in the Learning Gain Matrix is easier done in the FIR approach.