ILC Learning filter synthesis based on frequency response coefficients, application to a piezo shaker

Many control systems in the practical environment perform repetitive tasks. For this class of tasks, ILC has proven to be a successful approach to acquire a feedforward signal that results in high performance, i.e., a small tracking error. In this work, the continuously repeating behavior of signals is exploited to acquire a time-domain input-output mapping of the process-sensitivity based on frequency response coefficients, i.e. omitting the parametrization step of the plant. Using this mapping, the optimal iterative update law with respect to a general quadratic criterion is obtained. The link with the frequency domain is exploited to impose both time-domain as well as frequency domain weighting on: the error, the feed-forward signal and the change of the feed-forward signal. The proposed approach is practically evaluated on a piezo shaker application.