Iteration-domain closed-loop frequency response shaping for discrete-repetitive processes

Building from a recently-presented internal model principle for unit-memory discrete repetitive processes, this paper considers iteration-domain control algorithms to ensure tracking of iteration-varying reference signals with support over a range of iteration-domain frequencies. By lifting the time-domain signals on each pass and applying an iteration-domain complex frequency operator, the discrete repetitive process is transformed into a first-order (in the iteration frequency domain) multivariable system. It is shown that what can be considered “lead-lag” type compensation can be used to shape the maximum singular values of the closed-loop system transfer function, making it possible to track iteration-varying inputs that have prescribed iteration-domain frequency content.