Internal model principle for discrete repetitive processes

An approach is given for designing feedback controllers for unit memory discrete repetitive processes subject to iteration-varying reference signals. Using a lifting technique and defining an iteration-domain complex frequency operator, the two-dimensional single-input, single-output plant is changed into a one-dimensional multivariable system. Then, an internal model principle is given that ensures perfect tracking along-the-pass and asymptotically-convergent tracking along the iteration axis. The result requires the unstable iteration domain poles of the reference signal to be incorporated into the pass-to-pass update law. A key implication of this result is that for some discrete repetitive process problems it is necessary to use nonunit memory in the feedback controller.