Application of Fourier basis design for Iterative Learning and Repetitive Control

Lifted system description in Fourier basis is discussed for analysis and design of linear, cycle invariant Iterative Learning (ILC) and Repetitive Control (RC). ILC and RC can be bridged within an algebraic vector notation utilizing an infinite time Fourier basis model. This model allows a very illustrative, decoupled controller design for ILC and RC. To complete the bridging, it is shown that an internal model description for RC can be derived from the vector notation. However, some approximations in modeling are required. Therefore, the validity of the Fourier basis model is discussed and a q-filter design is recommended. The study closes with simulation and experimental results.