Iterative learning control design inspired by repetitive control

Discrete-time domain iterative learning control (TLC) design schemes inspired by repetitive control algorithms are proposed and analyzed. The well known relation between a filter and its Markov Toeplitz matrix representation has been exploited in previous ILC literature. However, this connection breaks down when the filters have anticausal components. In this paper, we provide a formal representation and analysis that recover the connections between anti-causal filters and Toeplitz matrices. This tool is then applied to translate the anti-causal zero-phase-error compensation used in designing the so called prototype repetitive control scheme to the design of stable and fast converging ILC. The learning filters are chosen such that the resulting system matrix has a band limited Toeplitz (BLT) structure. Several conditions for iteration convergence are derived. Particularly, it is shown that the well known sufficient condition for repetitive control based on filter´s frequency domain H_∞ norm is also sufficient for ILC convergence and that the condition becomes necessary as the data length approaches infinity. Thus the resulting ILC matrix design can be translated to repetitive control loop shaping filter design in the frequency domain.