Frequency-domain approach to robust iterative learning controller design for uncertain time-delay systems

This paper deals with the robust iterative learning control (ILC) for time-delay systems (TDS) with both model and delay uncertainties. An ILC algorithm with anticipation in time is considered, and a frequency-domain approach to its design is presented. It shows that a necessary and sufficient convergence condition can be provided in terms of three design parameters: the lead time, the learning gain, and the performance weighting function. In particular, if the lead time is chosen as just the delay estimate, then the convergence condition is derived independent of the delay and the uncertainties. In this case, with the selection of the performance weighting function, the perfect tracking can be achieved, or the least upper bound of the L-2-norm of the limit tracking error can be guaranteed less than the least upper bound of the L-2-norm of the initial tracking error.