Design of an iterative learning controller for a class of linear dynamic systems with time delay

In the paper, it is first observed that when a typical iterative learning control (ILC) algorithm is applied to a class of linear dynamic systems with time delay, erratic estimation of delay time may cause the control input to diverge. To resolve such a difficulty due to uncertainty of the delay time, a new ILC algorithm is proposed in which a holding mechanism is adopted to hold the control input at a constant value for the duration of the delay time uncertainty. As a consequence, the output of the system tracks a given desired trajectory at the discrete points which are spaced by the size of the uncertainty of delay time. A numerical example is given to show the effectiveness of the proposed algorithm