Iterative learning control for the linear model with a singular feedthrough term via LQAT

In this paper, we propose an iterative learning control (ILC) strategy for the continuous-time linear time-invariant (LTI) model with a singular feedthrough term, from input to output. By combining with the linear quadratic analogue tracker (LQAT), the transient performance improvement is achieved through the initial control input, at the 0th iteration, obtained by the LQAT. Initially, we propose the PD-type iterative learning controller together with initial statelearning law, and sufficient condition to guarantee the convergence of tracking error is derived. Thereafter, a novel LQAT, with a high-gain property, for the model under consideration is constructed. The role of LQAT is to obtain first (initial) control input of the ILC scheme. A numerical example illustrates the effectiveness of the proposed strategy.