Convergence characteristics of PI-type iterative learning control for linear time-invariant systems
The paper exploits the convergence characteristics of the first- and second-order PI-type iterative learning control (ILC) schemes for linear time-invariant (LTI) systems with direct-through terms. The aim is to investigate the effects of the integration embedments into the conventional P-type ILC rule. In the exploitation, the tracking errors are assessed in the form of the Lebesgue-p norm and the convergences are derived in virtue of the generalized Young inequality of convolution integral. The derivations convey that the convergence monotonicities are guaranteed for the first-order PI-type ILC. At the same time, the convergence is ensured for the case when the second-order PI-type ILC is implemented on the systems. Numerical simulations testify the validity and of the proposed schemes.