Normalized Learning Rule for Iterative Learning Control

The iterative learning control (ILC) is attractive for its simple structure, easy implementation. So the ILC is applied to various fields. But the unexpected huge overshoot can be observed as iteration repeat when we use the ILC to the real world applications. Such bad transient becomes an obstacle for using the ILC in the real field. Designers use a projection method to avoid the bad transient usually. However, the projection method does not show a good error performance enough. Therefore we propose a new learning rule to reduce such a bad transient effectively. The simple normalized learning rules for P-type and PD-type are presented and we prove their convergence. Numerical examples are given to show the effectiveness of the proposed learning control algorithms.