All-pass filtering in iterative learning control

In iterative learning control (ILC), it is highly desirable to have a learning compensator with a unit-gain for all frequencies, in order to avoid noise amplification and learning speed degradation during the learning process. In this paper, we show that the realization of a unit-gain compensator is straightforward in ILC, using both forward and backward filtering. As an illustrative example, a unit-gain derivative is proposed to overcome the drawbacks of the conventional derivative. The proposed scheme is equivalent to an all-pass unit-gain phase shifter; the forward filtering uses a 0.5-order derivative and the backward filtering employs a 0.5-order integral. The all-pass phase shifter is deployed in a unit-gain D-type ILC. The advantages of the unit-gain feature are demonstrated by some experimental results on a robot manipulator.