On the design of ILC schemes for finite frequency range tracking specifications

Many industrial systems perform the same task over a finite duration. For example, a robot placing objects on a conveyer where the exact sequence of operations is collect an object from a given location, transfer it over a finite time, place it on a moving conveyor and then return to the same location for the next one and so on. Iterative learning control emerged as a setting for controller design in such cases where information from previous executions, also termed trials, is used to update the control signal to be used on the next trial and thereby sequentially improve performance. Control laws designed in this setting can be activated in a number of ways, one of the most common is feedforward from the previous trial to track a specific reference signal or reject a repeating disturbance. Another option is to combine the feedforward term with feedback action on the current trial. For plants with linear dynamics, the learning filter, termed the L-filter in some of the literature, is a common approach to guarantee convergence in the trial-to-trial direction and is often combined with a robustness filter, termed the Q-filter in some literature. In this paper, we use the generalized Kalman-Yakubovich-Popov lemma to design the L and Q filters over a finite, as opposed to the complete, frequency range which is more practically relevant in many cases.