Iterative Learning Control with Input Shift

Iterative learning control (ILC) is a technique to realize system inversion in a run-to-run manner. Though most of the techniques presented in the literature consider zero tracking error between the desired and achieved outputs, perfect inversion is often not feasible and in many cases not even desirable. Approximate inversion with good convergence and robustness properties (at the cost of a nonzero tracking error) has been proposed by using a forgetting factor on the input of the previous run. In this paper, approximate inversion is achieved by shifting the input of the previous run backwards in time. In addition, anticipatory ILC and current cycle feedback are used. The advantage of input shift over the use of a forgetting factor is that, when the reference trajectory is constant and the system stable, the tracking error decreases with run time. The proposed scheme is illustrated in simulation on a batch distillation system.