Iterative Learning Control Approach to a Diffusion Control Problem in an Irrigation Application

In this paper we consider an iterative learning control-based approach to controlling a periodic distributed parameter system. The problem arises in the real-time control of flow rate in a center pivot irrigator used in dry-land farming. The system is modeled as a spatial-temporal diffusion process in three spatial dimensions coupled with flow in one dimension. First, a distributed parameter model of the process is presented. Then a finite differences approximation of the process is developed, after which an iterative learning controller is developed to regulate the maximum value of the measured variable over a single period of the irrigator´s motion. It is shown via simulation that the strategy can successfully generate the correct flow rates, even in the presence of regionally-varying diffusion rates