(eng): Iterative learning control is a well established area of research and applications in engineering and more recently healthcare. This form of control is especially suitable for applications where the system is required to make repeated executions of a finite duration task with resetting to the starting location at the end of each execution. The majority of the theory and designs are for systems described by finite dimensional differential or discrete dynamics but there is increasing interest in the extension to systems described by partial differential equations, where the interest in this paper is in the use of approximate finite dimensional models of the dynamics. The construction of such models studied using a regular hexagonal grid and polar coordinates, with a fourth order partial differential equation as an example. A supporting numerical application study is also given.