Abstract
This paper continues the development of an iterative learning control law for a class of spatially distributed systems based on the particular case of a circular deformable mirror. This system is described by a fourth-order partial differential equation but in many cases the design and implementation of control laws is based on a discrete model. In this paper, an unconditionally stable finite difference scheme motivated by the well-known Crank–Nicolson discretization and a regular hexagonal grid is used. In previous work, a model discrete in time and space together with an iterative learning control law design have been developed for this problem area but the control input was assumed to be a spatial variable, which is a serious obstacle to practical implementation since a large number of actuators must be deployed. To improve the applicability of this approach, a design based on a spatially homogeneous excitation at the optimally selected mirror subarea is developed. A simulation-based case study is provided including a comparison with previously published designs.
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