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Multidimensional control systems have been the subject of much productive research over more than three decades. In contrast to standard control systems, there has been much less reported on applications where the multidimensional setting is the only possible setting for design or produces implementations that perform to at least the same level. This paper addresses the latter area where case studies focusing on control law design and evaluation, including experimental results in one case, are reported. These demonstrate that movement towards the actual deployment of multidimensional control systems is increasing.

This paper considers iterative learning control law design using the theory of linear re-petitive processes. This setting enables trial-to-trial error convergence and along-the-trial performance to be considered simultaneously in the design. It is also shown that this design extends naturally to include robustness to unmodeled plant dynamics. The results from experimental application of these laws to a gantry robot performing a pick and place operation are given, together with a discussion of the positioning of this approach relative to alternatives and possible further research. [DOI: 10.1115/1.4005038]

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In this paper a new approach to iterative learning control for the practically relevant case of deterministic discrete linear plants with uniform rank greater than unity is developed. The analysis is undertaken in a 2D systems setting that, by using a strong form of stability for linear repetitive processes, allows simultaneous consideration of both trial-to-trial error convergence and along the trial performance, resulting in design algorithms that can be computed using Linear Matrix Inequalities (LMIs). Finally, the control laws are experimentally verified on a gantry robot that replicates a pick and place operation commonly found in a number of applications to which iterative learning control is applicable.