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A tracking problem is considered for a very recurring class of systems, such as Cartesian robots with real actuators, conveyor belts, and certain scanning devices used for medical and engineering applications, as near-field antenna characterization. Theorems are proven for the design of a PID controller with a possible compensation signal to track sufficiently regular trajectories with a prescribed maximum error. The developed design methodology is used to identify the current antenna scanning system without a controller and to design and construct a new controller that provides better performance than the current one. Moreover, this paper proposes an optimized raster scan acquisition scheme that reduces the number of field samples and the scanning path length compared with the more conventional approaches. By using the new controller and the proposed optimized sampling strategy, which provides a sparse distribution of the samples, the performance of an antenna can be evaluated in a considerably shorter time than that necessary using the pre-existing controller and standard scanning, as experimentally assessed in this paper.