Discrete frequency based learning control for precision motion control

Concerns MIMO learning control design with well behaved transients during the learning process. The method allows dynamic and inverse dynamic control laws. The theory gives a unifying understanding of the stability boundary for convergence to zero tracking error, and of a stability condition obtained by using frequency response arguments. The former is easy to satisfy, making learning control converge with little knowledge of the system. The much more restrictive frequency response condition is interpreted as a robustness condition, representing the robustness relative to good transient behavior during learning. This ensures that the amplitudes of the frequency components of the error signal decay in a monotonic and geometric manner with each successive repetition. Noncausal zero phase filtering is used both to facilitate the generation of learning controllers having this convergence at important frequencies, and to ensure that the learning controllers maintain this property in the presence of unmodeled dynamics. The approach is in discrete time. Experiments are performed on a 7 degree-of-freedom robot, demonstrating the effectiveness of the design process for producing precision motion control