Transient response of repetitive control systems

Upper bounds on transient response magnitudes for a SISO continuous-time repetitive control system are derived. The need to limit the size of transients is shown to translate to limiting the amplitude ratio of the frequency response of a certain filter in the repetitive controller. The decay rate of the transients is related to the peak of a function of frequency called the regeneration spectrum, which has previously been shown in the literature to be a measure of the relative stability of the system. Bounds derived here, although conservative, can be useful in the design of the repetitive controller, as illustrated by means of an example.