Design and analysis strategies for digital repetitive control systems with time-varying reference/disturbance period

This article introduces and analyzes the performance features of different design schemes for digital repetitive control systems subject to references/disturbances that exhibit non-uniform frequency. Aiming for the maintenance of a constant value for the ratio Tp/Ts, where Tp is the period of the reference/disturbance signal and Ts is the sampling period, two approaches are proposed. The first one deals with the realtime adaptation of Ts to the actual changes of Tp; the stability issue is studied by means of an LMI gridding method and also using robust control techniques. The second one propounds the introduction of an additional compensator that annihilates the effect of the time-varying sampling in the closed-loop system and forces its behavior to coincide with the one corresponding to an a priori selected nominal sampling period; the procedure needs the internal stability of the compensator-plant subsystem, which is checked by means of LMI gridding. The theoretical results are experimentally tested and compared through a mechatronic plant model.