Application to Repetitive Control

Abstract

In the early 1980s, Inoue et al. [75,76] and Hara et al. [59,60] laid the foundation of repetitive control. Facing the control problem of asymptotically rejecting periodic inputs of which only the period T_p is known, they relied on the Internal Model Principle [34,45,46,47,48] and included the signal generator shown in Figure 5.1(a) in the controller. This is the most general periodic signal generator as, determined by its initial conditions, it can generate any signal with period T_p. Although the first repetitive controllers were described in continuous-time, the discrete-time repetitive controller design got the upper hand [145,146]. The preference for the discrete-time design stems from the digital controller implementation and the advantage that the discrete-time counterpart of the infinite-dimensional continuous-time signal generator of Figure 5.1(a) is of finite dimension, provided that T_p contains an integer number N of sample periods T_s. Figure 5.1(b) shows the corresponding discrete-time signal generator.