Application to Repetitive Control
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 Tp 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 Tp. 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 Tp contains an integer number N of sample periods Ts. Figure 5.1(b) shows the corresponding discrete-time signal generator.
KeywordsRobust Stability Periodic Performance Step Response Optimal Design Problem Repetitive Control
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