Abstract
The repetitive control is a control scheme, in which the controlled variables follow the periodic reference commands with high accuracy under disturbance input with the same periods. The asymptotic tracking property can be achieved by locating the model 1/(1-exp(-Ls)), which generates a set of periodic signals with period L, in the closed-loop system. The error convergence condition, or the stability condition, is derived by applying the small gain theorem to an equivalent system of the repetitive control system. This condition is closely related to the generalized frequency domain optimality inequality for the Kalman filter and the optimal regulator. A synthesis algorithm using the methods of the Kalman filter and the parfect regulation is presented based on the derived stability condition. Furthermore, we propose a realizable repetitive control system with specified stability margins, which tracks only for periodic signals with lower freqency band, and properties such as error convergence, steady-state error, sensitivity and robustness are discussed.
