A new repetitive control scheme based on non-causal FIR filters

Repetitive Control (RC) is a popular technique for tracking periodic signals and rejecting periodic disturbances. Repetitive control achieves accurate tracking of periodic trajectories by incorporating a periodic signal generator within the feedback loop. The periodic signal generator provides an infinite loop-gain at the harmonic frequencies of the reference signal. However, this scheme cannot be used in isolation due to challenges with stability and robustness. The stability and robustness can be improved by incorporating appropriate filters. However, there is a trade-off between robustness and tracking performance. The current state-of-the art is to implement plant inversion and include phase compensators to improve the high-frequency tracking performance. In this work, a RC controller is combined with a non-causal FIR filter to improve the tracking performance without the requirement for phase compensators or plant inversion. The performance of the proposed RC design is demonstrated on a piezoelectric positioner.