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In this paper, a multirate cyclic pseudo-downsampled iterative learning control (ILC) scheme is proposed. The scheme has the ability to produce good learning transient for trajectories with high frequency components and/or initial state errors. The proposed scheme downsamples the feedback error and input signals every m samples to arrive at slow rate signals. Then, the downsampled slow rate signals are applied to ILC algorithm, whose output is then interpolated and applied to actuator. The novelty of the proposed scheme is that, for two successive iterations, the signal is downsampled with the same m but the downsampling points are time shifted along the time axis. This shifting process makes the ILC scheme cyclic along the iteration axis with a period of m cycles. Stability and robustness analysis shows that good learning transient can be guaranteed. Simulation results show significant tracking accuracy improvement. Additional advantages are that the proposed scheme does not need a filter design and reduces the computation load and memory size substantially. The proposed scheme can be applied to the control of other rotatory machinery.