Asymptotic rejection of periodic disturbances with fixed or varying period

A constructive derivation of repetitive control is obtained, through attemp ting to derive a control law for asymptotic rejection of periodic disturban ces. This derivation not only reveals a close relationship between iterativ e operator inversion and repetitive control, but also suggests a unified de sign method for a learning control algorithm. Also, based on the observatio n, digital repetitive control can be generalized to reject periodic disturb ance whose period is not exactly an integer multiple of the sampling interv al, This study introduces a delay filter in the digital repetitive control law, which optimally interpolates the signal between samples, thus effectiv ely reconstructing the signal of the previous period and making the learnin g process of repetitive control successful. The proposed optimal delay filt er can be updated easily according to different signal periods. Thus it is specifically suitable for on-line timing when the signal period is changing . Compared with the available tuning methods, the proposed tuning method ha s excellent steady-state performance while maintaining fast transient and s ystem robustness. The simulations on active noise cancellation within a duc t confirm the superiority of this tuning method.