Modifications to repetitive-based controllers using FIR filters for practical implementation

In this paper some modifications are proposed for the practical implementation of repetitive-based schemes used to compensate harmonic distortion. In a practical implementation, the repetitive schemes required both, to limit the gain originally infinite, and to restrict the bandwidth (BW) of the controller originally of infinite dimension. In general terms, each delay line in the repetitive scheme has an associated limiting gain and a low pass filter (LPF). However, it has been observed that this practical modifications can produce a considerable phase shift at the frequencies of interest. As a consequence, the compensation of harmonics cannot be guaranteed anymore. One possibility to compensate such a phase shift consists in the modification of the delay time in the delay line of the repetitive scheme. However, in the case of conventional LPFs, the phase shift is usually a nonlinear function of the frequency, which makes this task very difficult. To overcome this issue, this paper proposes the use of low pass FIR filters, whose phase shift can be made linear by following appropriate design rules. Notice that a low pass FIR filters with a linear phase shift produces a constant delay time, which is much easier to compensate. Numerical results are provided to illustrate the benefits of the modified schemes.