Filters With Linear-Phase Properties for Repetitive Feedback

This paper proposes some modifications aimed for the practical implementation of repetitive-based schemes used in harmonic distortion compensation schemes. Practical implementation of repetitive schemes requires both to limit the gain originally infinite and to restrict the bandwidth of the controller originally of infinite dimension. Roughly speaking, each delay line in the repetitive scheme must include 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 deterioration consists in modifying the delay time associated to the delay line of the repetitive scheme. However, in the case of conventional LPFs, this phase shift is usually a nonlinear function of the frequency, which makes this task extremely difficult if not impossible. To overcome this issue, this paper proposes the use of low-pass finite impulse response filters, whose phase shift can be made linear by following appropriate design rules. The idea behind this approach is that an LPF with a linear phase produces a constant delay time, which is much easier to compensate in the delay line. Experimental results are presented to confirm the benefits of the proposed scheme.