Implementation of repetitive controllers subject to fractional delays

Abstract

Repetitive schemes represent a very attractive solution for harmonics compensation, as they are simple to implement and the computational effort is reduced. Their implementation, usually performed in digital form, involves the interconnection of a single delay line or a simple array of delay lines. In discrete time domain, a delay line is implemented using a given number of memory locations, where samples are allocated and released after a specific number of sampling periods (discrete delay) equivalent to the delay time. This discrete delay is obtained as the ratio between the sampling period and the required delay time. The problem arises whenever the delay time is a noninteger multiple of the sampling period, in this case the discrete delay is a real positive number having a fractional part. This issue is referred in signal processing literature as fractional delay. This paper presents a solution for the practical implementation of repetitive schemes where the delay lines are subject to the fractional delay issue. The solution consists in the introduction, on each delay line, of an additional filter aimed to approximate such a fractional delay. This filter has the structure of a finite impulse response (FIR) filter, and thus, it is referred as FIR fractional delay (FIR-FD) filter. Its design follows a Lagrange interpolation technic, which relays in explicit formulae for the computation of the coefficients of the FIR filter. In particular, the present paper is focused in the repetitive scheme proposed in [11] for compensation of harmonics 6ℓ ± 1 (ℓ = 0, 1, 2, ...∞) of the fundamental frequency . Numerical results are presented to confirm the benefits of the proposed scheme. Experiments are in process and the results will be available in the final version of the paper.

Plug-in direct particle swarm repetitive controller with a reduced dimensionality of a fitness landscape – a multi-swarm approach

“…This means that the problem is not necessarily bound to be defined as (14). It has been illustrated with CACF VSI that for the online swarm-based optimization it is beneficial to redefine the problem into the form of (15) and its lack of equivalence to (14) occurs to be of little importance.…”

“…The multi-oscillatory controllers have also their limitations related to the problematic implementation of oscillatory terms near the controller bandwidth and the computational burden growing with the number of harmonics needed to be rejected. They are also sensitive to phase lags and in high-performance converters it is required to take special measures to compensate for these delays [15].…”

Virtual Variable Sampling Discrete Fourier Transform Based Selective Odd-Order Harmonic Repetitive Control of DC/AC Converters

“…One major limitation of this approach is that it is difficult to implement the complex correction factor in most digital controllers. Non-integer delay length approximated by a finite impulse response (FIR) filter [19]- [24] and linear-phase-lag low-pass filter for fractional delay length compensation [25] were also developed. However, these frequency adaptive methods cannot be applied to the DFTbased selective harmonic RC.…”

Virtual delay unit based digital nk ± m-order harmonic repetitive controller for PWM converter

“….) order power harmonics [11]- [15]. Thus, the selective harmonics compensation controller will be more effective to suppress output distortion.…”