Abstract
Repetitive controllers (RCs) are known for their ability of controlling periodic exogenous signals, even if these signals have high harmonic content. Due to the variety of repetitive controllers proposed in the literature, which are significantly different from each other, a comparative evaluation in a collective way is analytically complex. This fact implies a greater difficulty to select the appropriate RC strategy when designing a control system, what makes most control system designers to not use this class of controllers. In order to solve this problem, the present paper develops a unified approach for representation of (real and complex) repetitive controllers, which is based on the use of multiple primitive repetitive cells in parallel. Through this approach the main characteristics of a repetitive controller, such as stability properties, dynamic response, set of harmonic components that are effectively compensated and computational burden, are easily identified. Furthermore, in order to validate the potential of the proposed unified approach, comparative studies of nk ±m RCs and nk+m RCs are performed. An experimental application based on a three-phase shunt active power filter is implemented to validate the theoretical evaluation presented in this paper.
Highlights
Due to the increasing demand for solar and wind power sources, a substantial increase in the number of three-phase grid-connected inverters has been noticed in the recent decades
In view of the fact that nk ± m Repetitive controllers (RCs) can be used to control exogenous signals whose harmonic components belong to the union of families H0 = {nk + m | k ∈ Z} and H1 = {nk − m | k ∈ Z}, these nk ± m RC schemes can be represented by two primitive repetitive cell (PRC) in parallel with parameters n0 = n1 = n and m0 = −m1 = m
Besides the nk ± m RCs and the nk + m RCs shown in Fig. 1, the structure of PRCs in parallel presented in Fig. 4 can be used to represent other RC schemes with more specific functions, such as: RCs for controlling only odd harmonics [25]–[27]; the 6k ± 1 RC proposed in [28]; and the conventional RC [21]
Summary
Due to the increasing demand for solar and wind power sources, a substantial increase in the number of three-phase grid-connected inverters has been noticed in the recent decades. Several control strategies have been proposed in the literature in order to regulate the output currents of three-phase inverters, even if the reference signals have high harmonic content. Most of these solutions use linear control structures. When evaluating the comparative studies performed in [3] and [12], it is observed that several recently proposed control schemes were obviously not included in these studies, such as multiple ROGIs in parallel [7] and generic order repetitive controllers (nk ± m RCs and nk + m RCs) [13]–[16].
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