Complex $nk + m$ Repetitive Controller Applied to Space Vectors: Advantages and Stability Analysis

Neto, Rafael C.; Neves, Francisco A. S.; Souza, Helber E. P. de

doi:10.1109/tpel.2020.3017735

Cited by 12 publications

(7 citation statements)

References 31 publications

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“…• A constant gain a: This block represents the gain of the PRC's second direct path, which is used to establish a constant proportion between the repetitive action and a proportional action. If the value of the real constant gain a varies, then the control structure and its stability characteristics change [22]. As a matter of fact, as demonstrated in the next section, the controller has its zeros allocation changed when varying this parameter.…”

Section: Primitive Repetitive Cellmentioning

confidence: 97%

“…When re-evaluating the PRC used as basis for the PSRC control scheme [20], a second direct path can be added in parallel to this primitive structure, as done in [21] for the conventional RC. As a result of this approach, Neto et al [18] proposed a generic PRC (which was latter extented in [22]) that is composed by the following elements:…”

Section: Primitive Repetitive Cellmentioning

confidence: 99%

“…Since the generic nk ± m RC presented in Fig. 5 is formed by two configurable PRCs, its stability and performance characteristics can be inferred from the study of the configurable PRCs [22]. In fact, this methodology can be extended to all nk ± m RCs through their decompositions into the generic nk ± m RCs.…”

Section: A Study On Nk ± M Rcs Using the Proposed Structurementioning

confidence: 99%

“…This means that one PRC can be directly used as a complex RC [22]. The transfer function of this generic nk + m RC is…”

Section: B Study On Nk + M Rcs Using the Proposed Structurementioning

confidence: 99%

“…This means that a complex single-input singleoutput controller, whose input and output signals are space vectors, can be represented using a real multi-input multioutput representation, where the input and output signals are the real and imaginary components of the space vector. When doing this, the generic nk + m RC presented in ( 9) can be represented in terms of the inputs e α and e β , and outputs u α and u β , such as the complex RC proposed in [22].…”

Section: Real Axismentioning

confidence: 99%

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Unified Approach to Evaluation of Real and Complex Repetitive Controllers

2021

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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.INDEX TERMS Complex controller, harmonic compensation, repetitive control, stability analysis.

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Section: Primitive Repetitive Cellmentioning

confidence: 97%