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Second-order odd-harmonic repetitive control and its application to active filter control

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Second-Order Odd-Harmonic Repetitive Control and Its Application to Active Filter Control Second-order odd-harmonic repetitive control and its application to active filter control Ramon Costa-Castello´, Germa´n A. Ramos, Josep M. Olm, Maarten Steinbuch Abstract— High order repetitive control has been introduced to overcome performance decay of repetitive control systems under varying frequency of the signals to be tracked/rejected or improving the interhamonic behavior. However, most high order repetitive internal models used to improve frequency uncertainty are unstable, as a consequence practical imple- mentations are more difficult. In this work a stable, second order odd-harmonic repetitive control system is presented and studied. The proposed internal model has been implemented and validated in a shunt active filter current controller. This high order controller allows dealing with the grid frequency variations without using adaptive schemes. I. INTRODUCTION Repetitive Control [1], [2] is a well established, Internal Model Principle [3] based technique which allows track- ing/rejecting periodic signals of known frequency. Unfortu- nately, its performance decays dramatically when the signal frequency varies [4]. In order to overcome this problem two major approaches have been proposed. The first one is based on the adaptation of the sampling period in accordance with the signal frequency variation. Although this approach offers good results [5], [6], [7] it implies introducing frequency observers and moving the stability analysis from a Linear Time Invariant framework into a Linear Time Varying one. The second approach is based on the introduction of higher order internal models [8], [4]. The parameters of these high order controllers can be tuned according to different criteria: most of them are related with making the internal model robust in front frequency variations [9], [4], or with a trade- off between this robustness issue and amplification of non- harmonic freque

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