Necessary and Sufficient Conditions for Harmonic Control in Continuous Time

• 成果类型: Article
• 署名作者: Blin, Ncolas; Riedinger, Pierre; Daafouz, Jamal; Grimaud, Louis; Feyel, Philippe
• 署名单位: Universite de Lorraine; Safran S.A.; Safran S.A.
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3117540
• 发表日期: 2022
• 页码: 4013-4028
• 关键词: Harmonic analysis; Power system harmonics; Time-domain analysis; Aerospace electronics; mathematical models; control design; Power system stability; Bilinear affine systems; dynamic phasors; harmonic modeling and control; Lyapunov harmonic equations; power converters; repetitive control; Riccati harmonic equations; sliding fourier decomposition

摘要

In this article, we revisit the concepts and tools of harmonic analysis and control and provide a rigorous mathematical answer to the following question: When does an harmonic control have a representative in the time domain? By representative we mean a control in the time domain that leads by sliding Fourier decomposition to exactly the same harmonic control. Harmonic controls that do not have such representatives lead to erroneous results in practice. The main results of this article are: A one-to-one correspondence between ad hoc functional spaces guaranteeing the existence of a representative, a strict equivalence between the Caratheorody solutions of a differential system and the solutions of the associated harmonic differential model, and as a consequence, a general harmonic framework for linear time periodic systems and bilinear affine systems. The proposed framework allows to design globally stabilizing harmonic control laws. We illustrate the proposed approach on a single-phase rectifier bridge. Through this example, we show how one can design stabilizing control laws that guarantee periodic disturbance rejection and low harmonic content.