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Main Authors: Chen, Shen, Liu, Chaohou, Yao, Wei, Wang, Jisong, Guo, Shuaipo, Liu, Zeng, Liu, Jinjun
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.09549
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author Chen, Shen
Liu, Chaohou
Yao, Wei
Wang, Jisong
Guo, Shuaipo
Liu, Zeng
Liu, Jinjun
author_facet Chen, Shen
Liu, Chaohou
Yao, Wei
Wang, Jisong
Guo, Shuaipo
Liu, Zeng
Liu, Jinjun
contents In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $αβ$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods, the proposed method consists of two factors, i.e., shape factor ($α$) and time factor ($β$). Depending on the discretization technique applied, we identify two primary distortion modes in discrete resonant controllers: frequency warping and resonance damping. We further provide a theoretical explanation for these distortion modes, and demonstrate that the performance of the method is superior to all typical methods. The proposed method is implemented to discretize a quasi-resonant (QR) controller on a control board, achieving 25\% reduction in the root-mean-square error (RMSE) compared to the SOTA method. Finally, the approach is extended to discretizing a resonant controller of a grid-tied inverter. The efficacy of the proposed method is conclusively validated through favorable comparisons among the theory, simulation, and experiments.
format Preprint
id arxiv_https___arxiv_org_abs_2601_09549
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Novel $αβ$-Approximation Method Based on Numerical Integration for Discretizing Continuous Systems
Chen, Shen
Liu, Chaohou
Yao, Wei
Wang, Jisong
Guo, Shuaipo
Liu, Zeng
Liu, Jinjun
Systems and Control
In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $αβ$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods, the proposed method consists of two factors, i.e., shape factor ($α$) and time factor ($β$). Depending on the discretization technique applied, we identify two primary distortion modes in discrete resonant controllers: frequency warping and resonance damping. We further provide a theoretical explanation for these distortion modes, and demonstrate that the performance of the method is superior to all typical methods. The proposed method is implemented to discretize a quasi-resonant (QR) controller on a control board, achieving 25\% reduction in the root-mean-square error (RMSE) compared to the SOTA method. Finally, the approach is extended to discretizing a resonant controller of a grid-tied inverter. The efficacy of the proposed method is conclusively validated through favorable comparisons among the theory, simulation, and experiments.
title A Novel $αβ$-Approximation Method Based on Numerical Integration for Discretizing Continuous Systems
topic Systems and Control
url https://arxiv.org/abs/2601.09549