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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.09549 |
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| _version_ | 1866914255569158144 |
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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 |