dorsal/arxiv
View SchemaA Novel $\alpha\beta$-Approximation Method Based on Numerical Integration for Discretizing Continuous Systems
| Authors | Shen Chen, Chaohou Liu, Wei Yao, Jisong Wang, Shuaipo Guo, Zeng Liu, Jinjun Liu |
|---|---|
| Categories | |
| ArXiv ID | 2601.09549vv1 |
| URL | https://arxiv.org/abs/2601.09549 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $\alpha\beta$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods, the proposed method consists of two factors, i.e., shape factor ($\alpha$) and time factor ($\beta$). 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.
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"abstract": "In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $\\alpha\\beta$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods, the proposed method consists of two factors, i.e., shape factor ($\\alpha$) and time factor ($\\beta$). 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.",
"arxiv_id": "2601.09549",
"authors": [
"Shen Chen",
"Chaohou Liu",
"Wei Yao",
"Jisong Wang",
"Shuaipo Guo",
"Zeng Liu",
"Jinjun Liu"
],
"categories": [
"eess.SY",
"cs.SY"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A Novel $\\alpha\\beta$-Approximation Method Based on Numerical Integration for Discretizing Continuous Systems",
"url": "https://arxiv.org/abs/2601.09549",
"version": "v1"
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