A Novel $\alpha\beta$-Approximation Method Based on Numerical Integration for Discretizing Continuous Systems

TL;DR

This paper introduces a new discretization method called the $oldsymbol{ m f eta}$-approximation based on numerical integration, which improves the accuracy of discretizing continuous systems, especially in resonant control applications.

Contribution

The paper presents the $oldsymbol{ m f eta}$-approximation method, a novel discretization approach that reduces distortion modes and outperforms existing methods in control system discretization.

Findings

Achieved 25% reduction in RMSE over state-of-the-art methods.

Validated the method through theory, simulation, and experiments.

Effectively discretized a grid-tied inverter's resonant controller.

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.