In this article, a time-invariant polynomial model of fixed-frequency pulsewidth modulation dc–dc converter is proposed. Through normalized coordinate transformation, the time-varying model of the converter is transferred into a time-invariant model, whose state matrix and input matrix are obtained by the addition and multiplication of matrices simply and expressed by the polynomial of duty cycle concisely. The proposed model has the following advantages. Compared with the state-space average (SSA) model, the ripple of the state vector and the switching period are considered, thereby improving the accuracy. Contrary to other time-invariant models, the state matrix and input matrix instead of the state vector are expanded into series. Therefore, neither the number of state vectors nor the order of the matrices increases, and the proposed model has a simple structure similar to the SSA model. In addition, as a time-invariant polynomial model, the calculation and analysis of the proposed model are much simpler than the time-variant exact model. In order to prove the above advantages of the proposed model, the general expression of the proposed model is derived and the proposed model is compared with other models. These analyses and comparisons are verified through the simulation and experimental results.

中文翻译：

---

应用归一化坐标变换的定频PWM DC-DC转换器的时不变多项式模型

本文提出了一种定频脉宽调制dc-dc变换器的时不变多项式模型。通过归一化坐标变换，变换器的时变模型转化为时不变模型，其状态矩阵和输入矩阵由矩阵的简单加法和乘法得到，并用占空比多项式简洁地表示。所提出的模型具有以下优点。与状态空间平均（SSA）模型相比，考虑了状态向量的纹波和开关周期，从而提高了精度。与其他时不变模型相反，状态矩阵和输入矩阵而不是状态向量被扩展为系列。因此，状态向量的数量和矩阵的阶数都不会增加，并且所提出的模型具有类似于SSA模型的简单结构。此外，作为一种时不变多项式模型，该模型的计算和分析比时变精确模型要简单得多。为了证明所提模型的上述优点，推导了所提模型的一般表达式，并与其他模型进行了比较。通过模拟和实验结果验证了这些分析和比较。