线性周期快速切换系统的平衡截断模型降阶

杜鑫, 胡正, 王建英

doi:10.12066/j.issn.1007-2861.2114

上海大学学报(自然科学版) >

2021 , Vol. 27 >Issue 1: 59 - 77

DOI: https://doi.org/10.12066/j.issn.1007-2861.2114

研究论文

线性周期快速切换系统的平衡截断模型降阶

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1.上海大学机电工程与自动化学院, 上海 200444
2.上海大学计算中心, 上海 200444

杜鑫(1983---), 男, 副教授, 博士, 研究方向为模型降阶、控制系统频域分析与综合、智能无人系统等. E-mail: duxn@shu.edu.cn

收稿日期: 2018-12-26

网络出版日期: 2021-02-28

基金资助

国家自然科学基金资助项目(61873336);国家自然科学基金资助项目(61873335)

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Model reduction of linear fast periodically switched systems using balanced truncation

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1. School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China
2. Computer Center, Shanghai University, Shanghai, 200444, China

Received date: 2018-12-26

Online published: 2021-02-28

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摘要

针对电力电子领域中常见的线性周期快速切换系统, 研究了保持系统弱稳定性及平均动态特性的模型降阶问题. 针对输入为直流信号的情形, 引入周期切换系统的直流平均模型并在此基础上给出了可完全匹配其平均直流响应动态特性的平衡截断算法; 针对存在输入交流摄动信号以及切换时间摄动的情形, 引入周期切换系统的交流小信号平均模型, 并在此基础上给出了相应的奇异摄动型平衡截断模型降阶算法. 仿真应用算例验证了所得结果的有效性.

关键词： 模型降阶; 周期切换系统; 平均模型; 小信号平均模型; 平衡截断

本文引用格式

杜鑫, 胡正, 王建英 . 线性周期快速切换系统的平衡截断模型降阶[J]. 上海大学学报(自然科学版), 2021 , 27(1) : 59 -77 . DOI: 10.12066/j.issn.1007-2861.2114

Abstract

This study examines the model order reduction of linear fast periodically switched systems within the framework of a balanced truncation approach. The direct current (DC) averaged state-space model is introduced to describe the averaged dynamics of the given periodically switched systems in the presence of a DC input signal. In addition, a balanced truncation-based algorithm is developed to generate the desired reduced periodically switched model. A small-signal averaged state-space model is introduced to deal with cases in which the alternating current input signal is included. Similarly, an algorithm to generate the desired reduced model is proposed by exploiting the singular perturbation-type balanced truncation. Finally, numerical and experimental examples are presented to illustrate the effectiveness of the proposed results.

Key words： model reduction; periodically switched system; averaged model; small-signal average model; balanced truncation

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