基于分数阶微积分的电力滤波器建模与控制的研究

项目名称： 基于分数阶微积分的电力滤波器建模与控制的研究

项目编号： No.51307013

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 电工技术

项目作者： 李冠林

作者单位： 大连理工大学

项目金额： 24万元

中文摘要： 电力滤波器的建模是滤波器控制系统设计的基础。建模的准确与否直接关系到控制系统性能的高低。目前电力滤波器的建模多是用整数阶模型描述。然而，实际的电感和电容都具有分数阶特性，采用整数阶模型只能近似的描述其特性，从而使电路模型不够精确。另一方面，由于分数阶元件的阶数可以是任意数，采用分数阶电路元件，可以使滤波器系统的设计更加灵活，在某些情况下还可以改善电力滤波器的滤波效果。本课题基于电感和电容元件的分数阶特性，研究电力滤波器的建模和控制。针对几种典型的电力滤波器，建立分数阶系统模型。通过理论分析、仿真和实验，揭示元件阶数和系统稳定性及滤波性能之间的关系。研究成果将为电力滤波器的设计提供参考依据，亦对分数阶电路与系统理论的研究有所裨益。

中文关键词： 分数阶微积分；电力滤波器；建模；动力学特性；

英文摘要： Power filter modeling is a base for the design of the control system. Modeling accuracy determines the performance of the control system. At present,the modeling of the power filter usually use the integer-order model to describe the system.However,the actual capacitance and inductance are of the fractional electrical characteristics. The integer-order model can only describe the electrical characteristics approximately, and the circuit model is not precise enough. On the other hand,because the order of the fractional elements can be any number, applying the fractional elements can make the design of the power filter system more flexibal.This subject will study the modeling and the control of the power filter based on the fractional electrical characteristics of the inductors and capacitors. Several typical power filters are studied in the subject to build the fractional model of the system. The stability and the performance of the power filters affected by the fractional order are analyzed by the theoretical analysis,simulatoins and experimens. These studies will provide the references for the design of the power filter, and are of theoretical significance for the fractional circuits and systems.

英文关键词： fractional calculus；power filter；modeling；dynamics；