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应用科学学报 ›› 2011, Vol. 29 ›› Issue (2): 209-215.doi: 10.3969/j.issn.0255-8297.2011.02.015

• 控制与系统 • 上一篇    下一篇

基于短记忆原理的分数阶系统时域子空间辨识

廖增， 彭程， 王永   

  1. 中国科学技术大学自动化系，合肥230027
  • 收稿日期:2010-11-10 修回日期:2011-01-09 出版日期:2011-03-23 发布日期:2011-03-23
  • 作者简介:王永，教授，博导，研究方向：振动主动控制、飞行器制导与控制，E-mail: yongwang@ustc.edu.cn
  • 基金资助:

    国家自然科学基金(No.61004017, No.60974103)资助

Subspace Identification in Time-Domain for Fractional Order Systems Based on Short Memory Principle

LIAO Zeng, PENG Cheng, WANG Yong   

  1. Department of Automation, University of Science and Technology of China, Hefei 230027, China
  • Received:2010-11-10 Revised:2011-01-09 Online:2011-03-23 Published:2011-03-23
  • About author:王永，教授，博导，研究方向：振动主动控制、飞行器制导与控制，E-mail: yongwang@ustc.edu.cn
  • Supported by:

    国家自然科学基金(No.61004017, No.60974103)资助

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被引次数

3

摘要：

 针对多变量分数阶系统提出一种基于短记忆原理的时域子空间辨识算法. 该算法能够有效辨识多变量分数阶系统的系数矩阵和分数阶微分阶次. 利用Poisson 矩函数对输入输出信号进行滤波预处理，构造了子空间方法的输入输出矩阵. 通过代价函数将分数阶微分阶次辨识转化为参数寻优问题. 利用分数阶微分的短记忆原理，将分数阶微分阶次和输入输出数据矩阵进行分离，避免了输入输出信号的分数阶微分计算过程. 数值仿真对算法的有效性进行了验证.

关键词: 分数阶系统；子空间方法；短记忆原理；系统辨识

Abstract:

 A subspace identification algorithm in the time-domain based on short memory principle is given for multivariable fractional order systems. This algorithm can effectively identify the coefficient matrixes and the fractional differential order of multivariable fractional order systems. Utilizing the Poisson moment functionals (PMF), input and output signals are filtered, and the basic input and output data matrixes in subspace method constructed. The problem of identifying fractional differential order is transformed into a parameter optimization problem according to the cost function. Using the short memory principle of fractional differentiation, the fractional differential order is separated from input and output data matrixes, and differentiation calculation of input and output signals is avoided. A numerical example is given to validate the proposed algorithm.

Key words: fractional order systems, subspace method, short memory principle, system identification

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