引用本文:李旺,张国庆,王永.分数阶系统频域辨识算法[J].控制理论与应用,2010,27(8):1118~1122.[点击复制]
LI Wang,ZHANG Guo-qing,WANG Yong.Frequency domain identification of fractional order systems[J].Control Theory and Technology,2010,27(8):1118~1122.[点击复制]
分数阶系统频域辨识算法
Frequency domain identification of fractional order systems
摘要点击 2246  全文点击 1806  投稿时间：2008-10-06  修订日期：2010-06-12
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DOI编号  10.7641/j.issn.1000-8152.2010.8.CCTA081071
  2010,27(8):1118-1122
中文关键词  分数阶系统  频域辨识  极大似然算法
英文关键词  fractional-order systems  frequency domain identification  maximum likelihood algorithm
基金项目  
作者单位E-mail
李旺 中国科学技术大学 自动化系 aswanlw@mail.ustc.edu.cn 
张国庆 新加坡国立大学 互动数码媒体研究所  
王永* 中国科学技术大学 自动化系 yongwang@ustc.edu.cn,aswanlw@mail.ustc.edu.cn 
中文摘要
      分数阶微积分提供了一个很好的工具来描述一些复杂的实际系统, 比整数阶模型更简洁准确. 针对分数阶系统建模问题, 阐述了一种同元次分数阶系统频域辨识的极大似然算法.为此首先简要地介绍了同元次分数阶系统的传递函数表达形式, 然后在此基础上推导了分数阶系统频域极大似然算法, 利用拉格朗日法证明了似然函数和代价函数的等价性, 从而将辨识问题归结为一等价的优化问题, 并进一步对采用Gauss-Newton优化计算方法进行了讨论. 最后通过仿真实例验证了其有效性.
英文摘要
      Fractional order calculus provides an excellent tool to describe some complicated real systems more adequately than integer order models. For the identification of fractional order systems, a maximum likelihood algorithm based on the transfer function in frequency domain is proposed in this paper. First, the fractional order transfer function is briefly introduced. Second, the algorithm is deduced in detail and the equivalence between likelihood function and cost function is verified via Lagrange method, and the identification problem is converted to an equivalent optimization problem. Third, Gauss-Newton method is applied to solve the optimization problem. Finally, this algorithm is validated via an illustrative example.