分布阶次系统时域子空间辨识

Subspace identification of distributed order systems in time-domain

研究线性时不变分布阶次系统的时域辨识问题,提出一种基于主元分析的子空间辨识算法.该算法采用分数阶滤波器重构基本输入输出方程,利用主元分析辨识分布阶次系统的各项系数矩阵,通过代价函数将系统的各项分数阶微分阶次辨识问题转化为多变量参数优化问题,设计了辅助变量消除辨识过程中随机噪声的不利影响.数值仿真实例表明了算法的有效性.

The.problem of the identification of linear time invariant（LTI） distributed order systems in time-domain is firstly discussed, and a subspace identification algorithm based on principle component analysis（PCA） is proposed. The fractional order filter is designed to reconstruct the basic input and output equation. The principle component analysis is used to identify coefficient matrixes of distributed order systems. The cost function is utilized to transform the identification of fractional differential orders into multivariable optimization problem. An instrumental variable is chosen to eliminate the bad influence of random noises during the identification process. A numerical example is given to show the effectiveness of the proposed algorithm.