Numerical Study on Identification of Transfer Functions in a Feedback System and Model Reduction
Numerical Study on Identification of Transfer Functions in a Feedback System and Model Reduction
复制标题
反馈系统传递函数辨识及模型降阶的数值研究
DOI：
10.3327/jnst.34.1115
复制
发表时间：
1997
影响因子：
1.2
通讯作者：
K. Kishida
中科院分区：
文献类型：
--
作者：
K. Kishida
从反问题的观点出发，利用Hankel矩阵的奇异值分解讨论了反馈系统传递函数矩阵的辨识问题。模型降阶的方法被认为是，和选择标准，提出了他们的识别。从反馈回路的结构出发，确定了开环和闭环传递函数矩阵之间的转换公式，并在反馈系统处于最小相位的情况下，辨识开环传递函数矩阵时，需要这些转换公式。虽然开环传递函数矩阵的可辨识性可以在新息模型等效于反馈系统的框架下进行检验，但在辨识过程中存在零极点相消问题。利用高阶开环传递函数给出的格拉姆函数的奇异值分解，讨论了开环传递函数模型降阶的方法。为了验证该算法的可靠性，对一个算例进行了仿真研究。
Identification of transfer function matrices in a feedback system is discussed by using the singular value decomposition of Hankel matrix from the viewpoint of inverse problems. A method of model reduction is considered, and selection criteria are proposed for identification of them. Transformation formula between open loop and closed loop transfer function matrices are determined from the feedback loop structure, and they are needed for identification of open loop transfer function matrices under such a condition where the feedback system is in a minimum phase. Though the identifiability of open loop transfer function matrices can be examined in the framework of innovation model equivalent to the feedback system, there are pole-zero cancellations in the identification of them. The method to reduce a model order of an open loop transfer function is discussed by using the singular value decomposition of a gramian given by the open loop transfer function with higher degree. To check reliability of the present algorithm, a simulation study is performed for an example.