Computation of Orders of a Commensurable Fractional Order Model
Computation of Orders of a Commensurable Fractional Order Model
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DOI：
10.1109/cdc40024.2019.9029742
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Oliver Stark;Martin Kupper;Stefan Krebs;S. Hohmann
中科院分区：
文献类型：
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作者：
Oliver Stark;Martin Kupper;Stefan Krebs;S. Hohmann
本文讨论了一个可分解分数阶模型的系统阶数计算和输入阶数的确定。系统和输入阶数分别等于系统和输入参数的数量。所提出的方法的好处是，没有搜索算法或过度参数化的方程被使用。相反，系统阶数的计算被简化为分数积分和基于模型的替换系统的分数Gramian的正确秩的确定。通过检测与基于模型的替换系统的分数Gramian类似的矩阵何时失去满秩来确定输入阶。这种基于模型的替换系统可以通过将调制函数方法应用于原始分数阶模型来导出。最后给出了一个具体的实现方法，并给出了一个算例.
This paper deals with the calculation of the system order and the determination of the input order of a commensurable fractional order model. The system and input orders are equal to the number of system and input parameters, respectively. The benefit of the proposed method is that no search algorithms or over-parameterized equations have to be used. Instead, the calculation of the system order is reduced to fractional integration and the determination of the correct rank of the fractional Gramian of a model-based replacement system. The input order is determined by detecting when a matrix similar to the fractional Gramian of the model-based replacement system loses full rank. This model-based replacement system can be derived by applying the modulating function method to the original fractional order model. A view on practical implementation is given and a numerical example completes this paper.