分数阶系统时域子空间辨识

Time Domain Subspace Method for Fractional Order System Identification

  • 摘要: 研究了分数阶系统的时域辨识问题,给出了一种新的分数阶系统时域子空间辨识算法.当分数阶微分阶次已知时,通过计算输入输出信号的分数阶微分,构造新的输入输出数据方程对系统的参数进行子空间辨识.当分数阶微分阶次未知时,通过代价函数将阶次辨识问题转化为参数寻优问题.采用Poisson滤波器有效避免了在计算分数阶微分时输入输出信号必须高阶可导的问题.通过分析给出了权矩阵的选取方式,提高了时域子空间辨识结果的精度.数值仿真结果表明了该算法的有效性.

     

    Abstract: The problem of fractional order system identification in time domain is studied,and a new identification algorithm based on subspace method in time domain is presented.When the fractional differential order is known,the parameters of system are identified by utilizing subspace method after calculating the fractional differential of input and output signals and constructing a new input and output data equation.When the fractional differential order is unknown,the problem of order identification is transformed into parameter optimization problem by utilizing cost function.The Poisson filter is used to efficiently avoid the problem that input and output signals should have high order derivative during the calculation of fractional order differential.And the selecting method of weight matrix,which improves the accuracy of identification,is presented through analysis.The numerical simulation validates the algorithm.

     

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