基于hat函数运算矩阵的分数阶系统辨识

摘要

In this paper,a novel method is proposed to identify the parameters of fractional order systems.The proposed method con-verts the fractional differential equation to an algebraic one through a generalized operational matrix of hat functions.The parameter identification of the fractional order system is converted to a multi-dimensional optimization problem,whose goal is to minimize the error between the output of the actual fractional order system and that of the identified system.The proposed method can simultane-ously identify the parameters and the fractional differential orders of the fractional order system and avoid the drawbacks in the liter-ature that the fractional differential orders should be known or commensurate.Furthermore,the proposed method avoids complex cal-culations of the fractional derivative of input and output signals.%本文采用了一种新的辨识方法辨识单输入单输出线性时不变分数阶系统. 这种方法利用hat函数的运算矩阵将分数阶微分(积分)方程转变为代数方程. 它不仅能辨识系统的参数还能辨识分数阶系统的任意阶的阶次,解决了目前一些方法不能同时辨识参数和阶次的难题,而且能大大减少辨识过程中的计算量. 为了证明方法的有效性,采用一些实例进行验证,仿真结果显示了此方法的合理性和准确性.