This paper proposes a method of fractional order system (FOS) modelling with Legendre wavelet multi-resolution analysis. The proposed method expands the input and output signals of the system in the form of a Legendre wavelet, and constructs the Legendre wavelet integration operational matrix by use of a block-pulse function. To address the problem of the considerable volume of system identification data and system noise in practical engineering applications, the multi-resolution characteristics of the wavelet are combined to build a wavelet integration operational matrix from the multi-scale space. By continuously discarding the high-frequency information to reduce the length of the identification data, the identification speed of the system is accelerated and the influence of noise on the identification accuracy is reduced. In addition, the least squares method is used to find the optimal order in the identification interval and further accelerate the FOS modelling process. The proposed method rapidly identifies the FOS parameters with high accuracy, and is thus feasible for engineering applications. Its effectiveness is verified by simulation and photoelectric stabilized sighting platform experiment.

本文提出了一种基于勒让德小波多分辨率分析的分数阶系统建模方法。所提出的方法以勒让德小波的形式扩展系统的输入和输出信号，并利用块脉冲函数构造勒让德小波积分运算矩阵。为了解决实际工程应用中系统识别数据量大，系统噪声大的问题，结合了小波的多分辨率特征，从多尺度空间构建了小波积分运算矩阵。通过连续丢弃高频信息以减少识别数据的长度，可以加快系统的识别速度，并减少噪声对识别精度的影响。此外，最小二乘方法用于在识别间隔中找到最佳顺序，并进一步加快FOS建模过程。所提出的方法可以快速，准确地识别FOS参数，因此对于工程应用是可行的。通过仿真和光电稳定瞄准平台实验验证了其有效性。