Fractional order system modelling with Legendre wavelet multi-resolution analysis

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.