The invention discloses a
fractional order system identification method based on Legendre
wavelet multi-resolution analysis. The method comprises the following steps that firstly, Legendre
wavelet orders are selected in the interval of [0,1]; secondly, an operation matrix of Legendre
wavelet integration is derived by utilizing a block pulse function integral matrix; the input
signal and the outputsignal of the
system are expanded in the form of Legendre wavelet; the wavelet multi-fraction analysis characteristic is utilized, output signals are continuously decomposed, high-frequency information is discarded, the data length is reduced, and finally,
system parameters and orders are solved in a cyclic fractional order integral mode by adopting a least square method and taking an IAE index as a target function. According to the method, the problems that parameter
estimation is slow and a
noise pollution system cannot be identified due to single dimension, high order and multiple coefficients of a traditional Legendre wavelet integral operation matrix identification method are effectively solved, the
system identification speed is increased, and the influence of
noise on the identification precision is reduced.