Parameter identification of fractional-order time delay system based on Legendre wavelet

Abstract This paper proposes a parameter identification method of fractional-order time delay system based on Legendre wavelet. An integration operational matrix and delay operational matrix of a Legendre wavelet are constructed. The process is derived to convert a fractional-order time delay system based on a Legendre wavelet operational matrix to algebraic equation. The least squares method is used to simultaneously estimate the order, model parameters and time delay coefficient of a system. In addition, wavelet decomposition and reconstruction algorithm are used to pre-process the output signal, which separate the noise from signal. The proposed method overcomes the initial-state dependence and randomness of the identification result in the algebraic solution of the traditional operational matrix, and reduces the effect of noise on the accuracy of parameter identification. It is especially suitable for engineering application. The effectiveness is verified by numerical simulation and a temperature process control system.