Parameter identification of fractional order Hammerstein model with two-stage piecewise nonlinearity based on iterative algorithms

Abstract

This paper discusses identification of the fractional order Hammerstein model with colored noise. The static part of the Hammerstein model is a two-stage piecewise nonlinearity, while the dynamic part is a CARMA structure. We deduce the identification expression of the model through the definition of the Grünwald–Letnikov fractional differential. Then, two iterative algorithms are adopted to identify the unknown parameters. One of them is the Levenberg–Marquardt iterative algorithm, and the other is the particle swarm optimization iterative algorithm. The two algorithms are extended from the traditional integer order system identification field to the fractional order nonlinear colored noise system identification field. A numerical example and a case study of servo system identification are respectively presented to demonstrate the feasibility of the identification algorithms. It can be seen that the estimation errors of these two algorithms are relatively small, which reflects their good identification effect.