Vector Fitting fractional system identification using particle swarm optimization

Abstract

The optimal fractional system identification is a challenging problem as it requires the estimation of not only the numerator parameters, but also the poles transfer function model and the non-integer order reading to complex nonlinear optimization. In this paper, an algorithm using the least square method, called “Vector Fitting” (V.F.) developed by Gustavsen is extended to the fractional order system identification in frequency domain. This algorithm proceeds recursively contrarily to the well known Levy’s algorithm which uses only one iteration to calculate the model parameters. The use of an iterative method efficiently directs the model parameters evolution towards their optimal values. Indeed, during iteration the poles of the model are calculated and used as starting poles for the next one, the stability of the identified model can thus be imposed. The V.F. algorithm is then associated with the heuristic optimization method: particle swarm optimization (PSO), leading to a new fractional system identification algorithm. The algorithm works in a hierarchical way; in a higher level, PSO determines the non-integer order and in a lower stage, the V.F. algorithm identifies the other parameters.