Frequency domain identification of fractional order systems

Abstract

Fractional order calculus provides an excellent tool to describe some complicated real systems more adequately than integer order models. For the identification of fractional order systems, a maximum likelihood algorithm based on the transfer function in frequency domain is proposed in this paper. First, the fractional order transfer function is briefly introduced. Second, the algorithm is deduced in detail and the equivalence between likelihood function and cost function is verified via Lagrange method, and the identification problem is converted to an equivalent optimization problem. Third, Gauss-Newton method is applied to solve the optimization problem. Finally, this algorithm is validated via an illustrative example.