Parameter identification of fractional order systems using block pulse functions

In this paper, a novel method is proposed to identify the parameters of fractional-order systems. The proposed method converts the fractional differential equation to an algebraic one through a generalized operational matrix of block pulse functions. And thus, the output of the fractional system to be identified is represented by a matrix equation. The parameter identification of the fractional order system is converted to a multi-dimensional optimization problem, whose goal is to minimize the error between the output of the actual fractional order system and that of the identified system. The proposed method can simultaneously identify the parameters and the fractional differential orders of the fractional order system and avoid the drawbacks in the literature that the fractional differential orders should be known or commensurate. Furthermore, the proposed method avoids complex calculations of the fractional derivative of input and output signals. Illustrative examples covering both fractional and integer systems are given to demonstrate the validity of the proposed method.