Performance Analysis of Oustaloup Approximation for the Design of Fractional-Order Analogue Circuits

The description and definition of various systems using fractional-order calculus continues to gain attention in a variety of field of engineering. This is especially true for the design of analogue function blocks, where the factional-order Laplace operator $s^{\alpha}$, whereas $0 < \alpha < 1$, is frequently used to design the fractional to design the transfer functions of these blocks. In this paper we focus on analysing the Oustaloup approximation of $s^{\alpha}$ to provide a tool that can support selecting the appropriate approximation to obtain a response that satisfies the designers' requirements of approximation error in magnitude and/or phase in a specific frequency range for the minimal possible order $N$ of the approximation.