A Study on Fractional Power-Law Applications and Approximations

Abstract

The frequency response of the fractional-order power-law filter can be approximated by different techniques, which eventually affect the expected performance. Fractional-order control systems introduce many benefits for applications like compensators to achieve robust frequency and additional degrees of freedom in the tuning process. This paper is a comparative study of five of these approximation techniques. The comparison focuses on their magnitude error, phase error, and implementation complexity. The techniques under study are the Carlson, continued fraction expansion (CFE), Padé, Charef, and MATLAB curve-fitting tool approximations. Based on this comparison, the recommended approximation techniques are the curve-fitting MATLAB tool and the continued fraction expansion (CFE). As an application, a low-pass power-law filter is realized on a field-programmable analog array (FPAA) using two techniques, namely the curve-fitting tool and the CFE. The experiment aligns with and validates the numerical results.

Field-Programmable Analog Array Implementation of Neuromorphic Silicon Neurons with Fractional Dynamics

“…Likewise, an implementation based on Oustaloup's approximation combined with a curve-fitting-based method has been proposed in [14] for power-law filters (transfer functions raised to an FO) and using particle swarm optimization in [15]. A comparison study on the Carlson, continued fraction expansion, Padé, Charef, and curvefitting approximation techniques can be found in [16]. The curve-fitting methodology is tested for double-order filters (FO filters raised to an FO) in [17].…”