A comparative study on Tustin rule based discretization methods for fractional order differentiator

Abstract

Fractional order controller, which is actually an infinite dimensional linear filter, is increasingly becoming a focus of interest in control theory and engineering. The discretization of fractional order differentiator is the key step in digital implementation of a fractional order controller. Generally, there are two discretization methods, i.e., direct discretization and indirect discretization. Tustin operator is commonly used in discretization of continuous system. This paper focuses on the Tustin rule based direct discretization methods for fractional order differentiator. Firstly, fractional order derivative and its discretization are reviewed briefly. Secondly, power series expansion, continued fractional expansion and Muir-recursion are presented with MATLAB simulation scripts. Then simulations and comparisons are demonstrated with an illustrative example. Finally, this paper is concluded with future work.