Practical Applications of Diffusive Realization of Fractional Integrator with SoftFrac

Fractional calculus has found multiple applications around the world. It is especially prevalent in the domains of control and electronics. One of the key elements of fractional applications is the fractional integral (or integrator) which is a backbone of famous PI lambda D controller. It gives advantages of traditional PID with a limited phase lag. The are, however, issues with implementation, which will allow good low-frequency behavior. In this paper, we consider a diffusive realization of a fractional integrator with the use of quadratures. We implemented this method in numerical package SoftFrac, and we illustrate how different quadratures work for this purpose. We show superiority of bounded domain integration with logarithmic transformation and explain issues with behavior for extremely low frequencies.

Automated summary

This paper discusses the diffusive realization of the fractional integrator using quadratures, and demonstrates the implementation in the numerical package SoftFrac. The study shows the superiority of bounded domain integration with logarithmic transformation, while explaining issues with behavior at extremely low frequencies.