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 PIλD 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.

Hardware Implementation and Performance Study of Analog PIλDμ Controllers on DC Motor

In this paper, the performance of an analog PI λ D μ controller is done for speed regulation of a DC motor. The circuits for the fractional integrator and differentiator of PI λ D μ controller are designed by optimal pole-zero interlacing algorithm. The performance of the controller is compared with another PI λ D μ controller—in which the fractional integrator circuit employs a solid-state fractional capacitor. It can be verified from the results that using PI λ D μ controllers, the speed response of the DC motor has improved with reduction in settling time ( T s ), steady state error (SS error) and % overshoot (% M p ).