Fractional Calculus Helps Control Systems Hit Their Mark

Compared with classical (or integer-order) calculus, which forms the mathematical basis of most control systems, fractional calculus is better equipped to handle the time-dependent effects observed in real-world processes. These include the memory-like behavior of electrical circuits and chemical reactions in batteries. By recasting the design of a setpoint filter as a fractional calculus problem, researchers created a filter that could not only suppress overshooting but also minimize the response time of a virtual controller.

A side-by-side comparison showed that their fractional filter outperformed an integer-order filter, tracking the complex path of a given setpoint more closely.

One drawback of this fractional design is that it’s difficult to incorporate into existing automated systems, unlike integer-order filters, which are generally plug-and-play. But as the world of automation becomes increasingly complex, fractional filters may ultimately set the new standard for controlling everything from robotics and self-driving cars to medical devices.

Contacts and sources:
Yan Ou