A mathematical explanation via "intelligent" PID controllers of the strange ubiquity of PIDs

TL;DR

This paper offers a mathematical explanation for the widespread use of PID controllers by comparing them with recently introduced 'intelligent' PID controllers, supported by simulations showing the latter's advantages.

Contribution

It provides a novel mathematical analysis explaining why PID controllers are so prevalent, contrasting them with intelligent PID controllers and demonstrating their superiority through simulations.

Findings

Intelligent PID controllers outperform traditional PIDs in simulations.

Mathematical analysis explains the ubiquity of PIDs.

Simulations confirm the advantages of intelligent PID design.

Abstract

The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of "intelligent" PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent feedback design.