Model-free control

TL;DR

This paper introduces a unified framework for model-free control and intelligent PID controllers, highlighting their simplicity, effectiveness, and recent advances, especially in handling complex systems and friction.

Contribution

It presents a unified approach to model-free control and intelligent PID controllers, incorporating recent advances and estimation techniques, with demonstrations on complex and infinite-dimensional systems.

Findings

Intelligent controllers outperform classic PID in complex scenarios.

Simple tuning procedures are effective for a wide range of systems.

Numerical simulations confirm the power and simplicity of the proposed methods.

Abstract

"Model-free control" and the corresponding "intelligent" PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.