Flatness-based control revisited: The HEOL setting

TL;DR

This paper revisits flatness-based control by establishing algebraic foundations for the HEOL setting, integrating flatness and intelligent controllers to address feedback loop questions with practical algebraic tools.

Contribution

It introduces an algebraic framework for the HEOL setting, combining flatness-based control and model-free control using differential algebra and module theory.

Findings

Provides an algebraic foundation for HEOL control setting.

Demonstrates controllers through computer simulations.

Addresses feedback loop questions in flatness-based control.

Abstract

We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of K\"ahler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations.