From output regulation theory to flatness based tracking: a bridge for linear systems

TL;DR

This paper bridges output regulation theory and flatness-based tracking for linear systems, showing how to convert controllers between the two methods and demonstrating their equivalence for certain systems.

Contribution

It provides an analytic solution to regulator equations and establishes a link between ORT and FBT, unifying two approaches to trajectory tracking in linear systems.

Findings

ORT and FBT controllers are equivalent for certain systems

Analytic solution to regulator equations is derived

Conversion between ORT and FBT controllers is demonstrated

Abstract

The trajectory tracking problem for multivariable linear systems is considered. Two different techniques are examined: the output regulation theory (ORT) and the flatness based tracking (FBT). ORT and FBT are two different approaches to solve the tracking problem, and both methods have different restrictions. The tracking controller of the ORT furthermore depends on the solution of the so-called regulator equations. In this paper, a special analytic solution of the regulator equations is presented. Additionally, based on this analytic solution, a link from the ORT to the FBT approach is provided, and the connection of both tracking controllers is highlighted. It is shown how the ORT controller can be converted to the FBT controller and that both methods lead to identical control laws for a certain class of systems.