Tracking Control for $(x,u)$-Flat Systems by Quasi-Static Feedback of Classical States

TL;DR

This paper develops a systematic method for tracking control of (x,u)-flat systems using quasi-static feedback based solely on classical state measurements, avoiding the need for generalized Brunovský states.

Contribution

It introduces a novel approach to achieve tracking control with classical state feedback for (x,u)-flat systems, bypassing the need for higher-order derivatives.

Findings

Achieves asymptotically stable tracking error dynamics using classical states.

Provides a systematic solution for (x,u)-flat systems.

Enables practical implementation with measurable quantities.

Abstract

It is well known that for flat systems the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovsk\'y state are available, a linear, decoupled and asymptotically stable tracking error dynamics can be achieved. However, from a practical point of view, it is often desirable to achieve the same tracking error dynamics by feedback of a classical state instead of a generalized one. This is due to the fact that the components of a classical state typically correspond to measurable physical quantities, whereas a generalized Brunovsk\'y state often contains higher order time derivatives of the (fictitious) flat output which are not directly accessible by measurements. In this paper, a systematic solution for the tracking control problem based on quasi-static feedback and measurements of classical states only is derived for the subclass of $(x,u)$-flat systems.