Output feedback control with prescribed performance via funnel pre-compensator

TL;DR

This paper presents a method for output reference tracking with prescribed performance for systems with high relative degree using a funnel pre-compensator, enabling error control without output derivative knowledge.

Contribution

It proves that combining a funnel pre-compensator with a minimum phase system preserves the system's relative degree and phase properties, facilitating prescribed performance tracking.

Findings

Error remains within a predefined funnel

Derivatives of the pre-compensator output are explicitly known

Tracking achieved without output derivative knowledge

Abstract

We study output reference tracking of systems with high relative degree via output feedback only; this is, tracking where the output derivatives are unknown. To this end, we prove that the conjunction of the funnel pre-compensator with a minimum phase system of arbitrary relative degree yields a system of the same relative degree which is minimum phase as well. The error between the original system's output and the pre-compensator's output evolves within a prescribed performance funnel; and moreover, the derivatives of the funnel pre-compensator's output are known explicitly. Therefore, output reference tracking with prescribed transient behaviour of the tracking error is possible without knowledge of the derivatives of the original system's output; via funnel control schemes for instance.