Tracking with prescribed performance for linear non-minimum phase systems

TL;DR

This paper introduces a novel funnel control approach for uncertain linear non-minimum phase systems, ensuring the tracking error remains within a prescribed performance funnel despite unstable zero dynamics.

Contribution

A new output construction method is proposed to eliminate unstable zero dynamics, enabling effective funnel control for non-minimum phase systems.

Findings

The proposed controller guarantees bounded signals and prescribed tracking performance.

Simulation results validate the effectiveness of the control strategy.

The method extends funnel control to a broader class of systems with unstable zero dynamics.

Abstract

We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a low-complexity controller which achieves that the tracking error evolves within a prescribed performance funnel. We present a novel approach where a new output is constructed, with respect to which the system has a higher relative degree, but the unstable part of the zero dynamics is eliminated. Using recent results in funnel control, we then design a controller with respect to this new output, which also incorporates a new reference signal. We prove that the original output stays within a prescribed performance funnel around the original reference trajectory and all signals in the closed-loop system are bounded. The results are illustrated by some simulations.