Tracking with prescribed performance for linear non-minimum phase systems
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.
Cite
@article{arxiv.1912.02033,
title = {Tracking with prescribed performance for linear non-minimum phase systems},
author = {Thomas Berger},
journal= {arXiv preprint arXiv:1912.02033},
year = {2020}
}