Tracking with prescribed performance for linear non-minimum phase systems. (May 2020)

• Record Type: Journal Article
• Authors: Berger, Thomas
• Is Part Of: Automatica. Volume 115(2020)
• Publication Date: 2020-05
• Subjects: Linear systems -- Robust control -- Non-minimum phase -- Funnel control -- Relative degree; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108909
• Languages: English
• ISSNs: 0005-1098

Abstract

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.