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The funnel pre‐compensator
Author(s) -
Berger Thomas,
Reis Timo
Publication year - 2018
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4281
Subject(s) - funnel , control theory (sociology) , cascade , nonlinear system , interconnection , controller (irrigation) , computer science , transient (computer programming) , signal (programming language) , engineering , control (management) , physics , artificial intelligence , telecommunications , mechanical engineering , agronomy , quantum mechanics , chemical engineering , biology , programming language , operating system
Summary We introduce the funnel pre‐compensator as a novel and simple adaptive pre‐compensator of “high‐gain type”. We show that this pre‐compensator is feasible for a large class of signal pairs, which satisfy a certain relationship. We show that the funnel pre‐compensator guarantees prescribed transient behavior of the compensator error, it is of low complexity and inherently robust since its design is model‐free. As an application in adaptive control of nonlinear systems, a cascade of funnel pre‐compensators is exploited to obtain an artificial output with explicitly known derivatives, which tracks the system output with prescribed transient behavior. In some important cases the interconnection of the system with the pre‐compensator cascade is shown to have input‐to‐state stable internal dynamics. This guarantees feasibility of a novel funnel controller that consists of a funnel pre‐compensator cascade in conjunction with a recently developed funnel controller for systems with arbitrary relative degree. We illustrate the application of this interconnection for some mechanical systems.