On the relationship between the Absolute Vibration Suppression and Back-Stepping methods in control of the wave equation with possibly unstable boundary conditions

Lea Beilkin, Yoram Halevi, Miroslav Krstic

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper we compare two methods in control of the wave equation with a possibly destabilizing boundary force. Non-collocated actuation and measurement of boundary position is assumed. The Absolute Vibration Suppression (AVS) controller is based on an exact transfer function model and exploits the system traveling wave nature. It eliminates the wave reflections in the system and employs a dead time compensator that shifts the resulting poles to any desired location. The Back- Stepping (BS) controller is designed in time domain. Its general principle is using dedicated transformations to map the original unstable system to a stable target system. For the system at hand the target system is a wave equation with stable and adjustable boundary conditions. We show that for a certain choice of BS control parameters the methods coincide.

Original languageEnglish
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6709-6714
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - 28 Jul 2016
Externally publishedYes
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: 6 Jul 20168 Jul 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Conference

Conference2016 American Control Conference, ACC 2016
Country/TerritoryUnited States
CityBoston
Period6/07/168/07/16

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