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Integral control of infinite-dimensional systems in thepresence of hysteresis: an input-output approach

Published online by Cambridge University Press:  05 June 2007

Hartmut Logemann ,
Eugene P. Ryan  and
Ilya Shvartsman
Hartmut Logemann
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK; hl@maths.bath.ac.uk; epr@maths.bath.ac.uk; shvartia@muohio.edu
Eugene P. Ryan
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK; hl@maths.bath.ac.uk; epr@maths.bath.ac.uk; shvartia@muohio.edu
Ilya Shvartsman
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK; hl@maths.bath.ac.uk; epr@maths.bath.ac.uk; shvartia@muohio.edu
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Abstract

This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference signals, provided the positive integrator gain is smaller than a certain constant determined by a positivity condition in the frequency domain. The input-output results are applied in a general state-space setting wherein the linear component of the interconnection is a well-posed infinite-dimensional system.

Keywords

Actuator nonlinearitieshysteresisinfinite-dimensional systemsinput-output analysisintegral controlsensor nonlinearities
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 3 , July 2007 , pp. 458 - 483
Copyright
© EDP Sciences, SMAI, 2007

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