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

Hartmut Logemann; Eugene P. Ryan; Ilya Shvartsman

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 3, page 458-483
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Logemann, Hartmut, Ryan, Eugene P., and Shvartsman, Ilya. "Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 458-483. <http://eudml.org/doc/249991>.

@article{Logemann2007,
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. },
author = {Logemann, Hartmut, Ryan, Eugene P., Shvartsman, Ilya},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Actuator nonlinearities; hysteresis; infinite-dimensional systems; input-output analysis; integral control; sensor nonlinearities; actuator nonlinearities; infinite-dimensional systems; sensor nonlinearities},
language = {eng},
month = {6},
number = {3},
pages = {458-483},
publisher = {EDP Sciences},
title = {Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach},
url = {http://eudml.org/doc/249991},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Logemann, Hartmut
AU - Ryan, Eugene P.
AU - Shvartsman, Ilya
TI - Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/6//
PB - EDP Sciences
VL - 13
IS - 3
SP - 458
EP - 483
AB - 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.
LA - eng
KW - Actuator nonlinearities; hysteresis; infinite-dimensional systems; input-output analysis; integral control; sensor nonlinearities; actuator nonlinearities; infinite-dimensional systems; sensor nonlinearities
UR - http://eudml.org/doc/249991
ER -

References

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