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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 458-483 |
| Number of pages | 26 |
| Journal | ESAIM - Control, Optimisation and Calculus of Variations |
| Volume | 13 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 1 2007 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics
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Integral control of infinite-dimensional systems in the presence of hysteresis : An input-output approach. / Logemann, Hartmut; Ryan, Eugene P.; Shvartsman, Ilya.
In: ESAIM - Control, Optimisation and Calculus of Variations, Vol. 13, No. 3, 01.07.2007, p. 458-483.Research output: Contribution to journal › Article
TY - JOUR
T1 - Integral control of infinite-dimensional systems in the presence of hysteresis
T2 - An input-output approach
AU - Logemann, Hartmut
AU - Ryan, Eugene P.
AU - Shvartsman, Ilya
PY - 2007/7/1
Y1 - 2007/7/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=34648817140&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34648817140&partnerID=8YFLogxK
U2 - 10.1051/cocv:2007022
DO - 10.1051/cocv:2007022
M3 - Article
AN - SCOPUS:34648817140
VL - 13
SP - 458
EP - 483
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
SN - 1292-8119
IS - 3
ER -