A Mathematical Approach to Integral Resonant Control of Second-order Systems

Mohammad Namavar; Majid Aleyaasin; Nakkeeran Kaliyaperumal; Sumeet Sunil Aphale

doi:10.1109/CCDC.2012.6244105

A Mathematical Approach to Integral Resonant Control of Second-order Systems

Mohammad Namavar, Majid Aleyaasin, Nakkeeran Kaliyaperumal, Sumeet Sunil Aphale

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

1 Citation (Scopus)

Abstract

Systems with colocated sensor-actuator pairs exhibit an interesting property of pole-zero interlacing. Integral Resonant Control (IRC) exploits this property to result in superior damping performance over multiple resonant modes by prescribing an adequate feed-through term to swap the pole-zero interlacing to a zero-pole one - thus enabling a simple integral feedback controller to add substantial damping to the system. Over the past few years, the IRC has proved
extremely popular and versatile and has been applied to damp the resonance in a variety of systems. So far, a simulation based manual search has been used to determine the three main parameters of the IRC scheme namely: (i) feed-through term, d, (ii) integral gain, k and (iii) resulting damping, . In this paper, a full quantification of the effect of feed-through term on second-order colocated systems as well as a mathematical formulation for the relation between the feed-through term, integral gain and achievable damping are presented. These results add to the current understanding regarding the behaviour of colocated systems and facilitate the IRC design for a specified damping.

Original language	English
Title of host publication	Proceedings of the 24th Chinese Control and Decision Conference, Taiyuan China, 23 - 25 May 2012
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	700-705
Number of pages	6
ISBN (Electronic)	978-1-4577-2074-1
ISBN (Print)	978-1-4577-2073-4
DOIs	https://doi.org/10.1109/CCDC.2012.6244105
Publication status	Published - 19 Jul 2012
Event	2012 24th Chinese Control and Decision Conference (CCDC) - Taiyuan, China Duration: 23 May 2012 → 25 May 2012

Conference

Conference	2012 24th Chinese Control and Decision Conference (CCDC)
Country/Territory	China
City	Taiyuan
Period	23/05/12 → 25/05/12

Keywords

Colocated systems
damping
Integral Resonant Control
nanopositioning

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10.1109/CCDC.2012.6244105Licence: Unspecified

Cite this

A Mathematical Approach to Integral Resonant Control of Second-order Systems. / Namavar, Mohammad; Aleyaasin, Majid ; Kaliyaperumal, Nakkeeran et al.
Proceedings of the 24th Chinese Control and Decision Conference, Taiyuan China, 23 - 25 May 2012. Institute of Electrical and Electronics Engineers (IEEE), 2012. p. 700-705.

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

Namavar, M, Aleyaasin, M , Kaliyaperumal, N & Aphale, SS 2012, A Mathematical Approach to Integral Resonant Control of Second-order Systems. in Proceedings of the 24th Chinese Control and Decision Conference, Taiyuan China, 23 - 25 May 2012. Institute of Electrical and Electronics Engineers (IEEE), pp. 700-705, 2012 24th Chinese Control and Decision Conference (CCDC) , Taiyuan, China, 23/05/12. https://doi.org/10.1109/CCDC.2012.6244105

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abstract = "Systems with colocated sensor-actuator pairs exhibit an interesting property of pole-zero interlacing. Integral Resonant Control (IRC) exploits this property to result in superior damping performance over multiple resonant modes by prescribing an adequate feed-through term to swap the pole-zero interlacing to a zero-pole one - thus enabling a simple integral feedback controller to add substantial damping to the system. Over the past few years, the IRC has provedextremely popular and versatile and has been applied to damp the resonance in a variety of systems. So far, a simulation based manual search has been used to determine the three main parameters of the IRC scheme namely: (i) feed-through term, d, (ii) integral gain, k and (iii) resulting damping, . In this paper, a full quantification of the effect of feed-through term on second-order colocated systems as well as a mathematical formulation for the relation between the feed-through term, integral gain and achievable damping are presented. These results add to the current understanding regarding the behaviour of colocated systems and facilitate the IRC design for a specified damping. ",

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author = "Mohammad Namavar and Majid Aleyaasin and Nakkeeran Kaliyaperumal and Aphale, {Sumeet Sunil}",

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AU - Namavar, Mohammad

AU - Aleyaasin, Majid

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N2 - Systems with colocated sensor-actuator pairs exhibit an interesting property of pole-zero interlacing. Integral Resonant Control (IRC) exploits this property to result in superior damping performance over multiple resonant modes by prescribing an adequate feed-through term to swap the pole-zero interlacing to a zero-pole one - thus enabling a simple integral feedback controller to add substantial damping to the system. Over the past few years, the IRC has provedextremely popular and versatile and has been applied to damp the resonance in a variety of systems. So far, a simulation based manual search has been used to determine the three main parameters of the IRC scheme namely: (i) feed-through term, d, (ii) integral gain, k and (iii) resulting damping, . In this paper, a full quantification of the effect of feed-through term on second-order colocated systems as well as a mathematical formulation for the relation between the feed-through term, integral gain and achievable damping are presented. These results add to the current understanding regarding the behaviour of colocated systems and facilitate the IRC design for a specified damping.

AB - Systems with colocated sensor-actuator pairs exhibit an interesting property of pole-zero interlacing. Integral Resonant Control (IRC) exploits this property to result in superior damping performance over multiple resonant modes by prescribing an adequate feed-through term to swap the pole-zero interlacing to a zero-pole one - thus enabling a simple integral feedback controller to add substantial damping to the system. Over the past few years, the IRC has provedextremely popular and versatile and has been applied to damp the resonance in a variety of systems. So far, a simulation based manual search has been used to determine the three main parameters of the IRC scheme namely: (i) feed-through term, d, (ii) integral gain, k and (iii) resulting damping, . In this paper, a full quantification of the effect of feed-through term on second-order colocated systems as well as a mathematical formulation for the relation between the feed-through term, integral gain and achievable damping are presented. These results add to the current understanding regarding the behaviour of colocated systems and facilitate the IRC design for a specified damping.

KW - Colocated systems

KW - damping

KW - Integral Resonant Control

KW - nanopositioning

U2 - 10.1109/CCDC.2012.6244105

DO - 10.1109/CCDC.2012.6244105

M3 - Published conference contribution

SN - 978-1-4577-2073-4

SP - 700

EP - 705

BT - Proceedings of the 24th Chinese Control and Decision Conference, Taiyuan China, 23 - 25 May 2012

PB - Institute of Electrical and Electronics Engineers (IEEE)

T2 - 2012 24th Chinese Control and Decision Conference (CCDC)

Y2 - 23 May 2012 through 25 May 2012

ER -

A Mathematical Approach to Integral Resonant Control of Second-order Systems

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