Achievable PID performance using sums of squares programming

In addition to process elements like time delay, the PID structure of the controller can pose fundamental limitations on the achievable control performance. A key difficulty in characterizing the limitations due to controller structure is the non-convexity of the resulting optimization problem. In t...

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Main Authors: Sendjaja, Antonius Yudi, Kariwala, Vinay
Other Authors: School of Chemical and Biomedical Engineering
Format: Article
Language:English
Published: 2009
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Online Access:https://hdl.handle.net/10356/90997
http://hdl.handle.net/10220/4618
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-909972023-12-29T06:53:04Z Achievable PID performance using sums of squares programming Sendjaja, Antonius Yudi Kariwala, Vinay School of Chemical and Biomedical Engineering DRNTU::Engineering::Chemical engineering DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering DRNTU::Science::Mathematics::Applied mathematics::Optimization In addition to process elements like time delay, the PID structure of the controller can pose fundamental limitations on the achievable control performance. A key difficulty in characterizing the limitations due to controller structure is the non-convexity of the resulting optimization problem. In this paper, we present a global lower bound on the achievable PID performance, defined in terms of output variance, by solving a series of convex programs using sums of squares programming. This result is also extended to minimize the weighted sum of the variances of input rate and output. The tightness of the proposed bounds is demonstrated using several benchmark examples drawn from literature. Accepted version 2009-06-09T04:06:08Z 2019-12-06T17:57:51Z 2009-06-09T04:06:08Z 2019-12-06T17:57:51Z 2008 2008 Journal Article Sendjaja, A. Y., & Kariwala, V. (2008). Achievable PID performance using sums of squares programming. Journal of Process Control, 19(6), 1061-1065. 0959-1524 https://hdl.handle.net/10356/90997 http://hdl.handle.net/10220/4618 10.1016/j.jprocont.2008.12.005 en Journal of process control Journal of Process Control Copyright © 2008 Elsevier Ltd All rights reserved. The journal's website is located at http://www.sciencedirect.com/science/journal/09591524. 12 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Engineering::Chemical engineering
DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering
DRNTU::Science::Mathematics::Applied mathematics::Optimization
spellingShingle DRNTU::Engineering::Chemical engineering
DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering
DRNTU::Science::Mathematics::Applied mathematics::Optimization
Sendjaja, Antonius Yudi
Kariwala, Vinay
Achievable PID performance using sums of squares programming
description In addition to process elements like time delay, the PID structure of the controller can pose fundamental limitations on the achievable control performance. A key difficulty in characterizing the limitations due to controller structure is the non-convexity of the resulting optimization problem. In this paper, we present a global lower bound on the achievable PID performance, defined in terms of output variance, by solving a series of convex programs using sums of squares programming. This result is also extended to minimize the weighted sum of the variances of input rate and output. The tightness of the proposed bounds is demonstrated using several benchmark examples drawn from literature.
author2 School of Chemical and Biomedical Engineering
author_facet School of Chemical and Biomedical Engineering
Sendjaja, Antonius Yudi
Kariwala, Vinay
format Article
author Sendjaja, Antonius Yudi
Kariwala, Vinay
author_sort Sendjaja, Antonius Yudi
title Achievable PID performance using sums of squares programming
title_short Achievable PID performance using sums of squares programming
title_full Achievable PID performance using sums of squares programming
title_fullStr Achievable PID performance using sums of squares programming
title_full_unstemmed Achievable PID performance using sums of squares programming
title_sort achievable pid performance using sums of squares programming
publishDate 2009
url https://hdl.handle.net/10356/90997
http://hdl.handle.net/10220/4618
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