New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) o...

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Main Authors: Heonjong Yoo, Zoran Gajic
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2017/2859548
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spelling doaj-38e5d00a99a14b67bcdd4357915816162020-11-24T21:11:46ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/28595482859548New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear SystemsHeonjong Yoo0Zoran Gajic1Department of Electrical and Computer Engineering, Rutgers University, 94 Brett Road, Piscataway, NJ, USADepartment of Electrical and Computer Engineering, Rutgers University, 94 Brett Road, Piscataway, NJ, USAThe slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III)–(V), they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.http://dx.doi.org/10.1155/2017/2859548
collection DOAJ
language English
format Article
sources DOAJ
author Heonjong Yoo
Zoran Gajic
spellingShingle Heonjong Yoo
Zoran Gajic
New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
Mathematical Problems in Engineering
author_facet Heonjong Yoo
Zoran Gajic
author_sort Heonjong Yoo
title New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
title_short New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
title_full New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
title_fullStr New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
title_full_unstemmed New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
title_sort new designs of reduced-order observer-based controllers for singularly perturbed linear systems
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2017-01-01
description The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III)–(V), they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.
url http://dx.doi.org/10.1155/2017/2859548
work_keys_str_mv AT heonjongyoo newdesignsofreducedorderobserverbasedcontrollersforsingularlyperturbedlinearsystems
AT zorangajic newdesignsofreducedorderobserverbasedcontrollersforsingularlyperturbedlinearsystems
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