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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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 |
_version_ |
1716752802698493952 |