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

Heonjong Yoo, Zoran Gajic

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
Article number2859548
JournalMathematical Problems in Engineering
Volume2017
DOIs
StatePublished - Jan 1 2017

Fingerprint

Perturbed System
Singularly Perturbed
Linear systems
Observer
Linear Systems
Controller
Controllers
Ill-conditioning
Subsystem
Time Scales
Feedback
Observer Design
Singular Perturbation
Small Perturbations
State Space
Design
Decomposition
Decompose
Arbitrary

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

@article{c8ddc1d59c3640ecb2319538b4fa69ec,
title = "New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems",
abstract = "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.",
author = "Heonjong Yoo and Zoran Gajic",
year = "2017",
month = "1",
day = "1",
doi = "10.1155/2017/2859548",
language = "English (US)",
volume = "2017",
journal = "Mathematical Problems in Engineering",
issn = "1024-123X",
publisher = "Hindawi Publishing Corporation",

}

New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems. / Yoo, Heonjong; Gajic, Zoran.

In: Mathematical Problems in Engineering, Vol. 2017, 2859548, 01.01.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

AU - Yoo, Heonjong

AU - Gajic, Zoran

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85042416137&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042416137&partnerID=8YFLogxK

U2 - 10.1155/2017/2859548

DO - 10.1155/2017/2859548

M3 - Article

AN - SCOPUS:85042416137

VL - 2017

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 2859548

ER -