A Simplified Approach to Analyze Complementary Sensitivity Tradeoffs in Continuous-Time and Discrete-Time Systems

Neng Wan; Dapeng Li; Naira Hovakimyan

doi:10.1109/TAC.2019.2934010

A Simplified Approach to Analyze Complementary Sensitivity Tradeoffs in Continuous-Time and Discrete-Time Systems

Research output: Contribution to journal › Article › peer-review

Abstract

Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by 1ω² is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither the Cauchy integral theorem nor the Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

Original language	English (US)
Article number	8793137
Pages (from-to)	1697-1703
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	65
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2019.2934010
State	Published - Apr 2020

Keywords

Complementary sensitivity Bode integral (CSBI)
control tradeoffs
linear systems
simplified approach

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Online availability

10.1109/TAC.2019.2934010

Library availability

Discover UIUC Full Text

Cite this

@article{aee657c9d6b84950b8df9fbc27c3ae2d,

title = "A Simplified Approach to Analyze Complementary Sensitivity Tradeoffs in Continuous-Time and Discrete-Time Systems",

abstract = "Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by 1ω2 is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither the Cauchy integral theorem nor the Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.",

keywords = "Complementary sensitivity Bode integral (CSBI), control tradeoffs, linear systems, simplified approach",

author = "Neng Wan and Dapeng Li and Naira Hovakimyan",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2020",

month = apr,

doi = "10.1109/TAC.2019.2934010",

language = "English (US)",

volume = "65",

pages = "1697--1703",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}

TY - JOUR

T1 - A Simplified Approach to Analyze Complementary Sensitivity Tradeoffs in Continuous-Time and Discrete-Time Systems

AU - Wan, Neng

AU - Li, Dapeng

AU - Hovakimyan, Naira

PY - 2020/4

Y1 - 2020/4

N2 - Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by 1ω2 is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither the Cauchy integral theorem nor the Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

AB - Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by 1ω2 is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither the Cauchy integral theorem nor the Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

KW - Complementary sensitivity Bode integral (CSBI)

KW - control tradeoffs

KW - linear systems

KW - simplified approach

UR - http://www.scopus.com/inward/record.url?scp=85070671435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070671435&partnerID=8YFLogxK

U2 - 10.1109/TAC.2019.2934010

DO - 10.1109/TAC.2019.2934010

M3 - Article

AN - SCOPUS:85070671435

SN - 0018-9286

VL - 65

SP - 1697

EP - 1703

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 4

M1 - 8793137

ER -

A Simplified Approach to Analyze Complementary Sensitivity Tradeoffs in Continuous-Time and Discrete-Time Systems

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this